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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                              July 3, 2017
Expires: January 4, 2018


                Re-keying Mechanisms for Symmetric Keys
                      draft-irtf-cfrg-re-keying-05

Abstract

   A certain maximum amount of data can be safely encrypted when
   encryption is performed under a single key.  This amount is called
   "key lifetime".  This specification describes 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 modes of operations such 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
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   Internet-Drafts are draft documents valid for a maximum of six months
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   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 January 4, 2018.

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
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   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
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   include Simplified BSD License text as described in Section 4.e of



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   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.  Choosing Constructions and Security Parameters  . . . . . . .   6
   5.  External Re-keying Mechanisms . . . . . . . . . . . . . . . .   8
     5.1.  Methods of Key Lifetime Control . . . . . . . . . . . . .  11
     5.2.  Parallel Constructions  . . . . . . . . . . . . . . . . .  12
       5.2.1.  Parallel Construction Based on a KDF on a Block
               Cipher  . . . . . . . . . . . . . . . . . . . . . . .  13
       5.2.2.  Parallel Construction Based on HKDF . . . . . . . . .  13
     5.3.  Serial Constructions  . . . . . . . . . . . . . . . . . .  14
       5.3.1.  Serial Construction Based on a KDF on a Block Cipher   14
       5.3.2.  Serial Construction Based on HKDF . . . . . . . . . .  15
   6.  Internal Re-keying Mechanisms . . . . . . . . . . . . . . . .  15
     6.1.  Methods of Key Lifetime Control . . . . . . . . . . . . .  18
     6.2.  Constructions that Do Not Require Master Key  . . . . . .  18
       6.2.1.  ACPKM Re-keying Mechanisms  . . . . . . . . . . . . .  18
       6.2.2.  CTR-ACPKM Encryption Mode . . . . . . . . . . . . . .  20
       6.2.3.  GCM-ACPKM Authenticated Encryption Mode . . . . . . .  22
       6.2.4.  CCM-ACPKM Authenticated Encryption Mode . . . . . . .  24
     6.3.  Constructions that Require Master Key . . . . . . . . . .  26
       6.3.1.  ACPKM-Master Key Derivation from the Master Key . . .  26
       6.3.2.  CTR-ACPKM-Master Encryption Mode  . . . . . . . . . .  27
       6.3.3.  GCM-ACPKM-Master Authenticated Encryption Mode  . . .  30
       6.3.4.  CCM-ACPKM-Master Authenticated Encryption Mode  . . .  33
       6.3.5.  CBC-ACPKM-Master Encryption Mode  . . . . . . . . . .  33
       6.3.6.  CFB-ACPKM-Master Encryption Mode  . . . . . . . . . .  35
       6.3.7.  OFB-ACPKM-Master Encryption Mode  . . . . . . . . . .  37
       6.3.8.  OMAC-ACPKM-Master Mode  . . . . . . . . . . . . . . .  39
   7.  Joint Usage of External and Internal Re-keying  . . . . . . .  40
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  40
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  41
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  41
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  42
   Appendix A.  Test examples  . . . . . . . . . . . . . . . . . . .  42
   Appendix B.  Contributors . . . . . . . . . . . . . . . . . . . .  47
   Appendix C.  Acknowledgments  . . . . . . . . . . . . . . . . . .  47
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  47








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1.  Introduction

   A certain maximum amount of data can be safely encrypted when
   encryption is performed under a single key.  This amount is called
   "key lifetime" and can be calculated from the following
   considerations:

   1.  Methods based on the combinatorial properties of the used block
       cipher mode of operation

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

   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.  Limitations resulting from these considerations are
          usually the most restrictive ones.  [TEMPEST] is an example of
          attack that is based on such methods.

   3.  Methods based on the properties of the used block cipher

          The most common methods of this type are linear and
          differential cryptanalysis [LDC].  In most cases these methods
          do not depend on the used modes of operation.  In case of
          secure block ciphers, bounds resulting from such methods are
          roughly the same as the natural bounds of 2^n, and are
          dominated by the other bounds above.  Therefore, they can be
          excluded from the considerations here.

   As a result, it is important to replace a key as soon as the total
   size of the processed plaintext under that key reaches the lifetime
   limitation.  A specific value of the key lifetime should be
   determined in accordance with some safety margin for protocol
   security and the 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).






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

   Figure 1: Graphic display of the key lifetime limitation



   In practice, such amount of data that corresponds to limitation L may
   not be enough.  The simplest and obvious way in this situation is a
   regular renegotiation of a session key after processing this
   threshold amount of data L.  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 public key cryptography.

   This specification presents two approaches to extend the lifetime of
   a key while avoiding renegotiation: external and internal re-keying.

   External re-keying is performed by a protocol, and it is independent
   of the underlying block cipher and the mode of operation.  External
   re-keying can use parallel and serial constructions.  In the parallel
   case, subkeys K^1, K^2,... are generated directly from the key K
   independently of each other.  In the serial case, every subkey
   depends on the state that is updated after the generation of each new
   subkey.

   Internal re-keying is built into the mode, and it depends heavily on
   the properties of the mode of operation and the block size.

   The re-keying approaches extend the key lifetime for a single
   negotiated key by providing the possibility to limit the leakages
   (via side channels) and by improving combinatorial properties of the
   used block cipher mode of operation.

   In practical applications, re-keying can be useful for protocols that
   need to operate in hostile environments or under restricted resource
   conditions (e.g., that require lightweight cryptography, where
   ciphers have a small block size, that imposes strict combinatorial
   limitations).  Moreover, mechanisms that use external and internal



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   re-keying may provide some properties of forward security and
   potentially some protection against future attacks (by limiting the
   number of plaintext-ciphertext pairs that an adversary can collect).

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 bits) 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;




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   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 smallest integer that is greater than or equal to x;

   k       the bit-length of the K; k is assumed to be divisible by 8;

   n       the block size of the block cipher (in bits); n is assumed to
           be divisible by 8;

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

   N       the section size (the number of bits that are processed with
           one key before this key is transformed);

   l       the number of data sections in the plaintext.

   A plaintext message P and the corresponding ciphertext C are divided
   into b = ceil(|P|/n) blocks, denoted P = P_1 | P_2 | ... | P_b and C
   = C_1 | C_2 | ... | C_b, respectively.  The first b-1 blocks P_i and
   C_i are in V_n, for i = 1, 2, ... , b-1.  The b-th block P_b, C_b may
   be an incomplete block, i.e., in V_r, where r <= n if not otherwise
   specified.

4.  Choosing Constructions and Security Parameters

   External re-keying is an approach assuming that a key is transformed
   after encrypting a limited number of entire messages.  External re-
   keying method is chosen at the protocol level, regardless of the
   underlying block cipher or the encryption mode.  External re-keying
   is recommended for protocols that process relatively short messages
   or for protocols that have a way to divide a long message into
   manageable pieces.  Through external re-keying the number of messages
   that can be securely processed with a single symmetric key is
   substantially increased without loss in message length.

   External re-keying has the following advantages:

   1.  the lifetime of a key increases by increasing the number of
       messages processed with this key;




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   2.  it has negligible affect on the performance, when the number of
       messages processed under one key is sufficiently large;

   3.  provides forward and backward security of data processing keys.

   However, the use of external re-keying has the following
   disadvantage: 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.  E.g. if the
   key lifetime L is 1 GB and the message length m = 3 GB, then this
   message can not be processed as a whole and it should be divided into
   three fragments that will be processed separately.

   Internal re-keying is an approach assuming that a key is transformed
   during each separate message processing.  Such procedures are
   integrated into the base modes of operations, so every internal re-
   keying mechanism is defined for the particular operation mode and the
   block size of the used cipher.  Internal re-keying is recommended for
   protocols that process long messages: the size of each single message
   can be substantially increased without loss in number of messages
   that can be securely processed with a single key.

   Internal re-keying has the following advantages:

   1.  the lifetime of a key is increased by increasing the size of the
       messages processed with one key;

   2.  it has minimal impact on performance;

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

   4.  it is transparent (works like any mode of operation): 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 without a 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




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   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 if the adversary 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.

   Summing up the above-mentioned issues briefly:

   1.  If a protocol assumes processing long records (e.g., [CMS]),
       internal re-keying should be used.  If a protocol assumes
       processing a significant amount of ordered records, which can be
       considered as a single data stream (e.g., [TLS], [SSH]), internal
       re-keying may also be used.

   2.  For protocols which allow out-of-order delivery and lost records
       (e.g., [DTLS], [ESP]), external re-keying should be used.  If at
       the same time records are long enough, internal re-keying should
       be additionally used during each separate message processing.

   For external re-keying:

   1.  If it is desirable to separate transformations used for data
       processing and for key update, hash function based re-keying
       should be used.

   2.  If parallel data processing is required, then parallel external
       re-keying should be used.

   For internal re-keying:

   1.  If the property of forward and backward security is desirable for
       data processing keys and if additional key material can be easily
       obtained for the data processing stage, internal re-keying with
       master key should be used.

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 entire messages.  It provides external
   parallel and serial re-keying mechanisms (see [AbBell]).  These
   mechanisms use an initial (negotiated) key as a master key, which is



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   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 a 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 than L2 limitation (L1 < L2), the final key
   lifetime restriction is equal to the most restrictive limitation L1.
   Thus, as displayed in Figure 2, without re-keying only q1 (q1 * m <=
   L1) messages can be safely processed.


























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           <--------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'.














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                  <-------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 a 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 (or 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 4 and Figure 5) should be transformed after processing q_i



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   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 can be applied only in case when messages may not be lost or
      reordered (e.g., TLS records).

   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 records).

5.2.  Parallel Constructions

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





























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   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 the 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 the HMAC key derivation
   function HKDF-Expand, described in [RFC5869], and is used to generate
   t keys for t sections as follows:





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

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

5.3.  Serial Constructions

   The main idea behind external re-keying with a 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)),



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   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}(2
      * J - 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 operation and actually form new
   modes of operation, therefore they are called "internal re-keying"
   mechanisms in this document.

   Internal re-keying mechanisms are 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 provides almost no increase in the
   number of messages that can be processed with one key.

   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



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   limitations respectively and for some fixed amount of messages q let
   m1, m2 be the lengths of messages, 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 internal re-keying
   increases 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 internal re-keying can be
   increased up to L2'.













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          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 is
   used, more than 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 internal re-keying
   can be set to at least 10 TB (in the case when a single large message
   is processed using the key K).







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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 8 and Figure 9), 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 can be applied only in case when messages may not be lost
      or reordered (e.g., TLS records).

   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
      greater than 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 records).

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.  The section size N MUST be divisible by the block
   size n.

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



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   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}:










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   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 the c-th bit of D_t is equal to
   1 for any allowed n, k, c and t in {1, ... , J}.  This condition is
   important, as in conjunction with message length limitation it allows
   to prevent collisions of block cipher permutation inputs in case of
   key transformation and message processing.

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 basic encryption mode CTR
   (see [MODES]) extended by the ACPKM re-keying mechanism.

   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 a multiple of 8.

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





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   +----------------------------------------------------------------+
   |  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.








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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 a 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       |



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   |                          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:                                                           |



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   |  - 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 basic authenticated
   encryption mode CCM (see [RFC3610]) extended by the ACPKM re-keying
   mechanism.



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   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),
           ...




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6.3.  Constructions that Require Master Key

   This section describes the block cipher modes that use 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 that uses periodical
   key transformation with master key.  This extension can be considered
   as a new mode of operation.

   Additional parameters that define the functioning of basic modes of
   operation with the ACPKM-Master re-keying mechanism are the section
   size N and the 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 also 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:
























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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 is 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.





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

   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 a 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:
































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   +----------------------------------------------------------------+
   |  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.




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

   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 a 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)                                           |
   |-------------------------------------------------------------------|



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   |  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)                               |



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   |  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.







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

   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 out of 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:








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   +----------------------------------------------------------------+
   |  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 does not need to be secret, but must be unpredictable.



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

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

   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:



























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   +-------------------------------------------------------------+
   |  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.



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

   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:





























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   +----------------------------------------------------------------+
   |  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.








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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.

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

   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;




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

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


+----------------------------------------------------------------------+
| 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 the security of re-keying mechanisms is based on the security
   of a block cipher as a pseudorandom function.




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   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.

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

9.  References

9.1.  Normative References

   [CMS]      Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
              RFC 5652, DOI 10.17487/RFC5652, September 2009,
              <http://www.rfc-editor.org/info/rfc5652>.

   [DTLS]     Rescorla, E. and N. Modadugu, "Datagram Transport Layer
              Security Version 1.2", RFC 6347, DOI 10.17487/RFC6347,
              January 2012, <http://www.rfc-editor.org/info/rfc6347>.

   [ESP]      Kent, S., "IP Encapsulating Security Payload (ESP)",
              RFC 4303, DOI 10.17487/RFC4303, December 2005,
              <http://www.rfc-editor.org/info/rfc4303>.

   [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>.




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   [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>.

   [SSH]      Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Transport Layer Protocol", RFC 4253, DOI 10.17487/RFC4253,
              January 2006, <http://www.rfc-editor.org/info/rfc4253>.

   [TLS]      Dierks, T. and E. Rescorla, "The Transport Layer Security
              (TLS) Protocol Version 1.2", RFC 5246,
              DOI 10.17487/RFC5246, August 2008,
              <http://www.rfc-editor.org/info/rfc5246>.

   [TLSDraft]
              Rescorla, E., "The Transport Layer Security (TLS) Protocol
              Version 1.3", 2017, <https://tools.ietf.org/html/draft-
              ietf-tls-tls13-20>.

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.

   [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", Cryptology ePrint
              Archive Report 2016/798, 2016, <https://sweet32.info/
              SWEET32_CCS16.pdf>.

   [TEMPEST]  By Craig Ramsay, Jasper Lohuis, "TEMPEST attacks against
              AES. Covertly stealing keys for 200 euro", 2017,
              <https://www.fox-it.com/en/wp-content/uploads/sites/11/
              Tempest_attacks_against_AES.pdf>.

Appendix A.  Test examples


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



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   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

   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



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   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

   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



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   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)
   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



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   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)
   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






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Appendix B.  Contributors

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

   o  Evgeny Alekseev
      CryptoPro
      alekseev@cryptopro.ru

   o  Ekaterina Smyshlyaeva
      CryptoPro
      ess@cryptopro.ru

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

   o  Daniel Fox Franke
      Akamai Technologies
      dfoxfranke@gmail.com

   o  Lilia Ahmetzyanova
      CryptoPro
      lah@cryptopro.ru

Appendix C.  Acknowledgments

   We thank Mihir Bellare, Scott Fluhrer, Dorothy Cooley, Yoav Nir, Jim
   Schaad, Paul Hoffman and Dmitry Belyavsky 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









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