Network Working Group S. Smyshlyaev, Ed. Internet-Draft CryptoPro Intended status: Informational V. Nozdrunov Expires: September 2, 2018 V. Shishkin TK26 March 1, 2018 Re-keying Mechanisms for Symmetric Keys draft-smyshlyaev-mgm-00 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 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 https://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 2, 2018. Copyright Notice Copyright (c) 2018 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 (https://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must 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. Smyshlyaev, et al. Expires September 2, 2018 [Page 1]

Internet-Draft Re-keying Mechanisms for Symmetric Keys March 2018 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. Security Considerations . . . . . . . . . . . . . . . . . . . 8 7. Normative References . . . . . . . . . . . . . . . . . . . . 8 Appendix A. Contributors . . . . . . . . . . . . . . . . . . . . 8 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 9 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; Smyshlyaev, et al. Expires September 2, 2018 [Page 2]

Internet-Draft Re-keying Mechanisms for Symmetric Keys March 2018 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); Smyshlyaev, et al. Expires September 2, 2018 [Page 3]

Internet-Draft Re-keying Mechanisms for Symmetric Keys March 2018 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: Smyshlyaev, et al. Expires September 2, 2018 [Page 4]

Internet-Draft Re-keying Mechanisms for Symmetric Keys March 2018 +----------------------------------------------------------------+ | 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}. Smyshlyaev, et al. Expires September 2, 2018 [Page 5]

Internet-Draft Re-keying Mechanisms for Symmetric Keys March 2018 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: Smyshlyaev, et al. Expires September 2, 2018 [Page 6]

Internet-Draft Re-keying Mechanisms for Symmetric Keys March 2018 +----------------------------------------------------------------+ | 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 | | else | | | | 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. Smyshlyaev, et al. Expires September 2, 2018 [Page 7]

Internet-Draft Re-keying Mechanisms for Symmetric Keys March 2018 For providing parallelize authentication we use multilinear function. By encrypting second counter we produce elements H_i with the 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. Security Considerations TODO: 7. 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 Smyshlyaev, et al. Expires September 2, 2018 [Page 8]

Internet-Draft Re-keying Mechanisms for Symmetric Keys March 2018 Authors' Addresses Stanislav Smyshlyaev (editor) CryptoPro Phone: +7 (495) 995-48-20 Email: svs@cryptopro.ru Vladislav Nozdrunov TK26 Email: nozdrunov_vi@tc26.ru Vasily Shishkin TK26 Email: shishkin_va@tc26.ru Smyshlyaev, et al. Expires September 2, 2018 [Page 9]