[Docs] [txt|pdf|xml|html] [Tracker] [WG] [Email] [Diff1] [Diff2] [Nits]

Versions: (draft-cfrg-re-keying) 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

CFRG                                                  S. Smyshlyaev, Ed.
Internet-Draft                                                 CryptoPro
Intended status: Informational                             June 20, 2017
Expires: December 22, 2017


                Re-keying Mechanisms for Symmetric Keys
                      draft-irtf-cfrg-re-keying-03

Abstract

   If encryption is performed under a single key, there is a certain
   maximum threshold amount of data that can be safely encrypted.  This
   amount is called key lifetime.  This specification contains a
   description of a variety of methods to increase the lifetime of
   symmetric keys.  It provides external and internal re-keying
   mechanisms based on hash functions and on block ciphers that can be
   used with such modes of operations as CTR, GCM, CCM, CBC, CFB, OFB
   and OMAC.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on December 22, 2017.

Copyright Notice

   Copyright (c) 2017 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must



Smyshlyaev              Expires December 22, 2017               [Page 1]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Conventions Used in This Document . . . . . . . . . . . . . .   5
   3.  Basic Terms and Definitions . . . . . . . . . . . . . . . . .   5
   4.  Principles of Choice of Constructions and Security Parameters   6
   5.  External Re-keying Mechanisms . . . . . . . . . . . . . . . .   8
     5.1.  Methods of Key Lifetime Control . . . . . . . . . . . . .  10
     5.2.  Parallel Constructions  . . . . . . . . . . . . . . . . .  11
       5.2.1.  Parallel Construction Based on a KDF on a Block
               Cipher  . . . . . . . . . . . . . . . . . . . . . . .  12
       5.2.2.  Parallel Construction Based on HKDF . . . . . . . . .  12
     5.3.  Serial Constructions  . . . . . . . . . . . . . . . . . .  13
       5.3.1.  Serial Construction Based on a KDF on a Block Cipher   13
       5.3.2.  Serial Construction Based on HKDF . . . . . . . . . .  14
   6.  Internal Re-keying Mechanisms . . . . . . . . . . . . . . . .  14
     6.1.  Methods of Key Lifetime Control . . . . . . . . . . . . .  17
     6.2.  Constructions that Do Not Require Master Key  . . . . . .  17
       6.2.1.  ACPKM Re-keying Mechanisms  . . . . . . . . . . . . .  17
       6.2.2.  CTR-ACPKM Encryption Mode . . . . . . . . . . . . . .  19
       6.2.3.  GCM-ACPKM Authenticated Encryption Mode . . . . . . .  21
       6.2.4.  CCM-ACPKM Authenticated Encryption Mode . . . . . . .  23
     6.3.  Constructions that Require Master Key . . . . . . . . . .  25
       6.3.1.  ACPKM-Master Key Derivation from the Master Key . . .  25
       6.3.2.  CTR-ACPKM-Master Encryption Mode  . . . . . . . . . .  26
       6.3.3.  GCM-ACPKM-Master Authenticated Encryption Mode  . . .  29
       6.3.4.  CCM-ACPKM-Master Authenticated Encryption Mode  . . .  32
       6.3.5.  CBC-ACPKM-Master Encryption Mode  . . . . . . . . . .  32
       6.3.6.  CFB-ACPKM-Master Encryption Mode  . . . . . . . . . .  34
       6.3.7.  OFB-ACPKM-Master Encryption Mode  . . . . . . . . . .  36
       6.3.8.  OMAC-ACPKM-Master Mode  . . . . . . . . . . . . . . .  37
   7.  Joint Usage of External and Internal Re-keying  . . . . . . .  39
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  39
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  40
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  40
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  40
   Appendix A.  Test examples  . . . . . . . . . . . . . . . . . . .  41
   Appendix B.  Contributors . . . . . . . . . . . . . . . . . . . .  45
   Appendix C.  Acknowledgments  . . . . . . . . . . . . . . . . . .  46
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  46







Smyshlyaev              Expires December 22, 2017               [Page 2]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


1.  Introduction

   If encryption is performed under a single key, there is a certain
   maximum threshold amount of data that can be safely encrypted.  This
   amount is called key lifetime and can be calculated from the
   following considerations:

   1.  Methods based on the combinatorial properties of used encryption
       mode

          [Sweet32] is an example of attack that is based on such
          methods.  These methods do not depend on the used block cipher
          permutation E_{K}.  Common encryption modes restrictions
          resulting from such methods are of order 2^{n/2}.

   2.  Methods based on side-channel analysis issues

          In most cases these methods do not depend on the used
          encryption modes and weakly depend on the used block cipher
          features.  Restrictions resulting from these methods are
          usually the strongest ones.

   3.  Methods based on the properties of the used block cipher
       permutation E_{K}

          The most common methods of this type are linear and
          differential cryptanalysis [LDC].  In most cases these methods
          do not depend on the used encryption modes.  In case of secure
          block ciphers, restrictions resulting from such methods are
          roughly the same as the natural limitation 2^n and so can be
          excluded from consideration as they become trivial.

   Therefore, as soon as the total size of a plaintext processed with a
   single key reaches the key lifetime limitation, that key must be
   replaced.  A specific value of the key lifetime is determined in
   accordance with safety margin for protocol security and methods
   outlined above.

   Suppose L is a key lifetime limitation in some protocol P.  For
   simplicity, assume that all messages have the same length m.  Hence
   the number of messages q that can be processed with a single key K
   should be such that m*q <= L.  This can be depicted graphically as a
   rectangle with sides m and q which is enclosed by area L (see
   Figure 1).







Smyshlyaev              Expires December 22, 2017               [Page 3]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


             +------------------------+
             |                      L |
             | +--------m---------+   |
             | |==================|   |
             | |==================|   |
             | q==================|   |       m*q <= L
             | |==================|   |
             | |==================|   |
             | +------------------+   |
             +------------------------+

   Figure 1: Graphic display of the key lifetime limitation



   Thus, with increasing one of the parameters m or q, the second
   parameter should be reduced in proportion to the first.

   In practice, such amount of data that corresponds to limitation L may
   not be enough.  The most simple and obvious way in this situation is
   a regular renegotiation of a session key.  However, this reduces the
   total performance since it usually entails termination of application
   data transmission, additional service messages, the use of random
   number generator and many other additional calculations, including
   resource-intensive asymmetric cryptography.

   This specification presents two approaches that extend the key
   lifetime for a single symmetric key while avoiding renegotiation:
   external and internal re-keying.  External re-keying is performed by
   a protocol, and it is independent of block cipher, key size, and
   mode.  External re-keying can use parallel or serial construction.
   In the first case subkeys K^1, K^2,... are generated directly from
   the key K independently of each other, while in the second case every
   next subkey depends on the state that is updated after each new
   subkey generation.  Internal re-keying is built into the mode, and it
   depends heavily on the properties of the block cipher and key size.

   The re-keying approaches extend the key lifetime for a single agreed
   key by providing the possibility to strictly limit the key leakage
   (to meet side channel limitations) and by improving combinatorial
   properties of a used block cipher encryption mode.

   As for practical issues, re-keying can be particularly useful in such
   fields as protocols functioning in hostile environments (additional
   side channel resistance against DPA or EMI style attacks) or
   lightweight cryptography (usage of ciphers with small block size
   leads to very strong combinatorial limitations).  Moreover, many
   mechanisms that use external and internal re-keying provide



Smyshlyaev              Expires December 22, 2017               [Page 4]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   particular types of PFS security.  Also re-keying can provide
   additional security against possible future attacks on the used
   ciphers (by limiting the number of plaintext-ciphertext pairs
   collected by an adversary), however, it must not be used as a method
   to prolong life of ciphers that are already known to be vulnerable.

2.  Conventions Used in This Document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].

3.  Basic Terms and Definitions

   This document uses the following terms and definitions for the sets
   and operations on the elements of these sets:

   (xor)   exclusive-or of two binary vectors of the same length.

   V*      the set of all strings of a finite length (hereinafter
           referred to as strings), including the empty string;

   V_s     the set of all binary strings of length s, where s is a non-
           negative integer; substrings and string components are
           enumerated from right to left starting from one;

   |X|     the bit length of the bit string X;

   A|B     concatenation of strings A and B both belonging to V*, i.e.,
           a string in V_{|A|+|B|}, where the left substring in V_|A| is
           equal to A, and the right substring in V_|B| is equal to B;

   Z_{2^n} ring of residues modulo 2^n;

   Int_s: V_s -> Z_{2^s}    the transformation that maps a string a =
           (a_s, ... , a_1), a in V_s, into the integer Int_s(a) =
           2^{s-1}*a_s + ... + 2*a_2 + a_1;

   Vec_s: Z_{2^s} -> V_s  the transformation inverse to the mapping
           Int_s;

   MSB_i: V_s -> V_i  the transformation that maps the string a = (a_s,
           ... , a_1) in V_s, into the string MSB_i(a) = (a_s, ... ,
           a_{s-i+1}) in V_i;

   LSB_i: V_s -> V_i  the transformation that maps the string a = (a_s,
           ... , a_1) in V_s, into the string LSB_i(a) = (a_i, ... ,
           a_1) in V_i;



Smyshlyaev              Expires December 22, 2017               [Page 5]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   Inc_c: V_s -> V_s  the transformation that maps the string a = (a_s,
           ... , a_1) in V_s, into the string Inc_c(a) = MSB_{|a|-
           c}(a) | Vec_c(Int_c(LSB_c(a)) + 1(mod 2^c)) in V_s;

   a^s     denotes the string in V_s that consists of s 'a' bits;

   E_{K}: V_n -> V_n  the block cipher permutation under the key K in
           V_k;

   ceil(x) the least integer that is not less than x;

   k       the key K size (in bits), k is multiple of 8;

   n       the block size of the block cipher (in bits), n is multiple
           of 8;

   b       the total number of data blocks in the plaintext (b = ceil(m/
           n));

   N       the section size (the number of bits in a data section);

   l       the number of data sections in the plaintext;

   phi_i: V_s -> {0,1}  the transformation that maps a string a = (a_s,
           ... , a_1) into the value phi_i(a) = a_i for all i in {1, ...
           , s}.

   A plaintext message P and a ciphertext C are divided into b =
   ceil(|P|/n) blocks denoted as P = P_1 | P_2 | ... | P_b and C = C_1 |
   C_2 | ... | C_b, where P_i and C_i are in V_n, for i = 1, 2, ... ,
   b-1, and P_b, C_b are in V_r, where r <= n if not otherwise stated.

4.  Principles of Choice of Constructions and Security Parameters

   External re-keying provides an approach, decording to which a key is
   transformed after encrypting a limited number of messages.  A
   specific external re-keying method is chosen at the protocol level
   regardless of a used block cipher or encryption mode.  External re-
   keying approach is recommended for usage in protocols that process
   quite small messages or in protocols that have a way to break a large
   message into manageable parts.  As a result of external re-keying,
   the number of messages that can be processed with a single symmetric
   key is substantially increased without loss in message length.

   The use of external re-keying has the following advantages:

   1.  the lifetime of a negotiated key drastically increases by
       increasing the number of messages processed with one key;



Smyshlyaev              Expires December 22, 2017               [Page 6]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   2.  it almost does not affect performance in case when a number of
       messages processed with one key is sufficiently large;

   3.  provides forward and backward security of session keys for all
       messages.

   However, the use of external re-keying has the following
   disadvantages:

   1.  in case of restrictive key lifetime limitations the message sizes
       can become inconvenient due to impossibility of processing
       sufficiently large messages, so it could be necessary to perform
       additional fragmentation at the protocol level;

   2.  it is not transparent: procedures (like IVs generation) must be
       handled separately.

   Internal re-keying provides an approach according to which a key is
   transformed during each separate message processing.  Such approaches
   are integrated into the base modes of operations so every internal
   re-keying mechanism is defined for a particular mode and block cipher
   (e.g. depending of block and key sizes).  Internal re-keying approach
   is recommended to be used in protocols that process large messages.
   As a result of internal re-keying, the size of each single message
   can be substantially increased without loss in number of messages
   that can be processed with a single symmetric key.

   The use of internal re-keying has the following advantages:

   1.  the lifetime of a negotiated key drastically increases by
       increasing the size of messages processed with one key;

   2.  minimal impact on performance;

   3.  internal re-keying mechanisms without master key does not affect
       short messages transformation at all;

   4.  transparent (works like any encryption mode): does not require
       changes of IV's and restarting MACing.

   However, the use of internal re-keying has the following
   disadvantages:

   1.  a specific method must not be chosen independently of a mode of
       operation;

   2.  internal re-keying mechanisms with master key provide backward
       security of session keys only for one separate message;



Smyshlyaev              Expires December 22, 2017               [Page 7]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   3.  internal re-keying mechanisms without master key do not provide
       backward security of session keys.

   Any block cipher modes of operations with internal re-keying can be
   jointly used with any external re-keying mechanisms.  Such joint
   usage increases both the number of messages processed with one key
   and their maximum possible size.

   The use of the same cryptographic primitives both for data processing
   and re-keying transformation decreases the code size but can lead to
   some possible vulnerabilities because the adversary always has access
   to the data processing interface.  This vulnerability can be
   eliminated by using different primitives for data processing and re-
   keying, however, in this case the security of the whole scheme cannot
   be reduced to standard notions like PRF or PRP so security
   estimations become more difficult and unclear.

5.  External Re-keying Mechanisms

   This section presents an approach to increase the key lifetime by
   using a transformation of a previously negotiated key after
   processing a limited number of integral messages.  It provides an
   external parallel and serial re-keying mechanisms (see [AbBell]).
   These mechanisms use an initial (negotiated) key as a master key,
   which is never used directly for the data processing but is used for
   key generation.  Such mechanisms operate outside of the base modes of
   operations and do not change them at all, therefore they are called
   "external re-keying" mechanisms in this document.

   External re-keying mechanisms are recommended for usage in protocols
   that process quite small messages since the maximum gain in
   increasing the key lifetime is achieved by increasing the number of
   messages.

   External re-keying increases the key lifetime through the following
   approach.  Suppose there is a protocol P with some mode of operation
   (base encryption or authentication mode).  Let L1 be a key lifetime
   limitation induced by side-channel analysis methods (side-channel
   limitation), let L2 be a key lifetime limitation induced by methods
   based on the combinatorial properties of used mode of operation
   (combinatorial limitation) and let q1, q2 be the total numbers of
   messages of length m, that can be safely processed with a single key
   K according to these limitations.

   Let L = min(L1, L2), q = min (q1, q2), q*m <= L.  As L1 limitation is
   usually much stronger then L2 limitation (L1 < L2), the final key
   lifetime restriction is equal to the most restrictive limitation L1.




Smyshlyaev              Expires December 22, 2017               [Page 8]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   Thus, as displayed in Figure 2, without re-keying only q1 (q1*m <=
   L1) messages can be safely processed.


           <--------m------->
           +----------------+ ^ ^
           |================| | |
           |================| | |
       K-->|================| q1|
           |================| | |
           |==============L1| | |
           +----------------+ v |
           |                |   |
           |                |   |
           |                |   q2
           |                |   |
           |                |   |
           |                |   |
           |                |   |
           |                |   |
           |                |   |
           |                |   |
           |                |   |
           |              L2|   |
           +----------------+   v

Figure 2: Basic principles of message processing without external re-keying


   Suppose that the safety margin for the protocol P is fixed and the
   external re-keying approach is applied.  As the key is transformed
   with an external re-keying mechanism, the leakage of a previous key
   does not have any impact on the following one, so the side channel
   limitation L1 goes off.  Thus, the resulting key lifetime limitation
   of the negotiated key K can be calculated on the basis of a new
   combinatorial limitation L2'.  It is proven (see [AbBell]) that the
   security of the mode of operation that uses external re-keying leads
   to an increase when compared to base mode without re-keying (thus, L2
   < L2').  Hence, as displayed in Figure 3, the resulting key lifetime
   limitation in case of using external re-keying can be increased up to
   L2'.










Smyshlyaev              Expires December 22, 2017               [Page 9]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


                  <-------m------->
                 +----------------+
                 |================|
                 |================|
           K---> |================|
           |     |================|
           |     |==============L1|
           |     +----------------+
           |     |================|
           v     |================|
          K^2--> |================|
           |     |================|
           |     |==============L1|
           |     +----------------+
           |     |================|
           v     |================|
          ...    |      . . .     |
                 |                |
                 |                |
                 |              L2|
                 +----------------+
                 |             L2'|
                 +----------------+

Figure 3: Basic principles of message processing with external re-keying


   Note: the key transformation process is depicted in a simplified
   form.  A specific approach (parallel and serial) is described below.

   Consider an example.  Let the message size in protocol P be equal to
   1 KB.  Suppose L1 = 128 MB and L2 = 1 TB.  Thus, if an external re-
   keying mechanism is not used, the key K must be renegotiated after
   processing 128 MB / 1 KB = 131072 messages.

   If an external re-keying mechanism is used, the key lifetime
   limitation L1 goes off.  Hence the resulting key lifetime limitation
   in case of using external re-keying can be set to 1 TB (and even
   more).  Thus if an external re-keying mechanism is used, then 1 TB /
   1 KB = 2^30 messages can be processed before the master key K is
   renegotiated.  This is 8192 times greater than the number of messages
   that can be processed, when external re-keying mechanism is not used.

5.1.  Methods of Key Lifetime Control

   Suppose L is an amount of data that can be safely processed with one
   key (without re-keying).  For i in {1, 2, ..., t} the key K^i (see
   Figure 1 and Figure 2) should be transformed after processing q_i



Smyshlyaev              Expires December 22, 2017              [Page 10]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   integral messages, where q_i can be calculated in accordance with one
   of the following two approaches:

   o  Explicit approach:
      |M^{i,1}| + ... + |M^{i,q_i}| <= L, |M^{i,1}| + ... + |M^{i,q_i +
      1}| > L.
      This approach allows to use the key K^i in almost optimal way but
      it cannot be applied in case when messages may be lost or
      reordered (e.g.  DTLS packets).

   o  Implicit approach:
      q_i = L / m_max, i = 1, ... , t.
      The amount of data processed with one key K^i is calculated under
      the assumption that every message has the maximum length m_max.
      Hence this amount can be considerably less than the key lifetime
      limitation L.  On the other hand this approach can be applied in
      case when messages may be lost or reordered (e.g.  DTLS packets).

5.2.  Parallel Constructions

   The main idea behind external re-keying with parallel construction is
   presented in Figure 4:





























Smyshlyaev              Expires December 22, 2017              [Page 11]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   Maximum message size = m_max.
   _____________________________________________________________

                                   m_max
                             <---------------->
                   M^{1,1}   |===             |
                   M^{1,2}   |=============== |
         +--K^1-->   . . .
         |         M^{1,q_1} |========        |
         |
         |
         |         M^{2,1}   |================|
         |         M^{2,2}   |=====           |
   K-----|--K^2-->   . . .
         |         M^{2,q_2} |==========      |
         |
        ...
         |         M^{t,1}   |============    |
         |         M^{t,2}   |=============   |
         +--K^t-->   . . .
                   M^{t,q_t} |==========      |

   _____________________________________________________________

          Figure 4: External parallel re-keying mechanisms


   The key K^i, i = 1, ... , t-1, is updated after processing a certain
   amount of data (see Section 5.1).

5.2.1.  Parallel Construction Based on a KDF on a Block Cipher

   ExtParallelC re-keying mechanism is based on key derivation function
   on a block cipher and is used to generate t keys for t sections as
   follows:

      K^1 | K^2 | ... | K^t = ExtParallelC(K, t*k) =
      MSB_{t*k}(E_{K}(0) | E_{K}(1) | ... | E_{K}(R-1)),

   where R = ceil(t*k/n).

5.2.2.  Parallel Construction Based on HKDF

   ExtParallelH re-keying mechanism is based on HMAC key derivation
   function HKDF-Expand, described in [RFC5869], and is used to generate
   t keys for t sections as follows:





Smyshlyaev              Expires December 22, 2017              [Page 12]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


      K^1 | K^2 | ... | K^t = ExtParallelH(K, t*k) = HKDF-Expand(K,
      label, t*k),

   where label is a string (can be a zero-length string) that is defined
   by a specific protocol.

5.3.  Serial Constructions

   The main idea behind external re-keying with serial construction is
   presented in Figure 5:


   Maximum message size = m_max.
   _____________________________________________________________
                                        m_max
                                  <---------------->
                        M^{1,1}   |===             |
                        M^{1,2}   |=============== |
   K*_1 = K ----K^1-->   . . .
     |                  M^{1,q_1} |========        |
     |
     |
     |                  M^{2,1}   |================|
     v                  M^{2,2}   |=====           |
   K*_2 --------K^2-->   . . .
     |                  M^{2,q_2} |==========      |
     |
    ...
     |                  M^{t,1}   |============    |
     v                  M^{t,2}   |=============   |
   K*_t --------K^t-->   . . .
                        M^{t,q_t} |==========      |


   _____________________________________________________________

          Figure 5: External serial re-keying mechanisms


   The key K^i, i = 1, ... , t-1, is updated after processing a certain
   amount of data (see Section 5.1).

5.3.1.  Serial Construction Based on a KDF on a Block Cipher

   The key K^i is calculated using ExtSerialC transformation as follows:

      K^i = ExtSerialC(K, i) = MSB_k(E_{K*_i}(0) | E_{K*_i}(1) | ... |
      E_{K*_i}(J-1)),



Smyshlyaev              Expires December 22, 2017              [Page 13]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   where J = ceil(k/n), i = 1, ... , t, K*_i is calculated as follows:

      K*_1 = K,

      K*_{j+1} = MSB_k(E_{K*_j}(J) | E_{K*_j}(J+1) | ... | E_{K*_j}(2J-
      1)),

   where j = 1, ... , t-1.

5.3.2.  Serial Construction Based on HKDF

   The key K^i is calculated using ExtSerialH transformation as follows:

      K^i = ExtSerialH(K, i) = HKDF-Expand(K*_i, label1, k),

   where i = 1, ... , t, HKDF-Expand is an HMAC-based key derivation
   function, described in [RFC5869], K*_i is calculated as follows:

      K*_1 = K,

      K*_{j+1} = HKDF-Expand(K*_j, label2, k), where j = 1, ... , t-1,

   where label1 and label2 are different strings (can be a zero-length
   strings) that are defined by a specific protocol (see, for example,
   TLS 1.3 updating traffic keys algorithm [TLSDraft]).

6.  Internal Re-keying Mechanisms

   This section presents an approach to increase the key lifetime by
   using a transformation of a previously negotiated key during each
   separate message processing.

   It provides internal re-keying mechanisms called ACPKM (Advanced
   cryptographic prolongation of key material) and ACPKM-Master that do
   not use and use a master key respectively.  Such mechanisms are
   integrated into the base modes of operations and actually form new
   modes of operation, therefore they are called "internal re-keying"
   mechanisms in this document.

   Internal re-keying mechanism is recommended to be used in protocols
   that process large single messages (e.g.  CMS messages) since the
   maximum gain in increasing the key lifetime is achieved by increasing
   the length of a message, while it almost does not affect performance
   for increasing the number of messages.

   Internal re-keying increases the key lifetime through the following
   approach.  Suppose there is a protocol P with some base mode of
   operation.  Let L1 and L2 be a side channel and combinatorial



Smyshlyaev              Expires December 22, 2017              [Page 14]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   limitations respectively and for some fixed amount of messages q let
   m1, m2 be the length of each separate message, that can be safely
   processed with a single key K according to these limitations.

   Thus, by analogy with the Section 5 without re-keying the final key
   lifetime restriction, as displayed in Figure 6, is equal to L1 and
   only q messages of the length m1 can be safely processed.


             K
             |
             v
   ^ +----------------+------------------------------------+
   | |==============L1|                                  L2|
   | |================|                                    |
   q |================|                                    |
   | |================|                                    |
   | |================|                                    |
   v +----------------+------------------------------------+
     <-------m1------>
     <----------------------------m2----------------------->

Figure 6: Basic principles of message processing without internal re-keying



   Suppose that the safety margin for the protocol P is fixed and
   internal re-keying approach is applied to the base mode of operation.
   Suppose further that for every message the key is transformed after
   processing N bits of data, where N is a parameter.  If q*N does not
   exceed L1 then the side channel limitation L1 goes off and the
   resulting key lifetime limitation of the negotiated key K can be
   calculated on the basis of a new combinatorial limitation L2'.  The
   security of the mode of operation that uses external re-keying must
   lead to an increase when compared to base mode of operation without
   re-keying (thus, L2 < L2').  Hence, as displayed in Figure 7, the
   resulting key lifetime limitation in case of using external re-keying
   can be increased up to L2'.













Smyshlyaev              Expires December 22, 2017              [Page 15]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


          K -------------> K^2 -----------> . . .
          |                 |
          v                 v
^ +----------------+----------------+-------------------+----+
| |==============L1|==============L1|======           L2| L2'|
| |================|================|======             |    |
q |================|================|====== . . .       |    |
| |================|================|======             |    |
| |================|================|======             |    |
v +----------------+----------------+-------------------+----+
  <-------N-------->

Figure 7: Basic principles of message processing with internal re-keying



   Note: the key transformation process is depicted in a simplified
   form.  A specific approach (ACPKM and ACPKM-Master re-keying
   mechanisms) is described below.

   Since the performance of encryption can slightly decrease for rather
   small values of N, the parameter N should be selected for a
   particular protocol as maximum possible to provide necessary key
   lifetime for the adversary models that are considered.

   Consider an example.  Suppose L1 = 128 MB and L2 = 10 TB.  Let the
   message size in the protocol be large/unlimited (may exhaust the
   whole key lifetime L2').  The most restrictive resulting key lifetime
   limitation is equal to 128 MB.

   Thus, there is a need to put a limit on the maximum message size
   m_max.  For example, if m_max = 32 MB, it may happen that the
   renegotiation of key K would be required after processing only four
   messages.

   If an internal re-keying mechanism with section size N = 1 MB (see
   Figure 3 and Figure 4) is used, more then L1 / N = 128 MB / 1 MB =
   128 messages can be processed before the renegotiation of key K
   (instead of 4 messages in case when an internal re-keying mechanism
   is not used).  Note that only one section of each message is
   processed with one key K^i, and, consequently, the key lifetime
   limitation L1 goes off.  Hence the resulting key lifetime limitation
   in case of using external re-keying can be set to at least 10 TB (in
   the case when the single large message is processed using the key K).







Smyshlyaev              Expires December 22, 2017              [Page 16]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


6.1.  Methods of Key Lifetime Control

   Suppose L is an amount of data that can be safely processed with one
   key (without re-keying), N is a section size (fixed parameter).
   Suppose M^{i}_1 is the first section of message M^{i}, i = 1, ... , q
   (see Figure 3 and Figure 4), then the parameter q can be calculated
   in accordance with one of the following two approaches:

   o  Explicit approach:
      |M^{1}_1| + ... + |M^{q}_1| <= L, |M^{1}_1| + ... + |M^{q+1}_1| >
      L
      This approach allows to use the key K^i in an almost optimal way
      but it cannot be applied in case when messages may be lost or
      reordered (e.g.  DTLS packets).

   o  Implicit approach:
      q = L / N.
      The amount of data processed with one key K^i is calculated under
      the assumption that the length of every message is equal or more
      then section size N and so it can be considerably less than the
      key lifetime limitation L.  On the other hand this approach can be
      applied in case when messages may be lost or reordered (e.g.  DTLS
      packets).

6.2.  Constructions that Do Not Require Master Key

   This section describes the block cipher modes that use the ACPKM re-
   keying mechanism, which does not use master key: an initial key is
   used directly for the encryption of the data.

6.2.1.  ACPKM Re-keying Mechanisms

   This section defines periodical key transformation with no master key
   which is called ACPKM re-keying mechanism.  This mechanism can be
   applied to one of the basic encryption modes (CTR and GCM block
   cipher modes) for getting an extension of this encryption mode that
   uses periodical key transformation with no master key.  This
   extension can be considered as a new encryption mode.

   An additional parameter that defines the functioning of base
   encryption modes with the ACPKM re-keying mechanism is the section
   size N.  The value of N is measured in bits and is fixed within a
   specific protocol based on the requirements of the system capacity
   and key lifetime (some recommendations on choice of N will be
   provided in Section 8).  The section size N MUST be divisible by the
   block size n.





Smyshlyaev              Expires December 22, 2017              [Page 17]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   The main idea behind internal re-keying with no master key is
   presented in Figure 8:


   Section size = const = N,
   maximum message size = m_max.
   ____________________________________________________________________

                 ACPKM       ACPKM              ACPKM
          K^1 = K ---> K^2 ---...-> K^{l_max-1} ----> K^{l_max}
              |          |                |           |
              |          |                |           |
              v          v                v           v
   M^{1} |==========|==========| ... |==========|=======:  |
   M^{2} |==========|==========| ... |===       |       :  |
     .        .          .        .       .          .  :
     :        :          :        :       :          :  :
   M^{q} |==========|==========| ... |==========|=====  :  |
                      section                           :
                    <---------->                      m_max
                       N bit
   ___________________________________________________________________
   l_max = ceil(m_max/N).

               Figure 8: Internal re-keying with no master key


   During the processing of the input message M with the length m in
   some encryption mode that uses ACPKM key transformation of the key K
   the message is divided into l = ceil(m/N) sections (denoted as M =
   M_1 | M_2 | ... | M_l, where M_i is in V_N for i = 1, 2, ... , l-1
   and M_l is in V_r, r <= N).  The first section of each message is
   processed with the initial key K^1 = K.  To process the (i+1)-th
   section of each message the K^{i+1} key value is calculated using
   ACPKM transformation as follows:

      K^{i+1} = ACPKM(K^i) = MSB_k(E_{K^i}(D_1) | ... | E_{K^i}(D_J)),

   where J = ceil(k/n), parameter c is fixed by a specific encryption
   mode which uses ACPKM key transformation and D_1, D_2, ... , D_J are
   in V_n and are calculated as follows:

      D_1 | D_2 | ... | D_J = MSB_{J*n}(D),

   where D is the following constant in V_{1024}:






Smyshlyaev              Expires December 22, 2017              [Page 18]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   D = ( 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87
       | 88 | 89 | 8a | 8b | 8c | 8d | 8e | 8f
       | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97
       | 98 | 99 | 9a | 9b | 9c | 9d | 9e | 9f
       | a0 | a1 | a2 | a3 | a4 | a5 | a6 | a7
       | a8 | a9 | aa | ab | ac | ad | ae | af
       | b0 | b1 | b2 | b3 | b4 | b5 | b6 | b7
       | b8 | b9 | ba | bb | bc | bd | be | bf
       | c0 | c1 | c2 | c3 | c4 | c5 | c6 | c7
       | c8 | c9 | ca | cb | cc | cd | ce | cf
       | d0 | d1 | d2 | d3 | d4 | d5 | d6 | d7
       | d8 | d9 | da | db | dc | dd | de | df
       | e0 | e1 | e2 | e3 | e4 | e5 | e6 | e7
       | e8 | e9 | ea | eb | ec | ed | ee | ef
       | f0 | f1 | f2 | f3 | f4 | f5 | f6 | f7
       | f8 | f9 | fa | fb | fc | fd | fe | ff )

   N o t e : The constant D is such that D_1, ... , D_J are pairwise
   different for any allowed n, k values.

   N o t e : The constant D is such that phi_c(D_t) = 1 for any allowed
   n, k, c and t in {1, ... , J}.  This condition is important, as it
   allows to prevent collisions of blocks of transformed key and block
   cipher permutation inputs.

6.2.2.  CTR-ACPKM Encryption Mode

   This section defines a CTR-ACPKM encryption mode that uses internal
   ACPKM re-keying mechanism for the periodical key transformation.

   The CTR-ACPKM mode can be considered as the extended by the ACPKM re-
   keying mechanism basic encryption mode CTR (see [MODES]).

   The CTR-ACPKM encryption mode can be used with the following
   parameters:

   o  64 <= n <= 512;

   o  128 <= k <= 512;

   o  the number of bits c in a specific part of the block to be
      incremented is such that 16 <= c <= 3/4 n, c is multiple of 8.

   The CTR-ACPKM mode encryption and decryption procedures are defined
   as follows:






Smyshlyaev              Expires December 22, 2017              [Page 19]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   +----------------------------------------------------------------+
   |  CTR-ACPKM-Encrypt(N, K, ICN, P)                               |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - Section size N,                                             |
   |  - key K,                                                      |
   |  - initial counter nonce ICN in V_{n-c},                       |
   |  - plaintext P = P_1 | ... | P_b, |P| < n * 2^{c-1}.           |
   |  Output:                                                       |
   |  - Ciphertext C.                                               |
   |----------------------------------------------------------------|
   |  1. CTR_1 = ICN | 0^c                                          |
   |  2. For j = 2, 3, ... , b do                                   |
   |         CTR_{j} = Inc_c(CTR_{j-1})                             |
   |  3. K^1 = K                                                    |
   |  4. For i = 2, 3, ... , ceil(|P|/N)                            |
   |         K^i = ACPKM(K^{i-1})                                   |
   |  5. For j = 1, 2, ... , b do                                   |
   |         i = ceil(j*n / N),                                     |
   |         G_j = E_{K^i}(CTR_j)                                   |
   |  6. C = P (xor) MSB_{|P|}(G_1 | ... | G_b)                     |
   |  7. Return C                                                   |
   +----------------------------------------------------------------+

   +----------------------------------------------------------------+
   |  CTR-ACPKM-Decrypt(N, K, ICN, C)                               |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - Section size N,                                             |
   |  - key K,                                                      |
   |  - initial counter nonce ICN in V_{n-c},                       |
   |  - ciphertext C = C_1 | ... | C_b, |C| < n * 2^{c-1}.          |
   |  Output:                                                       |
   |  - Plaintext P.                                                |
   |----------------------------------------------------------------|
   |  1. P = CTR-ACPKM-Encrypt(N, K, ICN, C)                        |
   |  2. Return P                                                   |
   +----------------------------------------------------------------+

   The initial counter nonce ICN value for each message that is
   encrypted under the given key must be chosen in a unique manner.

   The message size MUST NOT exceed n * 2^{c-1} bits.








Smyshlyaev              Expires December 22, 2017              [Page 20]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


6.2.3.  GCM-ACPKM Authenticated Encryption Mode

   This section defines GCM-ACPKM authenticated encryption mode that
   uses internal ACPKM re-keying mechanism for the periodical key
   transformation.

   The GCM-ACPKM mode can be considered as the basic authenticated
   encryption mode GCM (see [GCM]) extended by the ACPKM re-keying
   mechanism.

   The GCM-ACPKM authenticated encryption mode can be used with the
   following parameters:

   o  n in {128, 256};

   o  128 <= k <= 512;

   o  the number of bits c in a specific part of the block to be
      incremented is such that 32 <= c <= 3/4 n, c is multiple of 8.;

   o  authentication tag length t.

   The GCM-ACPKM mode encryption and decryption procedures are defined
   as follows:


   +-------------------------------------------------------------------+
   |  GHASH(X, H)                                                      |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - Bit string X = X_1 | ... | X_m, X_i in V_n for i in 1, ... , m.|
   |  Output:                                                          |
   |  - Block GHASH(X, H) in V_n.                                      |
   |-------------------------------------------------------------------|
   |  1. Y_0 = 0^n                                                     |
   |  2. For i = 1, ... , m do                                         |
   |         Y_i = (Y_{i-1} (xor) X_i) * H                             |
   |  3. Return Y_m                                                    |
   +-------------------------------------------------------------------+

   +-------------------------------------------------------------------+
   |  GCTR(N, K, ICB, X)                                               |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - Section size N,                                                |
   |  - key K,                                                         |
   |  - initial counter block ICB,                                     |
   |  - X = X_1 | ... | X_b, X_i in V_n for i = 1, ... , b-1 and       |



Smyshlyaev              Expires December 22, 2017              [Page 21]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   |                          X_b in V_r, where r <= n.                |
   |  Output:                                                          |
   |  - Y in V_{|X|}.                                                  |
   |-------------------------------------------------------------------|
   |  1. If X in V_0 then return Y, where Y in V_0                     |
   |  2. GCTR_1 = ICB                                                  |
   |  3. For i = 2, ... , b do                                         |
   |         GCTR_i = Inc_c(GCTR_{i-1})                                |
   |  4. K^1 = K                                                       |
   |  5. For j = 2, ... , ceil(l*n / N)                                |
   |         K^j = ACPKM(K^{j-1})                                      |
   |  6. For i = 1, ... , b do                                         |
   |         j = ceil(i*n / N),                                        |
   |         G_i = E_{K_j}(GCTR_i)                                     |
   |  7. Y = X (xor) MSB_{|X|}(G_1 | ... | G_b)                        |
   |  8. Return Y.                                                     |
   +-------------------------------------------------------------------+

   +-------------------------------------------------------------------+
   |  GCM-ACPKM-Encrypt(N, K, IV, P, A)                                |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - Section size N,                                                |
   |  - key K,                                                         |
   |  - initial counter nonce ICN in V_{n-c},                          |
   |  - plaintext P, |P| <= n*(2^{c-1} - 2), P = P_1 | ... | P_b,      |
   |  - additional authenticated data A.                               |
   |  Output:                                                          |
   |  - Ciphertext C,                                                  |
   |  - authentication tag T.                                          |
   |-------------------------------------------------------------------|
   |  1. H = E_{K}(0^n)                                                |
   |  2. If c = 32, then ICB_0 = ICN | 0^31 | 1                        |
   |     if c!= 32, then s = n * ceil(|ICN| / n) - |ICN|,              |
   |                ICB_0 = GHASH(ICN | 0^{s+n-64} | Vec_64(|ICN|), H) |
   |  3. C = GCTR(N, K, Inc_32(ICB_0), P)                              |
   |  4. u = n*ceil(|C| / n) - |C|                                     |
   |     v = n*ceil(|A| / n) - |A|                                     |
   |  5. S = GHASH(A | 0^v | C | 0^u | 0^{n-128} | Vec_64(|A|) |       |
   |               | Vec_64(|C|), H)                                   |
   |  6. T = MSB_t(E_{K}(ICB_0) (xor) S)                               |
   |  7. Return C | T                                                  |
   +-------------------------------------------------------------------+

   +-------------------------------------------------------------------+
   |  GCM-ACPKM-Decrypt(N, K, IV, A, C, T)                             |
   |-------------------------------------------------------------------|
   |  Input:                                                           |



Smyshlyaev              Expires December 22, 2017              [Page 22]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   |  - Section size N,                                                |
   |  - key K,                                                         |
   |  - initial counter block ICB,                                     |
   |  - additional authenticated data A.                               |
   |  - ciphertext C, |C| <= n*(2^{c-1} - 2), C = C_1 | ... | C_b,     |
   |  - authentication tag T                                           |
   |  Output:                                                          |
   |  - Plaintext P or FAIL.                                           |
   |-------------------------------------------------------------------|
   |  1. H = E_{K}(0^n)                                                |
   |  2. If c = 32, then ICB_0 = ICN | 0^31 | 1                        |
   |     if c!= 32, then s = n*ceil(|ICN|/n)-|ICN|,                    |
   |                ICB_0 = GHASH(ICN | 0^{s+n-64} | Vec_64(|ICN|), H) |
   |  3. P = GCTR(N, K, Inc_32(ICB_0), C)                              |
   |  4. u = n*ceil(|C| / n)-|C|                                       |
   |     v = n*ceil(|A| / n)-|A|                                       |
   |  5. S = GHASH(A | 0^v | C | 0^u | 0^{n-128} | Vec_64(|A|) |       |
   |               | Vec_64(|C|), H)                                   |
   |  6. T' = MSB_t(E_{K}(ICB_0) (xor) S)                              |
   |  7. If T = T' then return P; else return FAIL                     |
   +-------------------------------------------------------------------+

   The * operation on (pairs of) the 2^n possible blocks corresponds to
   the multiplication operation for the binary Galois (finite) field of
   2^n elements defined by the polynomial f as follows (by analogy with
   [GCM]):

   n = 128:  f = a^128 + a^7 + a^2 + a^1 + 1.

   n = 256:  f = a^256 + a^10 + a^5 + a^2 + 1.

   The initial vector IV value for each message that is encrypted under
   the given key must be chosen in a unique manner.

   The plaintext size MUST NOT exceed n*(2^{c-1} - 2) bits.

   The key for computing values E_{K}(ICB_0) and H is not updated and is
   equal to the initial key K.

6.2.4.  CCM-ACPKM Authenticated Encryption Mode

   This section defines a CCM-ACPKM authenticated encryption block
   cipher mode that uses internal ACPKM re-keying mechanism for the
   periodical key transformation.

   The CCM-ACPKM mode can be considered as the extended by the ACPKM re-
   keying mechanism basic authenticated encryption mode CCM (see
   [RFC3610]).



Smyshlyaev              Expires December 22, 2017              [Page 23]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   Since [RFC3610] defines CCM authenticated encryption mode only for
   128-bit block size, the CCM-ACPKM authenticated encryption mode can
   be used only with the parameter n = 128.  However, the CCM-ACPKM
   design principles can easily be applied to other block sizes, but
   these modes will require their own specifications.

   The CCM-ACPKM authenticated encryption mode differs from CCM mode in
   keys that are used for encryption during CBC-MAC calculation (see
   Section 2.2 of [RFC3610]) and key stream blocks generation (see
   Section 2.3 of [RFC3610]).

   The CCM mode uses the same initial key K block cipher encryption
   operations, while the CCM-ACPKM mode uses the keys K^1, K^2, ...,
   which are generated from the key K as follows:

           K^1 = K,
           K^{i+1} = ACPKM( K^i ).

   The keys K^1, K^2, ..., which are used as follows.

   CBC-MAC calculation: under a separate message processing during the
   first N/n block cipher encryption operations the key K^1 is used, the
   key K^2 is used for the next N/n block cipher encryption operations
   and so on.  For example, if N = 2n, then CBC-MAC calculation for a
   sequence of t blocks B_0, B_1, ..., B_t is as follows:

           X_1 = E( K^1, B_0 ),
           X_2 = E( K^1, X_1 XOR B_1 ),
           X_3 = E( K^2, X_2 XOR B_2 ),
           X_4 = E( K^2, X_3 XOR B_3 ),
           X_5 = E( K^3, X_4 XOR B_4 ),
           ...
           T = first-M-bytes( X_t+1 )

   The key stream blocks generation: under a separate message processing
   during the first N/n block cipher encryption operations the key K^1
   is used, the key K^2 is used for the next N/n block cipher encryption
   operations and so on.  For example, if N = 2n, then the key stream
   blocks are generated as follows:

           S_0 = E( K^1, A_0 ),
           S_1 = E( K^1, A_1 ),
           S_2 = E( K^2, A_2 ),
           S_3 = E( K^2, A_3 ),
           S_4 = E( K^3, A_4 ),
           ...





Smyshlyaev              Expires December 22, 2017              [Page 24]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


6.3.  Constructions that Require Master Key

   This section describes the block cipher modes that uses the ACPKM-
   Master re-keying mechanism, which use the initial key K as a master
   key K, so K is never used directly for the data processing but is
   used for key derivation.

6.3.1.  ACPKM-Master Key Derivation from the Master Key

   This section defines periodical key transformation with master key K
   which is called ACPKM-Master re-keying mechanism.  This mechanism can
   be applied to one of the basic modes of operation (CTR, GCM, CBC,
   CFB, OFB, OMAC modes) for getting an extension of this modes of
   operations that uses periodical key transformation with master key.
   This extension can be considered as a new mode of operation .

   Additional parameters that defines the functioning of basic modes of
   operation with the ACPKM-Master re-keying mechanism are the section
   size N and change frequency T* of the key K.  The values of N and T*
   are measured in bits and are fixed within a specific protocol based
   on the requirements of the system capacity and key lifetime (some
   recommendations on choosing N and T* will be provided in Section 8).
   The section size N MUST be divisible by the block size n.  The key
   frequency T* MUST be divisible by n.

   The main idea behind internal re-keying with master key is presented
   in Figure 9:
























Smyshlyaev              Expires December 22, 2017              [Page 25]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


Change frequency T*,
section size N,
maximum message size = m_max.
__________________________________________________________________________________

                            ACPKM                   ACPKM
               K*_1 = K--------------> K*_2 ---------...---------> K*_l_max
              ___|___                ___|___                     ___|___
             |       |              |       |                   |       |
             v  ...  v              v  ...  v                   v  ...  v
            K[1]     K[t]          K[t+1]   K[2t]     K[(l_max-1)t+1]   K[l_max*t]
             |       |              |       |                   |       |
             |       |              |       |                   |       |
             v       v              v       v                   v       v
M^{1}||========|...|========||========|...|========||...||========|...|==    : ||
M^{2}||========|...|========||========|...|========||...||========|...|======: ||
 ... ||        |   |        ||        |   |        ||   ||        |   |      : ||
M^{q}||========|...|========||====    |...|        ||...||        |...|      : ||
       section                                                               :
      <-------->                                                             :
         N bit                                                             m_max
__________________________________________________________________________________
|K[i]| = d,
t = T*/d,
l_max = ceil(m_max/N).

                   Figure 9: Internal re-keying with master key


   During the processing of the input message M with the length m in
   some mode of operation that uses ACPKM-Master key transformation with
   the master key K and key frequency T* the message M is divided into l
   = ceil(m/N) sections (denoted as M = M_1 | M_2 | ... | M_l, where M_i
   is in V_N for i in {1, 2, ... , l-1} and M_l is in V_r, r <= N).  The
   j-th section of each message is processed with the key material K[j],
   j in {1, ... ,l}, |K[j]| = d, that has been calculated with the
   ACPKM-Master algorithm as follows:

      K[1] | ... | K[l] = ACPKM-Master(T*, K, d*l) = CTR-ACPKM-Encrypt
      (T*, K, 1^{n/2}, 0^{d*l}).

6.3.2.  CTR-ACPKM-Master Encryption Mode

   This section defines a CTR-ACPKM-Master encryption mode that uses
   internal ACPKM-Master re-keying mechanism for the periodical key
   transformation.





Smyshlyaev              Expires December 22, 2017              [Page 26]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   The CTR-ACPKM-Master encryption mode can be considered as the
   extended by the ACPKM-Master re-keying mechanism basic encryption
   mode CTR (see [MODES]).

   The CTR-ACPKM-Master encryption mode can be used with the following
   parameters:

   o  64 <= n <= 512;

   o  128 <= k <= 512;

   o  the number of bits c in a specific part of the block to be
      incremented is such that 32 <= c <= 3/4 n, c is multiple of 8.

   The key material K[j] that is used for one section processing is
   equal to K^j, |K^j| = k bits.

   The CTR-ACPKM-Master mode encryption and decryption procedures are
   defined as follows:
































Smyshlyaev              Expires December 22, 2017              [Page 27]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   +----------------------------------------------------------------+
   |  CTR-ACPKM-Master-Encrypt(N, K, T*, ICN, P)                    |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - Section size N,                                             |
   |  - master key K,                                               |
   |  - change frequency T*,                                        |
   |  - initial counter nonce ICN in V_{n-c},                       |
   |  - plaintext P = P_1 | ... | P_b, |P| <= 2^{n/2-1}*n*N / k.    |
   |  Output:                                                       |
   |  - Ciphertext C.                                               |
   |----------------------------------------------------------------|
   |  1. CTR_1 = ICN | 0^c                                          |
   |  2. For j = 2, 3, ... , b do                                   |
   |         CTR_{j} = Inc_c(CTR_{j-1})                             |
   |  3. l = ceil(b*n / N)                                          |
   |  4. K^1 | ... | K^l = ACPKM-Master(T*, K, k*l)                 |
   |  5. For j = 1, 2, ... , b do                                   |
   |         i = ceil(j*n / N),                                     |
   |         G_j = E_{K^i}(CTR_j)                                   |
   |  6. C = P (xor) MSB_{|P|}(G_1 | ... |G_b)                      |
   |  7. Return C                                                   |
   |----------------------------------------------------------------+

   +----------------------------------------------------------------+
   |  CTR-ACPKM-Master-Decrypt(N, K, T*, ICN, C)                    |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - Section size N,                                             |
   |  - master key K,                                               |
   |  - change frequency T*,                                        |
   |  - initial counter nonce ICN in V_{n-c},                       |
   |  - ciphertext C = C_1 | ... | C_b, |C| <= 2^{n/2-1}*n*N / k.   |
   |  Output:                                                       |
   |  - Plaintext P.                                                |
   |----------------------------------------------------------------|
   |  1. P = CTR-ACPKM-Master-Encrypt(N, K, T*, ICN, C)             |
   |  1. Return P                                                   |
   +----------------------------------------------------------------+

   The initial counter nonce ICN value for each message that is
   encrypted under the given key must be chosen in a unique manner.  The
   counter (CTR_{i+1}) value does not change during key transformation.

   The message size MUST NOT exceed (2^{n/2-1}*n*N / k) bits.






Smyshlyaev              Expires December 22, 2017              [Page 28]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


6.3.3.  GCM-ACPKM-Master Authenticated Encryption Mode

   This section defines a GCM-ACPKM-Master authenticated encryption mode
   that uses internal ACPKM-Master re-keying mechanism for the
   periodical key transformation.

   The GCM-ACPKM-Master authenticated encryption mode can be considered
   as the extended by the ACPKM-Master re-keying mechanism basic
   authenticated encryption mode GCM (see [GCM]).

   The GCM-ACPKM-Master authenticated encryption mode can be used with
   the following parameters:

   o  n in {128, 256};

   o  128 <= k <= 512;

   o  the number of bits c in a specific part of the block to be
      incremented is such that 32 <= c <= 3/4 n, c is multiple of 8;

   o  authentication tag length t.

   The key material K[j] that is used for one section processing is
   equal to K^j, |K^j| = k bits, that is calculated as follows:

      K^1 | ... | K^j | ... | K^l = ACPKM-Master(T*, K, k*l).

   The GCM-ACPKM-Master mode encryption and decryption procedures are
   defined as follows:


   +-------------------------------------------------------------------+
   |  GHASH(X, H)                                                      |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - Bit string X = X_1 | ... | X_m, X_i in V_n for i in {1, ... ,m}|
   |  Output:                                                          |
   |  - Block GHASH(X, H) in V_n                                       |
   |-------------------------------------------------------------------|
   |  1. Y_0 = 0^n                                                     |
   |  2. For i = 1, ... , m do                                         |
   |         Y_i = (Y_{i-1} (xor) X_i)*H                               |
   |  3. Return Y_m                                                    |
   +-------------------------------------------------------------------+

   +-------------------------------------------------------------------+
   |  GCTR(N, K, T*, ICB, X)                                           |
   |-------------------------------------------------------------------|



Smyshlyaev              Expires December 22, 2017              [Page 29]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   |  Input:                                                           |
   |  - Section size N,                                                |
   |  - master key K,                                                  |
   |  - change frequency T*,                                           |
   |  - initial counter block ICB,                                     |
   |  - X = X_1 | ... | X_b, X_i in V_n for i = 1, ... , b-1 and       |
   |                X_b in V_r, where r <= n.                          |
   |  Output:                                                          |
   |  - Y in V_{|X|}.                                                  |
   |-------------------------------------------------------------------|
   |  1. If X in V_0 then return Y, where Y in V_0                     |
   |  2. GCTR_1 = ICB                                                  |
   |  3. For i = 2, ... , b do                                         |
   |         GCTR_i = Inc_c(GCTR_{i-1})                                |
   |  4. l = ceil(b*n / N)                                             |
   |  5. K^1 | ... | K^l = ACPKM-Master(T*, K, k*l)                    |
   |  6. For j = 1, ... , b do                                         |
   |         i = ceil(j*n / N),                                        |
   |         G_j = E_{K^i}(GCTR_j)                                     |
   |  7. Y = X (xor) MSB_{|X|}(G_1 | ... | G_b)                        |
   |  8. Return Y                                                      |
   +-------------------------------------------------------------------+

   +-------------------------------------------------------------------+
   |  GCM-ACPKM-Master-Encrypt(N, K, T*, IV, P, A)                     |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - Section size N,                                                |
   |  - master key K,                                                  |
   |  - change frequency T*,                                           |
   |  - initial counter nonce ICN in V_{n-c},                          |
   |  - plaintext P, |P| <= n*(2^{c-1} - 2).                           |
   |  - additional authenticated data A.                               |
   |  Output:                                                          |
   |  - Ciphertext C,                                                  |
   |  - authentication tag T.                                          |
   |-------------------------------------------------------------------|
   |  1. K^1 = ACPKM-Master(T*, K, k)                                  |
   |  2. H = E_{K^1}(0^n)                                              |
   |  3. If c = 32, then ICB_0 = ICN | 0^31 | 1                        |
   |     if c!= 32, then s = n*ceil(|ICN|/n) - |ICN|,                  |
   |                ICB_0 = GHASH(ICN | 0^{s+n-64} | Vec_64(|ICN|), H) |
   |  4. C = GCTR(N, K, T*, Inc_32(J_0), P)                            |
   |  5. u = n*ceil(|C| / n) - |C|                                     |
   |     v = n*ceil(|A| / n) - |A|                                     |
   |  6. S = GHASH(A | 0^v | C | 0^u | 0^{n-128} | Vec_64(|A|) |       |
   |               | Vec_64(|C|), H)                                   |
   |  7. T = MSB_t(E_{K^1}(J_0) (xor) S)                               |



Smyshlyaev              Expires December 22, 2017              [Page 30]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   |  8. Return C | T                                                  |
   +-------------------------------------------------------------------+

   +-------------------------------------------------------------------+
   |  GCM-ACPKM-Master-Decrypt(N, K, T*, IV, A, C, T)                  |
   |-------------------------------------------------------------------|
   |  Input:                                                           |
   |  - Section size N,                                                |
   |  - master key K,                                                  |
   |  - change frequency T*,                                           |
   |  - initial counter nonce ICN in V_{n-c},                          |
   |  - additional authenticated data A.                               |
   |  - ciphertext C, |C| <= n*(2^{c-1} - 2),                          |
   |  - authentication tag T,                                          |
   |  Output:                                                          |
   |  - Plaintext P or FAIL.                                           |
   |-------------------------------------------------------------------|
   |  1. K^1 = ACPKM-Master(T*, K, k)                                  |
   |  2. H = E_{K^1}(0^n)                                              |
   |  3. If c = 32, then ICB_0 = ICN | 0^31 | 1                        |
   |     if c!= 32, then s = n*ceil(|ICN| / n) - |ICN|,                |
   |                ICB_0 = GHASH(ICN | 0^{s+n-64} | Vec_64(|ICN|), H) |
   |  4. P = GCTR(N, K, T*, Inc_32(J_0), C)                            |
   |  5. u = n*ceil(|C| / n) - |C|                                     |
   |     v = n*ceil(|A| / n) - |A|                                     |
   |  6. S = GHASH(A | 0^v | C | 0^u | 0^{n-128} |  Vec_64(|A|) |      |
   |               | Vec_64(|C|), H)                                   |
   |  7. T' = MSB_t(E_{K^1}(ICB_0) (xor) S)                            |
   |  8. IF T = T' then return P; else return FAIL.                    |
   +-------------------------------------------------------------------+

   The * operation on (pairs of) the 2^n possible blocks corresponds to
   the multiplication operation for the binary Galois (finite) field of
   2^n elements defined by the polynomial f as follows (by analogy with
   [GCM]):

   n = 128:  f = a^128 + a^7 + a^2 + a^1 + 1.

   n = 256:  f = a^256 + a^10 + a^5 + a^2 + 1.

   The initial vector IV value for each message that is encrypted under
   the given key must be chosen in a unique manner.

   The plaintext size MUST NOT exceed (2^{n/2-1}*n*N / k) bits.







Smyshlyaev              Expires December 22, 2017              [Page 31]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


6.3.4.  CCM-ACPKM-Master Authenticated Encryption Mode

   This section defines a CCM-ACPKM-Master authenticated encryption mode
   of operations that uses internal ACPKM-Master re-keying mechanism for
   the periodical key transformation.

   The CCM-ACPKM-Master authenticated encryption mode is differed from
   CCM-ACPKM mode in the way the keys K^1, K^2, ... are generated.  For
   CCM-ACPKM-Master mode the keys are generated as follows: K^i = K[i],
   where |K^i|=k and K[1]|K[2]|...|K[l] = ACPKM-Master( T*, K, k*l ).

6.3.5.  CBC-ACPKM-Master Encryption Mode

   This section defines a CBC-ACPKM-Master encryption mode that uses
   internal ACPKM-Master re-keying mechanism for the periodical key
   transformation.

   The CBC-ACPKM-Master encryption mode can be considered as the
   extended by the ACPKM-Master re-keying mechanism basic encryption
   mode CBC (see [MODES]).

   The CBC-ACPKM-Master encryption mode can be used with the following
   parameters:

   o  64 <= n <= 512;

   o  128 <= k <= 512.

   In the specification of the CBC-ACPKM-Master mode the plaintext and
   ciphertext must be a sequence of one or more complete data blocks.
   If the data string to be encrypted does not initially satisfy this
   property, then it MUST be padded to form complete data blocks.  The
   padding methods are outside the scope of this document.  An example
   of a padding method can be found in Appendix A of [MODES].

   The key material K[j] that is used for one section processing is
   equal to K^j, |K^j| = k bits.

   We will denote by D_{K} the decryption function which is a
   permutation inverse to the E_{K}.

   The CBC-ACPKM-Master mode encryption and decryption procedures are
   defined as follows:








Smyshlyaev              Expires December 22, 2017              [Page 32]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   +----------------------------------------------------------------+
   |  CBC-ACPKM-Master-Encrypt(N, K, T*, IV, P)                     |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - Section size N,                                             |
   |  - master key K,                                               |
   |  - change frequency T*,                                        |
   |  - initialization vector IV in V_n,                            |
   |  - plaintext P = P_1 | ... | P_b, |P| <= 2^{n/2-1}*n*N / k,    |
   |                  |P_b| = n.                                    |
   |  Output:                                                       |
   |  - Ciphertext C.                                               |
   |----------------------------------------------------------------|
   |  1. l = ceil(b*n/N)                                            |
   |  2. K^1 | ... | K^l = ACPKM-Master(T*, K, k*l)                 |
   |  3. C_0 = IV                                                   |
   |  4. For j = 1, 2, ... , b do                                   |
   |         i = ceil(j*n / N),                                     |
   |         C_j = E_{K^i}(P_j (xor) C_{j-1})                       |
   |  5. Return C = C_1 | ... | C_b                                 |
   |----------------------------------------------------------------+

   +----------------------------------------------------------------+
   |  CBC-ACPKM-Master-Decrypt(N, K, T*, IV, C)                     |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - Section size N,                                             |
   |  - master key K,                                               |
   |  - change frequency T*,                                        |
   |  - initialization vector IV in V_n,                            |
   |  - ciphertext C = C_1 | ... | C_b, |C| <= 2^{n/2-1}*n*N/k,     |
   |                  |C_b| = n.                                    |
   |  Output:                                                       |
   |  - Plaintext P.                                                |
   |----------------------------------------------------------------|
   |  1. l = ceil(b*n / N)                                          |
   |  2. K^1 | ... | K^l = ACPKM-Master(T*, K, k*l)                 |
   |  3. C_0 = IV                                                   |
   |  4. For j = 1, 2, ... , b do                                   |
   |         i = ceil(j*n/N)                                        |
   |         P_j = D_{K^i}(C_j) (xor) C_{j-1}                       |
   |  5. Return P = P_1 | ... | P_b                                 |
   +----------------------------------------------------------------+

   The initialization vector IV for each message that is encrypted under
   the given key need not to be secret, but must be unpredictable.

   The message size MUST NOT exceed (2^{n/2-1}*n*N / k) bits.



Smyshlyaev              Expires December 22, 2017              [Page 33]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


6.3.6.  CFB-ACPKM-Master Encryption Mode

   This section defines a CFB-ACPKM-Master encryption mode that uses
   internal ACPKM-Master re-keying mechanism for the periodical key
   transformation.

   The CFB-ACPKM-Master encryption mode can be considered as the
   extended by the ACPKM-Master re-keying mechanism basic encryption
   mode CFB (see [MODES]).

   The CFB-ACPKM-Master encryption mode can be used with the following
   parameters:

   o  64 <= n <= 512;

   o  128 <= k <= 512.

   The key material K[j] that is used for one section processing is
   equal to K^j, |K^j| = k bits.

   The CFB-ACPKM-Master mode encryption and decryption procedures are
   defined as follows:





























Smyshlyaev              Expires December 22, 2017              [Page 34]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   +-------------------------------------------------------------+
   |  CFB-ACPKM-Master-Encrypt(N, K, T*, IV, P)                  |
   |-------------------------------------------------------------|
   |  Input:                                                     |
   |  - Section size N,                                          |
   |  - master key K,                                            |
   |  - change frequency T*,                                     |
   |  - initialization vector IV in V_n,                         |
   |  - plaintext P = P_1 | ... | P_b, |P| <= 2^{n/2-1}*n*N / k. |
   |  Output:                                                    |
   |  - Ciphertext C.                                            |
   |-------------------------------------------------------------|
   |  1. l = ceil(b*n / N)                                       |
   |  2. K^1 | ... | K^l = ACPKM-Master(T*, K, k*l)              |
   |  3. C_0 = IV                                                |
   |  4. For j = 1, 2, ... , b do                                |
   |         i = ceil(j*n / N)                                   |
   |         C_j = E_{K^i}(C_{j-1}) (xor) P_j                    |
   |  5. Return C = C_1 | ... | C_b.                             |
   |-------------------------------------------------------------+

   +-------------------------------------------------------------+
   |  CFB-ACPKM-Master-Decrypt(N, K, T*, IV, C)                  |
   |-------------------------------------------------------------|
   |  Input:                                                     |
   |  - Section size N,                                          |
   |  - master key K,                                            |
   |  - change frequency T*,                                     |
   |  - initialization vector IV in V_n,                         |
   |  - ciphertext C = C_1 | ... | C_b, |C| <= 2^{n/2-1}*n*N / k.|
   |  Output:                                                    |
   |  - Plaintext P.                                             |
   |-------------------------------------------------------------|
   |  1. l = ceil(b*n / N)                                       |
   |  2. K^1 | ... | K^l = ACPKM-Master(T*, K, k*l)              |
   |  3. C_0 = IV                                                |
   |  4. For j = 1, 2, ... , b do                                |
   |         i = ceil(j*n / N),                                  |
   |         P_j = E_{K^i}(C_{j-1}) (xor) C_j                    |
   |  5. Return P = P_1 | ... | P_b                              |
   +-------------------------------------------------------------+

   The initialization vector IV for each message that is encrypted under
   the given key need not to be secret, but must be unpredictable.

   The message size MUST NOT exceed 2^{n/2-1}*n*N/k bits.





Smyshlyaev              Expires December 22, 2017              [Page 35]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


6.3.7.  OFB-ACPKM-Master Encryption Mode

   This section defines an OFB-ACPKM-Master encryption mode that uses
   internal ACPKM-Master re-keying mechanism for the periodical key
   transformation.

   The OFB-ACPKM-Master encryption mode can be considered as the
   extended by the ACPKM-Master re-keying mechanism basic encryption
   mode OFB (see [MODES]).

   The OFB-ACPKM-Master encryption mode can be used with the following
   parameters:

   o  64 <= n <= 512;

   o  128 <= k <= 512.

   The key material K[j] used for one section processing is equal to
   K^j, |K^j| = k bits.

   The OFB-ACPKM-Master mode encryption and decryption procedures are
   defined as follows:





























Smyshlyaev              Expires December 22, 2017              [Page 36]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   +----------------------------------------------------------------+
   |  OFB-ACPKM-Master-Encrypt(N, K, T*, IV, P)                     |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - Section size N,                                             |
   |  - master key K,                                               |
   |  - change frequency T*,                                        |
   |  - initialization vector IV in V_n,                            |
   |  - plaintext P = P_1 | ... | P_b, |P| <= 2^{n/2-1}*n*N / k.    |
   |  Output:                                                       |
   |  - Ciphertext C.                                               |
   |----------------------------------------------------------------|
   |  1. l = ceil(b*n / N)                                          |
   |  2. K^1 | ... | K^l = ACPKM-Master(T*, K, k*l)                 |
   |  3. G_0 = IV                                                   |
   |  4. For j = 1, 2, ... , b do                                   |
   |         i = ceil(j*n / N),                                     |
   |         G_j = E_{K_i}(G_{j-1})                                 |
   |  5. Return C = P (xor) MSB_{|P|}(G_1 | ... | G_b)              |
   |----------------------------------------------------------------+

   +----------------------------------------------------------------+
   |  OFB-ACPKM-Master-Decrypt(N, K, T*, IV, C)                     |
   |----------------------------------------------------------------|
   |  Input:                                                        |
   |  - Section size N,                                             |
   |  - master key K,                                               |
   |  - change frequency T*,                                        |
   |  - initialization vector IV in V_n,                            |
   |  - ciphertext C = C_1 | ... | C_b, |C| <= 2^{n/2-1}*n*N / k.   |
   |  Output:                                                       |
   |  - Plaintext P.                                                |
   |----------------------------------------------------------------|
   |  1. Return OFB-ACPKM-Master-Encrypt(N, K, T*, IV, C)           |
   +----------------------------------------------------------------+

   The initialization vector IV for each message that is encrypted under
   the given key need not be unpredictable, but it must be a nonce that
   is unique to each execution of the encryption operation.

   The message size MUST NOT exceed 2^{n/2-1}*n*N / k bits.

6.3.8.  OMAC-ACPKM-Master Mode

   This section defines an OMAC-ACPKM-Master message authentication code
   calculation mode that uses internal ACPKM-Master re-keying mechanism
   for the periodical key transformation.




Smyshlyaev              Expires December 22, 2017              [Page 37]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   The OMAC-ACPKM-Master mode can be considered as the extended by the
   ACPKM-Master re-keying mechanism basic message authentication code
   calculation mode OMAC, which is also known as CMAC (see [RFC4493]).

   The OMAC-ACPKM-Master message authentication code calculation mode
   can be used with the following parameters:

   o  n in {64, 128, 256};

   o  128 <= k <= 512.

   The key material K[j] that is used for one section processing is
   equal to K^j | K^j_1, where |K^j| = k and |K^j_1| = n.

   The following is a specification of the subkey generation process of
   OMAC:


   +-------------------------------------------------------------------+
   | Generate_Subkey(K1, r)                                            |
   |-------------------------------------------------------------------|
   | Input:                                                            |
   |  - Key K1,                                                        |
   |  Output:                                                          |
   |  - Key SK.                                                        |
   |-------------------------------------------------------------------|
   |   1. If r = n then return K1                                      |
   |   2. If r < n then                                                |
   |          if MSB_1(K1) = 0                                         |
   |              return K1 << 1                                       |
   |          else                                                     |
   |              return (K1 << 1) (xor) R_n                           |
   |                                                                   |
   +-------------------------------------------------------------------+

   Where R_n takes the following values:

   o  n = 64: R_{64} = 0^{59} | 11011;

   o  n = 128: R_{128} = 0^{120} | 10000111;

   o  n = 256: R_{256} = 0^{145} | 10000100101.

   The OMAC-ACPKM-Master message authentication code calculation mode is
   defined as follows:






Smyshlyaev              Expires December 22, 2017              [Page 38]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   +-------------------------------------------------------------------+
   | OMAC-ACPKM-Master(K, N, T*, M)                                    |
   |-------------------------------------------------------------------|
   | Input:                                                            |
   |  - Section size N,                                                |
   |  - master key K,                                                  |
   |  - key frequency T*,                                              |
   |  - plaintext M = M_1 | ... | M_b, |M| <= 2^{n/2}*n^2*N / (k + n). |
   |  Output:                                                          |
   |  - message authentication code T.                                 |
   |-------------------------------------------------------------------|
   | 1. C_0 = 0^n                                                      |
   | 2. l = ceil(b*n / N)                                              |
   | 3. K^1 | K^1_1 | ... | K^l | K^l_1 = ACPKM-Master(T*, K, (k+n)*l  |
   | 4. For j = 1, 2, ... , b-1 do                                     |
   |        i = ceil(j*n / N),                                         |
   |        C_j = E_{K^i}(M_j (xor) C_{j-1})                           |
   | 5. SK = Generate_Subkey(K^l_1, |M_b|)                             |
   | 6. If |M_b| = n then M*_b = M_b                                   |
   |                 else M*_b = M_b | 1 | 0^{n - 1 -|M_b|}            |
   | 7. T = E_{K^l}(M*_b (xor) C_{b-1} (xor) SK)                       |
   | 8. Return T                                                       |
   +-------------------------------------------------------------------+

   The message size MUST NOT exceed 2^{n/2}*n^2*N / (k + n) bits.

7.  Joint Usage of External and Internal Re-keying

   Any mechanism described in Section 5 can be used with any mechanism
   described in Section 6.

8.  Security Considerations

   Re-keying should be used to increase "a priori" security properties
   of ciphers in hostile environments (e.g. with side-channel
   adversaries).  If some non-negligible attacks are known for a cipher,
   it must not be used.  So re-keying cannot be used as a patch for
   vulnerable ciphers.  Base cipher properties must be well analyzed,
   because security of re-keying mechanisms is based on security of a
   block cipher as a pseudorandom function.

   Re-keying is not intended to solve any post-quantum security issues
   for symmetric crypto since the reduction of security caused by
   Grover's algorithm is not connected with a size of plaintext
   transformed by a cipher - only a negligible (sufficient for key
   uniqueness) material is needed and the aim of re-keying is to limit a
   size of plaintext transformed on one key.




Smyshlyaev              Expires December 22, 2017              [Page 39]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   Re-keying can provide backward security only if the previous traffic
   keys are securely deleted by all parties that have the keys.

9.  References

9.1.  Normative References

   [GCM]      McGrew, D. and J. Viega, "The Galois/Counter Mode of
              Operation (GCM)", Submission to NIST
              http://csrc.nist.gov/CryptoToolkit/modes/proposedmodes/
              gcm/gcm-spec.pdf, January 2004.

   [MODES]    Dworkin, M., "Recommendation for Block Cipher Modes of
              Operation: Methods and Techniques", NIST Special
              Publication  800-38A, December 2001.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <http://www.rfc-editor.org/info/rfc2119>.

   [RFC3610]  Whiting, D., Housley, R., and N. Ferguson, "Counter with
              CBC-MAC (CCM)", RFC 3610, DOI 10.17487/RFC3610, September
              2003, <http://www.rfc-editor.org/info/rfc3610>.

   [RFC4493]  Song, JH., Poovendran, R., Lee, J., and T. Iwata, "The
              AES-CMAC Algorithm", RFC 4493, DOI 10.17487/RFC4493, June
              2006, <http://www.rfc-editor.org/info/rfc4493>.

   [RFC5869]  Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
              Key Derivation Function (HKDF)", RFC 5869,
              DOI 10.17487/RFC5869, May 2010,
              <http://www.rfc-editor.org/info/rfc5869>.

   [TLSDraft]
              Rescorla, E., "The Transport Layer Security (TLS) Protocol
              Version 1.3", 2017, <https://tools.ietf.org/html/draft-
              ietf-tls-tls13-18>.

9.2.  Informative References

   [AbBell]   Michel Abdalla and Mihir Bellare, "Increasing the Lifetime
              of a Key: A Comparative Analysis of the Security of Re-
              keying Techniques", ASIACRYPT2000, LNCS 1976, pp. 546-559,
              2000.






Smyshlyaev              Expires December 22, 2017              [Page 40]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   [LDC]      Howard M. Heys, "A Tutorial on Linear and Differential
              Cryptanalysis", 2017,
              <http://www.cs.bc.edu/~straubin/crypto2017/heys.pdf>.

   [Sweet32]  Karthikeyan Bhargavan, Gaetan Leurent, "On the Practical
              (In-)Security of 64-bit Block Ciphers. Collision Attacks
              on HTTP over TLS and OpenVPN", 2016,
              <https://sweet32.info/SWEET32_CCS16.pdf>.

Appendix A.  Test examples


   CTR-ACPKM mode with AES-256
   *********
   c = 64
   k = 256
   N = 256
   n = 128

   D_1
   80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F

   D_2
   90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F

   Key K:
   88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
   FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF

   Plain text P:
   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
   00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
   11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
   22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
   33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
   44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
   55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44

   ICN:
   12 34 56 78 90 AB CE F0

   ACPKM's iteration 1
   Process block 1
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 00

   Output block (ctr)
   FD 7E F8 9A D9 7E A4 B8 8D B8 B5 1C 1C 9D 6D D0



Smyshlyaev              Expires December 22, 2017              [Page 41]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   Plain text
   11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88

   Cipher text
   EC 5C CB DE 8C 18 D3 B8 72 56 68 D0 A7 37 F4 58

   Process block 2
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 01

   Output block (ctr)
   19 98 C5 71 76 37 FB 17 11 E4 48 F0 0C 0D 60 B2

   Plain text
   00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A

   Cipher text
   19 89 E7 42 32 62 9D 60 99 7D E2 4B C0 E3 9F B8

   Input block (ctr)
   80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F

   Output block (ctr)
   F6 80 D1 21 2F A4 3D F4 EC 3A 91 DE 2A B1 6F 1B

   Input block (ctr)
   90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F

   Output block (ctr)
   36 B0 48 8A 4F C1 2E 09 98 D2 E4 A8 88 E8 4F 3D

   Updated key:
   F6 80 D1 21 2F A4 3D F4 EC 3A 91 DE 2A B1 6F 1B
   36 B0 48 8A 4F C1 2E 09 98 D2 E4 A8 88 E8 4F 3D

   ACPKM's iteration 2
   Process block 1
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 02

   Output block (ctr)
   E4 88 89 4F B6 02 87 DB 77 5A 07 D9 2C 89 46 EA

   Plain text
   11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00

   Cipher text
   F5 AA BA 0B E3 64 F0 53 EE F0 BC 15 C2 76 4C EA



Smyshlyaev              Expires December 22, 2017              [Page 42]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   Process block 2
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 03

   Output block (ctr)
   BC 4F 87 23 DB F0 91 50 DD B4 06 C3 1D A9 7C A4

   Plain text
   22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11

   Cipher text
   9E 7C C3 76 BD 87 19 C9 77 0F CA 2D E2 A3 7C B5

   Input block (ctr)
   80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F

   Output block (ctr)
   8E B9 7E 43 27 1A 42 F1 CA 8E E2 5F 5C C7 C8 3B

   Input block (ctr)
   90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F

   Output block (ctr)
   1A CE 9E 5E D0 6A A5 3B 57 B9 6A CF 36 5D 24 B8

   Updated key:
   8E B9 7E 43 27 1A 42 F1 CA 8E E2 5F 5C C7 C8 3B
   1A CE 9E 5E D0 6A A5 3B 57 B9 6A CF 36 5D 24 B8

   ACPKM's iteration 3
   Process block 1
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 04

   Output block (ctr)
   68 6F 22 7D 8F B2 9C BD 05 C8 C3 7D 22 FE 3B B7

   Plain text
   33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22

   Cipher text
   5B 2B 77 1B F8 3A 05 17 BE 04 2D 82 28 FE 2A 95

   Process block 2
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 05

   Output block (ctr)



Smyshlyaev              Expires December 22, 2017              [Page 43]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   C0 1B F9 7F 75 6E 12 2F 80 59 55 BD DE 2D 45 87

   Plain text
   44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33

   Cipher text
   84 4E 9F 08 FD F7 B8 94 4C B7 AA B7 DE 3C 67 B4

   Input block (ctr)
   80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F

   Output block (ctr)
   C5 71 6C C9 67 98 BC 2D 4A 17 87 B7 8A DF 94 AC

   Input block (ctr)
   90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F

   Output block (ctr)
   E8 16 F8 0B DB BC AD 7D 60 78 12 9C 0C B4 02 F5

   Updated key:
   C5 71 6C C9 67 98 BC 2D 4A 17 87 B7 8A DF 94 AC
   E8 16 F8 0B DB BC AD 7D 60 78 12 9C 0C B4 02 F5

   ACPKM's iteration 4
   Process block 1
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 06

   Output block (ctr)
   03 DE 34 74 AB 9B 65 8A 3B 54 1E F8 BD 2B F4 7D

   Plain text
   55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44

   Cipher text
   56 B8 43 FC 32 31 DE 46 D5 AB 14 F8 AC 09 C7 39

   Input block (ctr)
   80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F

   Output block (ctr)
   74 1E B5 88 D6 AB DA B6 89 AA FD BA A9 3E A2 46

   Input block (ctr)
   90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F

   Output block (ctr)



Smyshlyaev              Expires December 22, 2017              [Page 44]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   16 3A A6 C2 3C E7 C3 74 CD 38 BF C6 FE 8C C5 FF

   Updated key:
   74 1E B5 88 D6 AB DA B6 89 AA FD BA A9 3E A2 46
   16 3A A6 C2 3C E7 C3 74 CD 38 BF C6 FE 8C C5 FF

   Encrypted src
   EC 5C CB DE 8C 18 D3 B8 72 56 68 D0 A7 37 F4 58
   19 89 E7 42 32 62 9D 60 99 7D E2 4B C0 E3 9F B8
   F5 AA BA 0B E3 64 F0 53 EE F0 BC 15 C2 76 4C EA
   9E 7C C3 76 BD 87 19 C9 77 0F CA 2D E2 A3 7C B5
   5B 2B 77 1B F8 3A 05 17 BE 04 2D 82 28 FE 2A 95
   84 4E 9F 08 FD F7 B8 94 4C B7 AA B7 DE 3C 67 B4
   56 B8 43 FC 32 31 DE 46 D5 AB 14 F8 AC 09 C7 39





Appendix B.  Contributors

   o  Russ Housley
      Vigil Security, LLC
      housley@vigilsec.com

   o  Mihir Bellare
      University of California
      mihir@eng.ucsd.edu

   o  Evgeny Alekseev
      CryptoPro
      alekseev@cryptopro.ru

   o  Ekaterina Smyshlyaeva
      CryptoPro
      ess@cryptopro.ru

   o  Daniel Fox Franke
      Akamai Technologies
      dfoxfranke@gmail.com

   o  Lilia Ahmetzyanova
      CryptoPro
      lah@cryptopro.ru

   o  Ruth Ng
      University of California, San Diego
      ring@eng.ucsd.edu



Smyshlyaev              Expires December 22, 2017              [Page 45]


Internet-Draft   Re-keying Mechanisms for Symmetric Keys       June 2017


   o  Shay Gueron
      University of Haifa, Israel
      Intel Corporation, Israel Development Center, Israel
      shay.gueron@gmail.com

Appendix C.  Acknowledgments

   We thank Scott Fluhrer, Dorothy Cooley, Yoav Nir, Jim Schaad and Paul
   Hoffman for their useful comments.

Author's Address

   Stanislav Smyshlyaev (editor)
   CryptoPro
   18, Suschevsky val
   Moscow  127018
   Russian Federation

   Phone: +7 (495) 995-48-20
   Email: svs@cryptopro.ru































Smyshlyaev              Expires December 22, 2017              [Page 46]


Html markup produced by rfcmarkup 1.129c, available from https://tools.ietf.org/tools/rfcmarkup/