Internet Engineering Task Force V. Dolmatov, Ed. Internet-Draft JSC "NPK Kryptonite" Updates: 5830 (if approved) D. Baryshkov Intended status: Informational Auriga, Inc Expires: September 23, 2020 March 22, 2020 GOST R 34.12-2015: Block Cipher "Magma" draft-dolmatov-magma-06 Abstract In addition to a new cipher with block length of n=128 bits (referred to as "Kyznyechik" and described in RFC 7801) Russian Federal standard GOST R 34.12-2015 includes an updated version of the block cipher with block length of n=64 bits and key length k=256 bits, which is also referred to as "Magma". The algorithm is an updated version of an older block cipher with block length of n=64 bits described in GOST 28147-89 (RFC 5830). This document is intended to be a source of information about the updated version of the 64-bit cipher. It may facilitate the use of the block cipher in Internet applications by providing information for developers and users of GOST 64-bit cipher with the revised version of the cipher for encryption and decryption. 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 23, 2020. Copyright Notice Copyright (c) 2020 IETF Trust and the persons identified as the document authors. All rights reserved. Dolmatov & Baryshkov Expires September 23, 2020 [Page 1]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 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. Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 2. General Information . . . . . . . . . . . . . . . . . . . . . 3 3. Definitions and Notations . . . . . . . . . . . . . . . . . . 3 3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 3 3.2. Notations . . . . . . . . . . . . . . . . . . . . . . . . 4 4. Parameter Values . . . . . . . . . . . . . . . . . . . . . . 5 4.1. Nonlinear Bijection . . . . . . . . . . . . . . . . . . . 5 4.2. Transformations . . . . . . . . . . . . . . . . . . . . . 6 4.3. Key Schedule . . . . . . . . . . . . . . . . . . . . . . 6 5. Basic Encryption Algorithm . . . . . . . . . . . . . . . . . 7 5.1. Encryption . . . . . . . . . . . . . . . . . . . . . . . 7 5.2. Decryption . . . . . . . . . . . . . . . . . . . . . . . 7 6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 7 7. Security Considerations . . . . . . . . . . . . . . . . . . . 7 8. References . . . . . . . . . . . . . . . . . . . . . . . . . 8 8.1. Normative References . . . . . . . . . . . . . . . . . . 8 8.2. Informative References . . . . . . . . . . . . . . . . . 8 Appendix A. Test Examples . . . . . . . . . . . . . . . . . . . 9 A.1. Transformation t . . . . . . . . . . . . . . . . . . . . 9 A.2. Transformation g . . . . . . . . . . . . . . . . . . . . 9 A.3. Key schedule . . . . . . . . . . . . . . . . . . . . . . 9 A.4. Test Encryption . . . . . . . . . . . . . . . . . . . . . 10 A.5. Test Decryption . . . . . . . . . . . . . . . . . . . . . 11 Appendix B. Background . . . . . . . . . . . . . . . . . . . . . 12 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 13 1. Introduction The Russian Federal standard [GOSTR3412-2015] specifies basic block ciphers used as cryptographic techniques for information processing and information protection including the provision of confidentiality, authenticity, and integrity of information during information transmission, processing and storage in computer-aided systems. Dolmatov & Baryshkov Expires September 23, 2020 [Page 2]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 The cryptographic algorithms defined in this specification are designed both for hardware and software implementation. They comply with modern cryptographic requirements, and put no restrictions on the confidentiality level of the protected information. This document is intended to be a source of information about the updated version of 64-bit cipher. It may facilitate the use of the block cipher in Internet applications by providing information for developers and users of GOST 64-bit cipher with the revised version of the cipher for encryption and decryption. 2. General Information The Russian Federal standard [GOSTR3412-2015] was developed by the Center for Information Protection and Special Communications of the Federal Security Service of the Russian Federation with participation of the Open Joint-Stock company "Information Technologies and Communication Systems" (InfoTeCS JSC). GOST R 34.12-2015 was approved and introduced by Decree #749 of the Federal Agency on Technical Regulating and Metrology on 19.06.2015. Terms and concepts in the specification comply with the following international standards: o ISO/IEC 10116 [ISO-IEC10116], o series of standards ISO/IEC 18033 [ISO-IEC18033-1], [ISO-IEC18033-3]. 3. Definitions and Notations The following terms and their corresponding definitions are used in the specification. 3.1. Definitions Definitions encryption algorithm: process which transforms plaintext into ciphertext (Clause 2.19 of [ISO-IEC18033-1]), decryption algorithm: process which transforms ciphertext into plaintext (Clause 2.14 of [ISO-IEC18033-1]), basic block cipher: block cipher which for a given key provides a single invertible mapping of the set of fixed-length plaintext blocks into ciphertext blocks of the same length, Dolmatov & Baryshkov Expires September 23, 2020 [Page 3]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 block: string of bits of a defined length (Clause 2.6 of [ISO-IEC18033-1]), block cipher: symmetric encipherment system with the property that the encryption algorithm operates on a block of plaintext, i.e. a string of bits of a defined length, to yield a block of ciphertext (Clause 2.7 of [ISO-IEC18033-1]), Note: In GOST R 34.12-2015, it is established that the terms "block cipher" and "block encryption algorithm" are synonyms. encryption: reversible transformation of data by a cryptographic algorithm to produce ciphertext, i.e., to hide the information content of the data (Clause 2.18 of [ISO-IEC18033-1]), round key: sequence of symbols which is calculated from the key and controls a transformation for one round of a block cipher, key: sequence of symbols that controls the operation of a cryptographic transformation (e.g., encipherment, decipherment) (Clause 2.21 of [ISO-IEC18033-1]), Note: In GOST R 34.12-2015, the key must be a binary sequence. plaintext: unencrypted information (Clause 3.11 of [ISO-IEC10116]), key schedule: calculation of round keys from the key, decryption: reversal of a corresponding encipherment (Clause 2.13 of [ISO-IEC18033-1]), symmetric cryptographic technique: cryptographic technique that uses the same secret key for both the originator's and the recipient's transformation (Clause 2.32 of [ISO-IEC18033-1]), cipher: alternative term for encipherment system (Clause 2.20 of [ISO-IEC18033-1]), ciphertext: data which has been transformed to hide its information content (Clause 3.3 of [ISO-IEC10116]). 3.2. Notations The following notations are used in the specification: Dolmatov & Baryshkov Expires September 23, 2020 [Page 4]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 V* the set of all binary vector-strings of a finite length (hereinafter referred to as the 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 zero, U[*]W direct (Cartesian) product of two sets U and W, |A| the number of components (the length) of a string A belonging to V* (if A is an empty string, then |A| = 0), A||B concatenation of strings A and B both belonging to V*, i.e., a string from V_(|A|+|B|), where the left substring from V_|A| is equal to A and the right substring from V_|B| is equal to B, A<<<_11 cyclic rotation of string A belonging to V_32 by 11 components in the direction of components having greater indices, Z_(2^n) ring of residues modulo 2^n, (xor) exclusive-or of the two binary strings of the same length, [+] addition in the ring Z_(2^32) Vec_s: Z_(2^s) -> V_s bijective mapping which maps an element from ring Z_(2^s) into its binary representation, i.e., for an element z of the ring Z_(2^s), represented by the residue z_0 + (2*z_1) + ... + (2^(s-1)*z_(s-1)), where z_i in {0, 1}, i = 0, ..., n-1, the equality Vec_s(z) = z_(s-1)||...||z_1||z_0 holds, Int_s: V_s -> Z_(2^s) the mapping inverse to the mapping Vec_s, i.e., Int_s = Vec_s^(-1), PS composition of mappings, where the mapping S applies first, P^s composition of mappings P^(s-1) and P, where P^1=P, 4. Parameter Values 4.1. Nonlinear Bijection The bijective nonlinear mapping is a set of substitutions: Pi_i = Vec_4 Pi'_i Int_4: V_4 -> V_4, Dolmatov & Baryshkov Expires September 23, 2020 [Page 5]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 where Pi'_i: Z_(2^4) -> Z_(2^4), i = 0, 1, ..., 7. The values of the substitution Pi' are specified below as arrays Pi'_i = (Pi'_i(0), Pi'_i(1), ... , Pi'_i(15)), i = 0, 1, ..., 7: Pi'_0 = (12, 4, 6, 2, 10, 5, 11, 9, 14, 8, 13, 7, 0, 3, 15, 1); Pi'_1 = (6, 8, 2, 3, 9, 10, 5, 12, 1, 14, 4, 7, 11, 13, 0, 15); Pi'_2 = (11, 3, 5, 8, 2, 15, 10, 13, 14, 1, 7, 4, 12, 9, 6, 0); Pi'_3 = (12, 8, 2, 1, 13, 4, 15, 6, 7, 0, 10, 5, 3, 14, 9, 11); Pi'_4 = (7, 15, 5, 10, 8, 1, 6, 13, 0, 9, 3, 14, 11, 4, 2, 12); Pi'_5 = (5, 13, 15, 6, 9, 2, 12, 10, 11, 7, 8, 1, 4, 3, 14, 0); Pi'_6 = (8, 14, 2, 5, 6, 9, 1, 12, 15, 4, 11, 0, 13, 10, 3, 7); Pi'_7 = (1, 7, 14, 13, 0, 5, 8, 3, 4, 15, 10, 6, 9, 12, 11, 2); 4.2. Transformations The following transformations are applicable for encryption and decryption algorithms: t: V_32 -> V_32 t(a) = t(a_7||...||a_0) = Pi_7(a_7)||...||Pi_0(a_0), where a=a_7||...||a_0 belongs to V_32, a_i belongs to V_4, i=0, 1, ..., 7; g[k]: V_32 -> V_32 g[k](a) = (t(Vec_32(Int_32(a) [+] Int_32(k)))) <<<_11, where k, a belong to V_32; G[k]: V_32[*]V_32 -> V_32[*]V_32 G[k](a_1, a_0) = (a_0, g[k](a_0) (xor) a_1), where k, a_0, a_1 belong to V_32; G^*[k]: V_32[*]V_32 -> V_64 G^*[k](a_1, a_0) = (g[k](a_0) (xor) a_1) || a_0, where k, a_0, a_1 belong to V_32. 4.3. Key Schedule Round keys K_i belonging to V_32, i=1, 2, ..., 32 are derived from key K=k_255||...||k_0 belonging to V_256, k_i belongs to V_1, i=0, 1, ..., 255, as follows: Dolmatov & Baryshkov Expires September 23, 2020 [Page 6]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 K_1=k_255||...||k_224; K_2=k_223||...||k_192; K_3=k_191||...||k_160; K_4=k_159||...||k_128; K_5=k_127||...||k_96; K_6=k_95||...||k_64; K_7=k_63||...||k_32; K_8=k_31||...||k_0; K_(i+8)=K_i, i = 1, 2, ..., 8; K_(i+16)=K_i, i = 1, 2, ..., 8; K_(i+24)=K_(9-i), i = 1, 2, ..., 8. 5. Basic Encryption Algorithm 5.1. Encryption Depending on the values of round keys K_1,...,K_32, the encryption algorithm is a substitution E_(K_1,...,K_32) defined as follows: E_(K_1,...,K_32)(a)=G^*[K_32]G[K_31]...G[K_2]G[K_1](a_1, a_0), where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32. 5.2. Decryption Depending on the values of round keys K_1,...,K_32, the decryption algorithm is a substitution D_(K_1,...,K_32) defined as follows: D_(K_1,...,K_32)(a)=G^*[K_1]G[K_2]...G[K_31]G[K_32](a_1, a_0), where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32. 6. IANA Considerations This memo includes no request to IANA. 7. Security Considerations This entire document is about security considerations. Unlike [RFC5830] (GOST 28147-89), but like [RFC7801] this specification does not define exact block modes which should be used together with updated Magma cipher. One is free to select block modes depending on the protocol and necessity. Dolmatov & Baryshkov Expires September 23, 2020 [Page 7]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 8. References 8.1. Normative References [GOSTR3412-2015] Federal Agency on Technical Regulating and Metrology, "Information technology. Cryptographic data security. Block ciphers. GOST R 34.12-2015", 2015. [RFC5830] Dolmatov, V., Ed., "GOST 28147-89: Encryption, Decryption, and Message Authentication Code (MAC) Algorithms", RFC 5830, DOI 10.17487/RFC5830, March 2010, <https://www.rfc-editor.org/info/rfc5830>. [RFC7801] Dolmatov, V., Ed., "GOST R 34.12-2015: Block Cipher "Kuznyechik"", RFC 7801, DOI 10.17487/RFC7801, March 2016, <https://www.rfc-editor.org/info/rfc7801>. 8.2. Informative References [GOST28147-89] Government Committee of the USSR for Standards, ""Cryptographic Protection for Data Processing System", GOST 28147-89, Gosudarstvennyi Standard of USSR", 1989. [ISO-IEC10116] ISO-IEC, "Information technology - Security techniques - Modes of operation for an n-bit block cipher, ISO-IEC 10116", 2006. [ISO-IEC18033-1] ISO-IEC, "Information technology - Security techniques - Encryption algorithms - Part 1: General, ISO-IEC 18033-1", 2013. [ISO-IEC18033-3] ISO-IEC, "Information technology - Security techniques - Encryption algorithms - Part 3: Block ciphers, ISO-IEC 18033-3", 2010. [RFC7836] Smyshlyaev, S., Ed., Alekseev, E., Oshkin, I., Popov, V., Leontiev, S., Podobaev, V., and D. Belyavsky, "Guidelines on the Cryptographic Algorithms to Accompany the Usage of Standards GOST R 34.10-2012 and GOST R 34.11-2012", RFC 7836, DOI 10.17487/RFC7836, March 2016, <https://www.rfc-editor.org/info/rfc7836>. Dolmatov & Baryshkov Expires September 23, 2020 [Page 8]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 Appendix A. Test Examples This section is for information only and is not a normative part of the specification. A.1. Transformation t t(fdb97531) = 2a196f34, t(2a196f34) = ebd9f03a, t(ebd9f03a) = b039bb3d, t(b039bb3d) = 68695433. A.2. Transformation g g[87654321](fedcba98) = fdcbc20c, g[fdcbc20c](87654321) = 7e791a4b, g[7e791a4b](fdcbc20c) = c76549ec, g[c76549ec](7e791a4b) = 9791c849. A.3. Key schedule With key set to K = ffeeddccbbaa99887766554433221100f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff, following round keys are generated: Dolmatov & Baryshkov Expires September 23, 2020 [Page 9]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 K_1 = ffeeddcc, K_2 = bbaa9988, K_3 = 77665544, K_4 = 33221100, K_5 = f0f1f2f3, K_6 = f4f5f6f7, K_7 = f8f9fafb, K_8 = fcfdfeff, K_9 = ffeeddcc, K_10 = bbaa9988, K_11 = 77665544, K_12 = 33221100, K_13 = f0f1f2f3, K_14 = f4f5f6f7, K_15 = f8f9fafb, K_16 = fcfdfeff, K_17 = ffeeddcc, K_18 = bbaa9988, K_19 = 77665544, K_20 = 33221100, K_21 = f0f1f2f3, K_22 = f4f5f6f7, K_23 = f8f9fafb, K_24 = fcfdfeff, K_25 = fcfdfeff, K_26 = f8f9fafb, K_27 = f4f5f6f7, K_28 = f0f1f2f3, K_29 = 33221100, K_30 = 77665544, K_31 = bbaa9988, K_32 = ffeeddcc. A.4. Test Encryption In this test example, encryption is performed on the round keys specified in clause A.3. Let the plaintext be a = fedcba9876543210, then Dolmatov & Baryshkov Expires September 23, 2020 [Page 10]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 (a_1, a_0) = (fedcba98, 76543210), G[K_1](a_1, a_0) = (76543210, 28da3b14), G[K_2]G[K_1](a_1, a_0) = (28da3b14, b14337a5), G[K_3]...G[K_1](a_1, a_0) = (b14337a5, 633a7c68), G[K_4]...G[K_1](a_1, a_0) = (633a7c68, ea89c02c), G[K_5]...G[K_1](a_1, a_0) = (ea89c02c, 11fe726d), G[K_6]...G[K_1](a_1, a_0) = (11fe726d, ad0310a4), G[K_7]...G[K_1](a_1, a_0) = (ad0310a4, 37d97f25), G[K_8]...G[K_1](a_1, a_0) = (37d97f25, 46324615), G[K_9]...G[K_1](a_1, a_0) = (46324615, ce995f2a), G[K_10]...G[K_1](a_1, a_0) = (ce995f2a, 93c1f449), G[K_11]...G[K_1](a_1, a_0) = (93c1f449, 4811c7ad), G[K_12]...G[K_1](a_1, a_0) = (4811c7ad, c4b3edca), G[K_13]...G[K_1](a_1, a_0) = (c4b3edca, 44ca5ce1), G[K_14]...G[K_1](a_1, a_0) = (44ca5ce1, fef51b68), G[K_15]...G[K_1](a_1, a_0) = (fef51b68, 2098cd86) G[K_16]...G[K_1](a_1, a_0) = (2098cd86, 4f15b0bb), G[K_17]...G[K_1](a_1, a_0) = (4f15b0bb, e32805bc), G[K_18]...G[K_1](a_1, a_0) = (e32805bc, e7116722), G[K_19]...G[K_1](a_1, a_0) = (e7116722, 89cadf21), G[K_20]...G[K_1](a_1, a_0) = (89cadf21, bac8444d), G[K_21]...G[K_1](a_1, a_0) = (bac8444d, 11263a21), G[K_22]...G[K_1](a_1, a_0) = (11263a21, 625434c3), G[K_23]...G[K_1](a_1, a_0) = (625434c3, 8025c0a5), G[K_24]...G[K_1](a_1, a_0) = (8025c0a5, b0d66514), G[K_25]...G[K_1](a_1, a_0) = (b0d66514, 47b1d5f4), G[K_26]...G[K_1](a_1, a_0) = (47b1d5f4, c78e6d50), G[K_27]...G[K_1](a_1, a_0) = (c78e6d50, 80251e99), G[K_28]...G[K_1](a_1, a_0) = (80251e99, 2b96eca6), G[K_29]...G[K_1](a_1, a_0) = (2b96eca6, 05ef4401), G[K_30]...G[K_1](a_1, a_0) = (05ef4401, 239a4577), G[K_31]...G[K_1](a_1, a_0) = (239a4577, c2d8ca3d). Then the ciphertext is b = G^*[K_32]G[K_31]...G[K_1](a_1, a_0) = 4ee901e5c2d8ca3d. A.5. Test Decryption In this test example, decryption is performed on the round keys specified in clause A.3. Let the ciphertext be b = 4ee901e5c2d8ca3d, then Dolmatov & Baryshkov Expires September 23, 2020 [Page 11]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 (b_1, b_0) = (4ee901e5, c2d8ca3d), G[K_32](b_1, b_0) = (c2d8ca3d, 239a4577), G[K_31]G[K_32](b_1, b_0) = (239a4577, 05ef4401), G[K_30]...G[K_32](b_1, b_0) = (05ef4401, 2b96eca6), G[K_29]...G[K_32](b_1, b_0) = (2b96eca6, 80251e99), G[K_28]...G[K_32](b_1, b_0) = (80251e99, c78e6d50), G[K_27]...G[K_32](b_1, b_0) = (c78e6d50, 47b1d5f4), G[K_26]...G[K_32](b_1, b_0) = (47b1d5f4, b0d66514), G[K_25]...G[K_32](b_1, b_0) = (b0d66514, 8025c0a5), G[K_24]...G[K_32](b_1, b_0) = (8025c0a5, 625434c3), G[K_23]...G[K_32](b_1, b_0) = (625434c3, 11263a21), G[K_22]...G[K_32](b_1, b_0) = (11263a21, bac8444d), G[K_21]...G[K_32](b_1, b_0) = (bac8444d, 89cadf21), G[K_20]...G[K_32](b_1, b_0) = (89cadf21, e7116722), G[K_19]...G[K_32](b_1, b_0) = (e7116722, e32805bc), G[K_18]...G[K_32](b_1, b_0) = (e32805bc, 4f15b0bb), G[K_17]...G[K_32](b_1, b_0) = (4f15b0bb, 2098cd86), G[K_16]...G[K_32](b_1, b_0) = (2098cd86, fef51b68), G[K_15]...G[K_32](b_1, b_0) = (fef51b68, 44ca5ce1), G[K_14]...G[K_32](b_1, b_0) = (44ca5ce1, c4b3edca), G[K_13]...G[K_32](b_1, b_0) = (c4b3edca, 4811c7ad), G[K_12]...G[K_32](b_1, b_0) = (4811c7ad, 93c1f449), G[K_11]...G[K_32](b_1, b_0) = (93c1f449, ce995f2a), G[K_10]...G[K_32](b_1, b_0) = (ce995f2a, 46324615), G[K_9]...G[K_32](b_1, b_0) = (46324615, 37d97f25), G[K_8]...G[K_32](b_1, b_0) = (37d97f25, ad0310a4), G[K_7]...G[K_32](b_1, b_0) = (ad0310a4, 11fe726d), G[K_6]...G[K_32](b_1, b_0) = (11fe726d, ea89c02c), G[K_5]...G[K_32](b_1, b_0) = (ea89c02c, 633a7c68), G[K_4]...G[K_32](b_1, b_0) = (633a7c68, b14337a5), G[K_3]...G[K_32](b_1, b_0) = (b14337a5, 28da3b14), G[K_2]...G[K_32](b_1, b_0) = (28da3b14, 76543210). Then the plaintext is a = G^*[K_1]G[K_2]...G[K_32](b_1, b_0) = fedcba9876543210. Appendix B. Background This specification is a translation of relevant parts of [GOSTR3412-2015] standard. The order of terms in both parts of Section 3 comes from original text. If one combines [RFC7801] with this document, he will have complete translation of [GOSTR3412-2015] into English. Algoritmically Magma is a variation of block cipher defined in [RFC5830] ([GOST28147-89]) with the following clarifications and minor modifications: Dolmatov & Baryshkov Expires September 23, 2020 [Page 12]

Internet-Draft GOST R 34.12-2015: Block Cipher "Magma" March 2020 1. S-BOX set is fixed at id-tc26-gost-28147-param-Z (See Appendix C of [RFC7836]); 2. key is parsed as a single big-endian integer (compared to little- endian approach used in [GOST28147-89]), which results in different subkey values being used; 3. data bytes are also parsed as single big-endian integer (instead of being parsed as little-endian integer). Authors' Addresses Vasily Dolmatov (editor) JSC "NPK Kryptonite" Spartakovskaya sq., 14, bld 2, JSC "NPK Kryptonite" Moscow 105082 Russian Federation Email: vdolmatov@gmail.com Dmitry Baryshkov Auriga, Inc Torfyanaya Doroga, 7F, office 1410 Saint-Petersburg 197374 Russian Federation Email: dbaryshkov@gmail.com Dolmatov & Baryshkov Expires September 23, 2020 [Page 13]