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Network Working Group                                 S. Smyshlyaev, Ed.
Internet-Draft                                                 CryptoPro
Intended status: Informational                              V. Nozdrunov
Expires: September 2, 2018                                   V. Shishkin
                                                                    TC26
                                                           March 1, 2018


               Multiline Galois Mode (MGM) Specification
                        draft-smyshlyaev-mgm-01

Abstract

   Multiline Galois Mode (MGM) is an authenticated encryption with
   associated data block cipher mode based on EtM principle.  MGM is
   defined for use with 64-bit and 128-bit block ciphers.

Status of This Memo

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   This Internet-Draft will expire on September 2, 2018.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Conventions Used in This Document . . . . . . . . . . . . . .   2
   3.  Basic Terms and Definitions . . . . . . . . . . . . . . . . .   2
   4.  Specification . . . . . . . . . . . . . . . . . . . . . . . .   4
     4.1.  MGM Encryption and Authentication Procedure . . . . . . .   4
     4.2.  MGM Decryption and Authentication Check Procedure . . . .   6
   5.  Rationale . . . . . . . . . . . . . . . . . . . . . . . . . .   7
   6.  Normative References  . . . . . . . . . . . . . . . . . . . .   8
   Appendix A.  Contributors . . . . . . . . . . . . . . . . . . . .   8
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .   8

1.  Introduction

   Multiline Galois Mode (MGM) is an authenticated encryption with
   associated data block cipher mode based on EtM principle.  MGM is
   defined for use with 64-bit and 128-bit block.  The MGM design
   principles can easily be applied to other block sizes and other block
   cipher.

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:

   V*      the set of all bit strings of a finite length (hereinafter
           referred to as strings), including the empty string;
           substrings and string components are enumerated from right to
           left starting from zero;

   V_s     the set of all bit strings of length s, where s is a non-
           negative integer;

   |X|     the bit length of the bit string X (if X is an empty string,
           then |X| = 0);

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




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   a^s     the string in V_s that consists of s 'a' bits: a^s = (a, a,
           ... , a), 'a' in V_1;

   (xor)   exclusive-or of the two bit strings of the same length,

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

   MSB_i: V_s -> V_i   the transformation that maps the string X =
           (x_{s-1}, ... , x_0) in V_s into the string MSB_i(X) =
           (x_{s-1}, ... , x_{s-i}) in V_i, i <= s, (most significant
           bits);

   Int_s: V_s -> Z_{2^s}    the transformation that maps a string X =
           (x_{s-1}, ... , x_0) in V_s into the integer Int_s(X) =
           2^{s-1} * x_{s-1} + ... + 2 * x_1 + x_0 (the interpretation
           of the bit string as an integer);

   Vec_s: Z_{2^s} -> V_s  the transformation inverse to the mapping
           Int_s (the interpretation of an integer as a bit string);

   E_K: V_n -> V_n  the block cipher permutation under the key K in V_k;

   k       the bit length of the block cipher key;

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

   len: V_s -> V_{n/2}  the transformation that maps a string X in V_s,
           0 <= s <= 2^{n/2} - 1, into the string len(X) =
           Vec_{n/2}(|X|) in V_{n/2}, where n is the block size of the
           used block cipher;

   [+]     the addition operation in Z_{2^{n/2}}, where n is the block
           size of the used block cipher;

   (x)     multiplication in GF(2^n), where n is the block size of the
           used block cipher;

   incr_l: V_n -> V_n  the transformation that maps a string L || R,
           where L, R in V_{n/2}, into the string incr_l(L || R ) =
           Vec_{n/2}(Int_{n/2}(L) [+] 1) || R;

   incr_r: V_n -> V_n  the transformation that maps a string L || R,
           where L, R in V_{n/2}, into the string incr_r(L || R ) = L ||
           Vec_{n/2}(Int_{n/2}(R) [+] 1);







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4.  Specification

   Additional parameter that define the functioning of MGM mode is the
   the size S of the authentication field (in bits).  The value of S
   MUST be such that 32 <= S <= 128 The choice of the value S involves a
   trade-off between message expansion and the probability that an
   attacker can undetectably modify a message.

4.1.  MGM Encryption and Authentication Procedure

   The MGM encryption and authentication procedure takes as inputs the
   following parameters:

   1.  Encryption key K in V_k.

   2.  Initial counter nonce ICN in V_{n-1}.

   3.  Plaintext P, 0 <= |P| < 2^{n/2}. P = P_1 || ... || P*_q, P_i in
       V_n, i = 1, ... , q - 1, P*_q in V_u, 1 <= u <= n.

   4.  Associated authenticated data A, 0 <= |A| < 2^{n/2}. A = A_1 ||
       ... || A*_h, A_j in V_n, j = 1, ... , h - 1, A*_h in V_t, 1 <= t
       <= n.  The associated data is authenticated but is not encrypted.

   The MGM encryption and authentication procedure outputs the following
   parameters:

   1.  Initial counter nonce ICN.

   2.  Associated authenticated data A.

   3.  Ciphertext C in V_{|P|}.

   4.  Authentication tag T in V_S.

   The MGM encryption and authentication procedure consists of the
   following steps:














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   +----------------------------------------------------------------+
   |  MGM-Encrypt(K, ICN, P, A)                                     |
   |----------------------------------------------------------------|
   |  1. Encryption step:                                           |
   |      - Y_1 = E_K(0^1 || ICN),                                  |
   |      - For i = 2, 3, ... , q do                                |
   |              Y_i = incr_r(Y_{i-1}),                            |
   |      - For i = 1, 2, ... , q - 1 do                            |
   |              C_i = P_i (xor) E_K(Y_i),                         |
   |      - C*_q = P*_q (xor) MSB_u(E_K(Y_q)),                      |
   |      - C = C_1 || ... || C*_q.                                 |
   |                                                                |
   |  2. Padding step:                                              |
   |      - A_h = A*_h || 0^{n-t},                                  |
   |      - C_q = C*_q || 0^{n-u}.                                  |
   |                                                                |
   |  3. Authentication tag T generation step:                      |
   |      - Z_1 = E_K(1^1 || ICN),                                  |
   |      - sum1 = 0, sum2 = 0,                                     |
   |      - For i = 1, 2, ..., h do                                 |
   |              H_i = E_K(Z_i),                                   |
   |              sum1 = sum1 (xor) H_i (x) A_i,                    |
   |              Z_{i+1} = incr_l(Z_i),                            |
   |      - For j = 1, 2, ..., q do                                 |
   |              H_{h+j} = E_K(Z_{h+j}),                           |
   |              sum2 = sum2 (xor) H_{h+j} (x) C_j,                |
   |              Z_{h+j+1} = incr_l(Z_{h+j}),                      |
   |      - H_{h+q+1} = E_K(Z_{h+q+1}),                             |
   |      - T = MSB_S(E_K(sum1 (xor) sum2 (xor)                     |
   |                      H_{h+q+1} (x) (len(A) || len(C)))).       |
   |                                                                |
   |  4. Return (ICN, A, C, T).                                     |
   |----------------------------------------------------------------+


   The ICN value for each message that is encrypted under the given key
   K must be chosen in a unique manner.  Using the same ICN values for
   two different messages encrypted with the same key destroys the
   security properties of this mode.

   Users who do not wish to encrypt plaintext can provide a string P of
   length zero.  Users who do not wish to authenticate associated data
   can provide a string A of length zero.  The length of the associated
   data A and of the plaintext P MUST be such that 0 < |A| + |P| <
   2^{n/2}.






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4.2.  MGM Decryption and Authentication Check Procedure

   The MGM decryption and authentication procedure takes as inputs the
   following parameters:

   1.  The encryption key K in V_k.

   2.  The initial counter nonce ICN in V_{n-1}.

   3.  The associated authenticated data A, 0 <= |A| < 2^{n/2}. A =
       A_1 || ... || A*_h, A_j in V_n, j = 1, ... , h - 1, A*_h in V_t,
       1 <= t <= n.

   4.  The ciphertext C, 0 <= |C| < 2^{n/2}. C = C_1 || ... || C*_q, C_i
       in V_n, i = 1, ... , q - 1, C*_q in V_u, 1 <= u <= n.

   5.  The authenticated tag T in V_S.

   The MGM decryption and authentication procedure outputs FAIL or the
   following parameters:

   1.  Plaintext P in V_{|C|}.

   2.  Associated authenticated data A.

   The MGM decryption and authentication procedure consists of the
   following steps:
























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   +----------------------------------------------------------------+
   |  MGM-Encrypt(K, ICN, P, A)                                     |
   |----------------------------------------------------------------|
   |  1. Padding step:                                              |
   |      - A_h = A*_h || 0^{n-t},                                  |
   |      - C_q = C*_q || 0^{n-u}.                                  |
   |                                                                |
   |  2. Authentication tag T' generation step:                     |
   |      - Z_1 = E_K(1^1 || ICN),                                  |
   |      - sum1 = 0, sum2 = 0,                                     |
   |      - For i = 1, 2, ..., h do                                 |
   |              H_i = E_K(Z_i),                                   |
   |              sum1 = sum1 (xor) H_i (x) A_i,                    |
   |              Z_{i+1} = incr_l(Z_i),                            |
   |      - For j = 1,  2, ..., q do                                |
   |              H_{h+j} = E_K(Z_{h+j}),                           |
   |              sum2 = sum2 (xor) H_{h+j} (x) C_j,                |
   |              Z_{h+j+1} = incr_l(Z_{h+j}),                      |
   |      - H_{h+q+1} = E_K(Z_{h+q+1}),                             |
   |      - T' = MSB_S(E_K(sum1 (xor) sum2 (xor)                    |
   |                       H_{h+q+1} (x) (len(A) || len(C)))),      |
   |      - If T' != T then return FAIL                             |
   |             return FAIL.                                       |
   |                                                                |
   |  3. Decryption step:                                           |
   |      - Y_1 = E_K(0^1 || ICN),                                  |
   |      - For i = 2, 3, ... , q do                                |
   |              Y_i = incr_r(Y_{i-1}),                            |
   |      - For i = 1, 2, ... , q - 1 do                            |
   |              P_i = C_i (xor) E_K(Y_i),                         |
   |      - P*_q = C*_q (xor) MSB_u(E_K(Y_q)),                      |
   |      - P = P_1 || ... || P*_q.                                 |
   |                                                                |
   |  4. Return (P, A).                                             |
   |----------------------------------------------------------------+


5.  Rationale

   During the construction of MGM mode our task was to create fast,
   paralleziable, inverse free, online and secure block cipher mode.  It
   is well known that one of the fastest mode for encryption is CTR.
   That's why we developed MGM mode based on counters.  The first
   counter is used for message encryption, the second counter is used
   for authentication.

   For providing parallelize authentication we use multilinear function.
   By encrypting second counter we produce elements H_i with the



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   property that if you know any information about value H_k you can't
   obtain any information about value H_l ( l not equal k ) besides that
   H_k not equal H_l.

   By adding the length of associated data A and encrypted message C and
   encrypting authentication tag we avoid attacks based on padding and
   linear properties of multilinear function.

   Collision of "usual" counters lead to obtaining information about
   values H_i, that could be dangerous to authentication.  For
   minimizing probability of this event we change the principle of
   counters operating by functions incr_l and incr_l.  To avoid a
   theoretical ability to calculate a point of counters collision we
   encrypt the initialization value of each counter.

6.  Normative References

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

Appendix A.  Contributors

   o  Evgeny Alekseev
      CryptoPro
      alekseev@cryptopro.ru

   o  Ekaterina Smyshlyaeva
      CryptoPro
      ess@cryptopro.ru

   o  Lilia Ahmetzyanova
      CryptoPro
      lah@cryptopro.ru

   o  Grigory Marshalko
      TK26
      marshalko_gb@tc26.ru

Authors' Addresses

   Stanislav Smyshlyaev (editor)
   CryptoPro

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




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   Vladislav Nozdrunov
   TC26

   Email: nozdrunov_vi@tc26.ru


   Vasily Shishkin
   TC26

   Email: shishkin_va@tc26.ru









































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