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CFRG                                                  S. Smyshlyaev, Ed.
Internet-Draft                                                 CryptoPro
Intended status: Informational                                R. Housley
Expires: September 8, 2017                           Vigil Security, LLC
                                                              M. Bellare
                                     University of California, San Diego
                                                             E. Alekseev
                                                          E. Smyshlyaeva
                                                               CryptoPro
                                                           March 7, 2017


                Re-keying Mechanisms for Symmetric Keys
                      draft-irtf-cfrg-re-keying-01

Abstract

   This specification contains a description of a variety of methods to
   increase the lifetime of symmetric keys.  It provides external and
   internal re-keying mechanisms that can be used with such modes of
   operations as CTR, GCM, CBC, CFB, OFB and OMAC.

Status of This Memo

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

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

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

   This Internet-Draft will expire on September 8, 2017.

Copyright Notice

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

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents



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   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Conventions Used in This Document . . . . . . . . . . . . . .   3
   3.  Basic Terms and Definitions . . . . . . . . . . . . . . . . .   3
   4.  External Re-keying Mechanisms . . . . . . . . . . . . . . . .   5
     4.1.  Parallel Constructions  . . . . . . . . . . . . . . . . .   5
       4.1.1.  Parallel Construction Based on a KDF on a Block
               Cipher  . . . . . . . . . . . . . . . . . . . . . . .   6
       4.1.2.  Parallel Construction Based on HKDF . . . . . . . . .   6
     4.2.  Serial Constructions  . . . . . . . . . . . . . . . . . .   7
       4.2.1.  Serial Construction Based on a KDF on a Block Cipher    7
       4.2.2.  Serial Construction Based on HKDF . . . . . . . . . .   8
   5.  Internal Re-keying Mechanisms . . . . . . . . . . . . . . . .   8
     5.1.  Constructions that Do Not Require Master Key  . . . . . .   8
       5.1.1.  ACPKM Re-keying Mechanisms  . . . . . . . . . . . . .   8
       5.1.2.  CTR-ACPKM Encryption Mode . . . . . . . . . . . . . .  10
       5.1.3.  GCM-ACPKM Encryption Mode . . . . . . . . . . . . . .  12
     5.2.  Constructions that Require Master Key . . . . . . . . . .  14
       5.2.1.  ACPKM-Master Key Generation from the Master Key . . .  15
       5.2.2.  CTR Mode Key Meshing  . . . . . . . . . . . . . . . .  16
       5.2.3.  GCM Mode Key Meshing  . . . . . . . . . . . . . . . .  19
       5.2.4.  CBC Mode Key Meshing  . . . . . . . . . . . . . . . .  22
       5.2.5.  CFB Mode Key Meshing  . . . . . . . . . . . . . . . .  24
       5.2.6.  OFB Mode Key Meshing  . . . . . . . . . . . . . . . .  26
       5.2.7.  OMAC Mode Key Meshing . . . . . . . . . . . . . . . .  27
   6.  Joint Usage of External and Internal Re-keying  . . . . . . .  29
   7.  Scope of Usage of Rekeying-Based Schemas  . . . . . . . . . .  29
     7.1.  Key Transformation Rules  . . . . . . . . . . . . . . . .  29
     7.2.  Principles of Choice of Constructions and Security
           Parameters  . . . . . . . . . . . . . . . . . . . . . . .  30
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  32
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  32
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  33
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  33
   Appendix A.  Test examples  . . . . . . . . . . . . . . . . . . .  34
   Appendix B.  Contributors . . . . . . . . . . . . . . . . . . . .  37
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  38







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1.  Introduction

   Common cryptographic attacks base their success on the ability to get
   many encryptions under a single key.  If encryption is performed
   under a single key, there is a certain maximum threshold number of
   messages that can be safely encrypted.  These restrictions can come
   either from combinatorial properties of the used cipher modes of
   operation (for example, birthday attack [BDJR]) or from particular
   cryptographic attacks on the used block cipher (for example, linear
   cryptanalysis [Matsui]).  Moreover, most strict restrictions here
   follow from the need to resist side-channel attacks.  The adversary's
   opportunity to obtain an essential amount of data processed with a
   single key leads not only to theoretic but also to practical
   vulnerabilities (see [BL]).  Therefore, when the total size of a
   plaintext processed with a single key reaches the threshold, this key
   must be replaced.

   The most simple and obvious way for overcoming the key lifetimes
   limitations is a renegotiation of a regular session key.  However,
   this reduces the total performance since it usually entails the
   frequent use of a public key cryptography.

   Another way is to use a transformation of a previously negotiated
   key.  This specification presents the description of such mechanisms
   and the description of the cases when these mechanisms should be
   applied.

2.  Conventions Used in This Document

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

3.  Basic Terms and Definitions

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

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

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

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

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



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   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*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;

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

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

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

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

   k       the key K size (in bits);

   n       the block size of the block cipher (in bits);

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

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

   l       the number of data sections in the plaintext;

   m       the message M size (in bits);

   phi_i: V_s -> V_s  the transformation that maps a string a = (a_s,
           ... , a_1) into the string phi_i(a) = a' = (a'_s, ... ,




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           a'_1), 1 <= i <= s, such that a'_i = 1 and a'_j = a_j for all
           j in {1, ... , s}\{i}.

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

4.  External Re-keying Mechanisms

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

4.1.  Parallel Constructions

   The main idea behind external re-keying with parallel construction is
   presented in Fig.1:



























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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 1: External parallel re-keying mechanisms


   The key K^i, i = 1, ... , t-1, is updated after processing a certain
   amount of data (see Section 7.1).

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

   ExtParallelC re-keying mechanism is based 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}(J-1)),

   where J = ceil(k/n).

4.1.2.  Parallel Construction Based on HKDF

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

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



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

4.2.  Serial Constructions

   The main idea behind external re-keying with serial construction is
   presented in Fig.2:


   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 2: External serial re-keying mechanisms


   The key K^i, i = 1, ... , t-1, is updated after processing a certain
   amount of data (see Section 7.1).

4.2.1.  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)),

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




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      K*_1 = K,

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

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

4.2.2.  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]).

5.  Internal Re-keying Mechanisms

   This section presents an approach to increase the lifetime of
   negotiated key by re-keying during each separate message processing.
   It provides an internal re-keying mechanisms called ACPKM and ACPKM-
   Master that do not use and use a master key respectively.  Such
   mechanisms are integrated into the base modes of operations and can
   be considered as the base mode extensions, therefore they are called
   "internal re-keying" in this document.

5.1.  Constructions that Do Not Require Master Key

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

5.1.1.  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.



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   An additional parameter that defines the functioning of basic
   encryption modes with the ACPKM re-keying mechanism is the section
   size N.  The value of N is measured in bits and is fixed within a
   specific protocol based on the requirements of the system capacity
   and key lifetime (some recommendations on choosing N will be provided
   in Section 8).  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 Fig.3:


   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 3: Key meshing 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}(W_1) | ... | E_{K^i}(W_J)),

   where J = ceil(k/n), W_t = phi_c(D_t) for any t in {1, ... ,J} and
   D_1, D_2, ... , D_J are in V_n and are calculated as follows:



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

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

   D = ( F3 | 74 | E9 | 23 | FE | AA | D6 | DD
       | 98 | B4 | B6 | 3D | 57 | 8B | 35 | AC
       | A9 | 0F | D7 | 31 | E4 | 1D | 64 | 5E
       | 40 | 8C | 87 | 87 | 28 | CC | 76 | 90
       | 37 | 76 | 49 | 9F | 7D | F3 | 3B | 06
       | 92 | 21 | 7B | 06 | 37 | BA | 9F | B4
       | F2 | 71 | 90 | 3F | 3C | F6 | FD | 1D
       | 70 | BB | BB | 88 | E7 | F4 | 1B | 76
       | 7E | 44 | F9 | 0E | 46 | 91 | 5B | 57
       | 00 | BC | 13 | 45 | BE | 0D | BD | C7
       | 61 | 38 | 19 | 3C | 41 | 30 | 86 | 82
       | 1A | A0 | 45 | 79 | 23 | 4C | 4C | F3
       | 64 | F2 | 6A | CC | EA | 48 | CB | B4
       | 0C | B9 | A9 | 28 | C3 | B9 | 65 | CD
       | 9A | CA | 60 | FB | 9C | A4 | 62 | C7
       | 22 | C0 | 6C | E2 | 4A | C7 | FB | 5B).

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

   N o t e : The constant D is such that D =
   sha512(streebog512(0^1024)) | sha512(streebog512(1^1024)), where
   sha512 is a hash function with 512-bit output corresponding to the
   algorithm SHA-512 [SHA-512], streebog512 is a hash function with
   512-bit output, corresponding to the algorithm GOST R 34.11-2012
   [GOST3411-2012], [RFC6986].

5.1.2.  CTR-ACPKM Encryption Mode

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

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

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

   o  64 <= n <= 512;

   o  128 <= k <= 512;

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



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


   +----------------------------------------------------------------+
   |  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 m MUST NOT exceed n * 2^{c-1} bits.




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5.1.3.  GCM-ACPKM Encryption Mode

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

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

   The GCM-ACPKM 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;

   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       |
   |                          X_b in V_r, where r <= n.                |
   |  Output:                                                          |



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   |  - 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:                                                           |
   |  - Section size N,                                                |
   |  - key K,                                                         |



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   |  - 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 message size m 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.

5.2.  Constructions that Require Master Key

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








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5.2.1.  ACPKM-Master Key Generation 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 encryption modes (CTR, GCM, CBC, CFB,
   OFB, OMAC encryption modes) for getting an extension of this
   encryption mode that uses periodical key transformation with master
   key.  This extension can be considered as a new encryption mode.

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

   The main idea behind internal re-keying with master key is presented
   in Fig.4:































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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 4: Key meshing with master key


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

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

5.2.2.  CTR Mode Key Meshing

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

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

   o  64 <= n <= 512;

   o  128 <= k <= 512;

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

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






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5.2.3.  GCM Mode Key Meshing

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

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

   The GCM-ACPKM-Master 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;

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







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5.2.4.  CBC Mode Key Meshing

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

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

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

   o  64 <= n <= 512;

   o  128 <= k <= 512.

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

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

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

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



















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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 need not to be secret, but must be unpredictable.

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



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5.2.5.  CFB Mode Key Meshing

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

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

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

   o  64 <= n <= 512;

   o  128 <= k <= 512.

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

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





























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





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5.2.6.  OFB Mode Key Meshing

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

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

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

   o  64 <= n <= 512;

   o  128 <= k <= 512.

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

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





























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

5.2.7.  OMAC Mode Key Meshing

   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.




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

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

   o  n in {64, 128, 256};

   o  128 <= k <= 512.

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

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


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

   Where R_n takes the following values:

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

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

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

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





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   +-------------------------------------------------------------------+
   | 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 m MUST NOT exceed 2^{n/2}*n^2*N / (k + n) bits.

6.  Joint Usage of External and Internal Re-keying

   Any mechanism described in Section 4 can be used with any mechanism
   described in Section 5.

7.  Scope of Usage of Rekeying-Based Schemas

7.1.  Key Transformation Rules

   External re-keying mechanisms increase the number of messages that
   can be processed with one negotiated key.

   The key K^i (see Figure 1 and Figure 2) can be transformed 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, i = 1, ... , t.
      This approach allows to use the key K^i in almost optimal way but
      it cannot be applied in case when messages may be lost or
      reordered (e.g.  DTLS packets).




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

   Internal re-keying mechanisms increase the length of messages that
   can be processed with one negotiated key.

   The key K (see Figure 3 and Figure 4) can be updated 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 (where M^{i}_1 is the first section of message M^{i}, i = 1, ...
      , q).
      This approach allows to use the key K^i in almost optimal way but
      it cannot be applied in case messages data may be lost or
      reordered (e.g.  DTLS packets).

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

7.2.  Principles of Choice of Constructions and Security Parameters

   External re-keying mechanism is recommended to be used in protocols
   that process pretty small messages (e.g.  TLS records are 2^14 bytes
   or less).

   Consider an example.  Let the message size in some protocol P be
   equal to 1 KB (m_max = 1 KB).  Suppose a cipher E is used for
   encrypting and L1 = 128 MB is the key lifetime limitation induced by
   side channels analysis methods.  Let the key lifetime limitation L2
   induced by the analysis of encryption mode used in this protocol be
   equal to 1 TB.  The most restrictive resulting key lifetime
   limitation is equal to 128 MB.

   Thus, if external re-keying mechanism is not used, the key K must be
   renegotiated after processing 128 MB / 1 KB = 131072 messages.




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   If an external re-keying mechanism with parameter L = 64 MB (see
   Section 7.1 ) that limits the amount of data processed with one key
   K^i is used, the key lifetime limitation L1 induced by the side
   channels analysis methods goes off.  Thus the resulting key lifetime
   limitation of the negotiated key K can be calculated on the basis of
   the used encryption mode analysis.  It is proven that the security of
   the encryption mode that uses external re-keying leads to an increase
   when compared to base encryption mode without re-keying (see
   [AbBell]).  Hence the resulting key lifetime limitation in case of
   using external re-keying is equal to 1 TB.

   Thus if an external re-keying mechanism is used, then 1 TB / 1 KB =
   2^30 messages can be processed before the key K is renegotiated,
   which is 8192 times greater than the number of messages that can be
   processed, when external re-keying mechanism is not used.

   An internal re-keying mechanism is recommended to be used in
   protocols that can process large single messages (e.g.  CMS
   messages).

   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.  Let the message size in some protocol P' is
   large/unlimited.  Suppose a cipher E is used for encrypting and L1 =
   128 MB is the most restrictive key lifetime limitation induced by the
   side channels analysis methods.

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

   If an internal re-keying mechanism with section size N = 1 MB (see
   Figure 3 and Figure 4) is used, maximum message size limit m_max can
   be increased to hundreds of terabytes and L / 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).

   For the protocols that process messages of different lengths it is
   recommended to use joint methods (see Section 6).








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8.  Security Considerations

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

   The key lifetime limitation can be subject to the following
   considerations:

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

       *  These methods do not depend on the used block cipher
          permutation E_{K}.

       *  For standard encryption modes this restriction has the order
          2^{n/2}.

   2.  Methods based on the side channels analysis.

       *  These methods do not depend on the used encryption modes.

       *  These methods are weakly dependent on the used block cipher
          features (only the way of elementary internal transformation
          that uses key material matter, in most cases this is (xor)).

       *  Restrictions resulting from these methods are usually the
          strongest ones.

   3.  Methods based on the properties of the used block cipher
       permutation E_{K} (for example, linear or differential
       cryptanalysis).

       *  In most cases these methods do not depend on the used
          encryption modes.

       *  In case of secure block ciphers restrictions resulting from
          such methods are roughly the same as the natural limitation
          2^n.

9.  References







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9.1.  Normative References

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

   [GOST3411-2012]
              Federal Agency on Technical Regulating and Metrology (In
              Russian), "Information technology. Cryptographic Data
              Security. Hashing function", GOST R 34.11-2012, 2012.

   [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>.

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

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

   [SHA-512]  National Institute of Standards and Technology., "Secure
              Hash Standard", FIPS 180-2, August, with Change Notice 1
              dated February 2004 2002.

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

9.2.  Informative References

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






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   [BDJR]     Bellare M., Desai A., Jokipii E., Rogaway P., "A concrete
              security treatment of symmetric encryption", In
              Proceedings of 38th Annual Symposium on Foundations of
              Computer Science (FOCS '97), pages 394-403. 97, 1997.

   [BL]       Bhargavan K., Leurent G., "On the Practical (In-)Security
              of 64-bit Block Ciphers: Collision Attacks on HTTP over
              TLS and OpenVPN", Cryptology ePrint Archive Report 798,
              2016.

   [Matsui]   Matsui M., "Linear Cryptanalysis Method for DES Cipher",
              Advanced in Cryptology- EUROCRYPT'93. Lect. Notes in Comp.
              Sci., Springer. V.765.P. 386-397, 1994.

   [RFC6986]  Dolmatov, V., Ed. and A. Degtyarev, "GOST R 34.11-2012:
              Hash Function", RFC 6986, DOI 10.17487/RFC6986, August
              2013, <http://www.rfc-editor.org/info/rfc6986>.

Appendix A.  Test examples


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

   W_0:
   F3 74 E9 23 FE AA D6 DD 98 B4 B6 3D 57 8B 35 AC

   W_1:
   A9 0F D7 31 E4 1D 64 5E C0 8C 87 87 28 CC 76 90

   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:



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   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

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

   Updated key
   C6 C1 AF 82 3F 52 22 F8 97 CF F1 94 5D F7 21 9E
   21 6F 29 0C EF C4 C7 E6 DC C8 B7 DD 83 E0 AE 60

   ACPKM's iteration 2

   Process block 3
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 02

   Output block (ctr)
   92 B4 85 B5 B7 AD 3C 19 7E 53 92 32 13 9C 8E 7A

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




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   Cipher text
   83 96 B6 F1 E2 CB 4B 91 E7 F9 29 FE FD 63 84 7A

   Process block 4
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 03

   Output block (ctr)
   59 3A AA 96 7C E3 58 FB 1B 7E 41 A1 77 34 B1 4A

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

   Cipher text
   7B 09 EE C3 1A 94 D0 62 B1 C5 8D 4F 88 3E B1 5B

   Updated key
   65 3E FA 18 0B 0E 68 01 6F 56 54 A5 F3 EE BC D5
   04 F1 1F E3 F1 7A 92 07 57 A8 82 BE A5 9E CA 16

   ACPKM's iteration 3
   Process block 5
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 04

   Output block (ctr)
   CE E5 51 54 12 2F 3F E7 8D 8E 86 21 C5 E5 47 12

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

   Cipher text
   FD A1 04 32 65 A7 A6 4D 36 42 68 DE CF E5 56 30

   Process block 6
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 05

   Output block (ctr)
   DE D6 8F 03 FA C5 C5 B6 16 11 A3 78 2C 0D C1 EB

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

   Cipher text
   9A 83 E9 74 72 5C 6F 0D DA FF 5C 72 2C 1C E3 D8

   Updated key



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   C0 D5 50 26 4F DA CE 59 EF 80 9A 50 24 72 06 7D
   29 83 74 25 78 C9 60 4F E3 B8 88 4F F8 F5 E2 BD

   ACPKM's iteration 4
   Process block 7
   Input block (ctr)
   12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 06

   Output block (ctr)
   D9 23 A6 CD 8A 00 A1 55 90 09 EC 87 40 B9 D6 AB

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

   Cipher text
   8C 45 D1 45 13 AA 1A 99 7E F6 E6 87 51 9B E5 EF

   Updated key
   6A A0 92 07 73 31 63 50 46 FA 48 1C 9C 98 7B 6B
   FC 99 48 DC BC AE AB C2 6D 46 E9 DD 43 F6 CA 56

   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
   83 96 B6 F1 E2 CB 4B 91 E7 F9 29 FE FD 63 84 7A
   7B 09 EE C3 1A 94 D0 62 B1 C5 8D 4F 88 3E B1 5B
   FD A1 04 32 65 A7 A6 4D 36 42 68 DE CF E5 56 30
   9A 83 E9 74 72 5C 6F 0D DA FF 5C 72 2C 1C E3 D8
   8C 45 D1 45 13 AA 1A 99 7E F6 E6 87 51 9B E5 EF



Appendix B.  Contributors

   o  Daniel Fox Franke
      Akamai Technologies
      dfoxfranke@gmail.com

   o  Lilia Ahmetzyanova
      CryptoPro
      lah@cryptopro.ru

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

   o  Shay Gueron
      University of Haifa, Israel



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      Intel Corporation, Israel Development Center, Israel
      shay.gueron@gmail.com

Authors' Addresses

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

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


   Russ Housley
   Vigil Security, LLC
   918 Spring Knoll Drive
   Herndon  VA 20170
   USA

   Email: housley@vigilsec.com


   Mihir Bellare
   University of California, San Diego
   9500 Gilman Drive
   La Jolla  California 92093-0404
   USA

   Phone: (858) 534-4544
   Email: mihir@eng.ucsd.edu


   Evgeny Alekseev
   CryptoPro
   18, Suschevsky val
   Moscow  127018
   Russian Federation

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









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   Ekaterina Smyshlyaeva
   CryptoPro
   18, Suschevsky val
   Moscow  127018
   Russian Federation

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











































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