Algebra, Codes and Cryptology: First International Conference, A2C 2019 in honor of Prof. Mamadou Sanghare, Dakar, Senegal, December 5–7, 2019, Proceedings ... Computer and Information Science Book 1133)

This book presents refereed proceedings of the First International Conference on Algebra, Codes and Cryptology, A2C 2019, held in Dakar, Senegal, in December 2019. The 14 full papers were carefully reviewed and selected from 35 submissions. The papers are organized in topical sections on non-associative and non-commutative algebra; code, cryptology and information security. Preface 6 Organization 7 Contents 11 Non-associative and Non-commutative Algebra 13 Hopficity of Modules and Rings (Survey) 14 1 Generality of Modules 15 1.1 Notations 15 1.2 Properties (C) and (D) 15 1.3 Dedekind-Finite Module B.C.S,L3 15 1.4 Endo-Regular Module H.L.P.S.Y,Le,L.R.R5 16 1.5 Morphic Modules Ca,Ca1,C.N1,C.P,H.K.K,N.S2,P.M.M 16 1.6 Modules on a Dedekind Domain 17 1.7 Abelian Groups 19 2 The Hopficity of Modules 20 2.1 Hopfian and co-Hopfian Modules 20 2.2 Generalized Hopfian Modules and Weakly-co-Hopfian Modules 23 2.3 Generalized co-Hopfian Module and Weakly-Hopfian 24 2.4 Strongly-Hopfian and Strongly-co-Hopfian Modules 25 2.5 Endo-Noetherian and Endo-Artinian Modules 27 2.6 Semi-Hopfian and Semi-co-Hopfian Modules (in the Sense of Aydogdu-Ozcan) 31 3 Commutative Case 32 3.1 Semi-Hopfian and Semi-co-Hopfian modules (in the Sense of Diviani-Azar and Mafi) 32 3.2 S.S.H and S.S.C.H Modules 32 4 Diagram 34 5 Abelian Groups 36 5.1 Hopfian and co-Hopfian Abelian Groups 36 5.2 Strongly-Hopfian or Strongly-co-Hopfian Abelian Groups 37 5.3 Endo-Artinian or Endo-Noetherian Abelian Groups 38 6 Hopficity of Rings 38 6.1 Generalities 38 6.2 Endo-Artinian or Endo-Noetherian Rings 39 6.3 Hilbert's Property 41 6.4 Hopficity and Extensions for Matrices 43 7 Extension to Banach Spaces 44 7.1 Banach Space Hopfian or co-Hopfian Ka1 44 7.2 Semi-Hopfian or Semi-co-Hopfian Banach Spaces Ka1 45 7.3 Open Questions Ka1 45 References 46 Functor (S)-1( ) and Functorial Isomorphisms 50 1 Introduction 50 2 Recalls and Preliminary Results 51 2.1 Definition 51 2.2 Definition 52 2.3 Definition 52 2.4 Proposition 52 2.5 Notation 53 2.6 Theorem 53 2.7 Proposition and Definition 53 2.8 Theorem 54 2.9 Corollary 56 3 Functorial Isomorphisms with Functors Tor, Ext and S-1( ) 56 3.1 Theorem 56 3.2 Corollary 57 3.3 Theorem 57 3.4 Corollary 57 4 Adjoint Functors with Tor, Ext and S-1( ) 58 4.1 Proposition 58 4.2 Proposition 58 4.3 Proposition 59 4.4 Theorem 59 4.5 Theorem 59 4.6 Corollary 61 References 61 On the Computation of Minimal Free Resolutions with Integer Coefficients 62 1 From Special to Weak Gröbner Bases 63 2 Syzygy Theorems 65 3 Minimal Free Resolution in Z[x1,...,xn] 70 3.1 Construction of a Free Resolution 70 4 Conclusion 75 A Appendix 75 References 82 On the Splitting Field of Some Polynomials with Class Number One 84 1 Introduction 84 2 Proof of the Main Theorem 86 2.1 Case Where n = 3 86 2.2 Case Where n = 4 88 2.3 Case Where n 5 89 2.4 Conclusions 90 References 91 Code, Cryptology and Information Security 92 Group Codes 93 1 Group Codes 94 2 Dimension of Non-abelian Group Codes 96 3 Semisimple Case 97 4 Modular Case 98 4.1 Case |F|=p=char F 99 4.2 Case |F|=p2 99 5 An Example 104 References 106 Designing a Public Key Cryptosystem Based on Quasi-cyclic Subspace Subcodes of Reed-Solomon Codes 107 1 Introduction 107 2 Background on Block Codes 108 2.1 Binary m-block Codes 108 2.2 Isometries of m-block Codes 109 2.3 Subspace Subcodes 110 2.4 Generalized Subspace Subcodes 110 3 Quasi-cyclic Codes in the Context of GSS Codes 111 3.1 Induced Quasi-cyclic GSS Codes of GRS Codes 112 3.2 Permutations Preserving the Quasi-cyclicity 113 4 PKE Based on Subspace Subcodes of QC-GRS Codes 113 4.1 Key Derivation Algorithm 114 4.2 Decoding Algorithm 115 4.3 Encryption and Decryption Algorithm 116 5 Design Rationale 116 6 Security Analysis 117 7 Instantiation 119 8 Comparison with Other Proposals 120 References 121 Quantum Resistant Public Key Encryption Scheme polarRLCE 124 1 Introduction 124 2 Preliminaries 126 2.1 Coding Theory 126 2.2 McEliece's Public-Key Cryptosystem 127 2.3 Polar Codes Construction 127 2.4 The Proposal by Hooshmand et al. HSEA14 128 3 Our Proposed Scheme of polarRLCE 128 4 Security Analysis 130 4.1 Brute Force Attack 130 4.2 Square Attack 130 4.3 Key-Recovery Attack 132 4.4 Message Decoding Attack 133 4.5 Suggested Parameters for PolarRLCE 133 5 Conclusion 135 References 135 Security Evaluation Against Side-Channel Analysis at Compilation Time 139 1 Introduction 140 2 Reminder About Automated Proof of Masking Schemes 142 2.1 Multi-variate and High-Order Side-Channel Attacks 142 2.2 Analysis of Code at Intermediate Representation 144 2.3 Probing Leakage Model 144 3 Contribution: Automated Attack Construction 144 3.1 Framework Concept 144 3.2 Framework Implementation 146 3.3 Why Check at the IR Level? 147 3.4 Application 147 3.5 Limitations 151 4 Conclusion and Perspectives 151 A Example of Input Codes For Analysis 152 A.1 Codes Which can be Analyzed in Our Framework 152 A.2 Code Which Cannot be Analyzed 155 B Multi-variate Attack at Degrees Two and Three 156 References 156 Subliminal Hash Channels 159 1 Introduction 159 2 Preliminaries 160 2.1 Diffie-Hellman Assumptions 160 2.2 Digital Signatures 161 2.3 Subliminal Channels and SETUP Attacks 162 3 Hash Channels 163 4 Stochastic Detection 165 5 Marketing Backdoors 168 5.1 Russel et al. Subversion-Free Proposal 168 5.2 Hanzlik et al. Controlled Randomness Proposal 169 5.3 Choi et al. Tamper-Evident Digital Signatures 169 5.4 Ateniese et al. and Bohli et al. Subversion-Free Proposals 170 6 Conclusions 170 A Additional Preliminaries 171 A.1 Definitions 171 A.2 Covert Channels 171 References 172 Boolean Functions for Homomorphic-Friendly Stream Ciphers 176 1 Introduction 176 2 Preliminaries 182 2.1 Boolean Functions and Cryptographic Criteria 182 3 Parameters of Direct Sums of Monomials 186 4 Parameters of Threshold, and XOR-THR Functions 188 4.1 Threshold Functions 189 4.2 Parameters of XOR-THR Functions 190 References 191 Jacobian Versus Infrastructure in Split Hyperelliptic Curves 193 1 Introduction 193 2 Hyperelliptic Curves 195 2.1 Jacobian 196 2.2 Infrastructure 197 2.3 Connection Between G and R 199 3 Explicit Formulas 201 4 Conclusion 203 A Basic Algorithms 204 B Genus 3 Explicit Formulas 205 References 212 Proposition of a Model for Securing the Neighbor Discovery Protocol (NDP) in IPv6 Environment 214 1 Introduction 214 2 Background 215 2.1 Neighbor Discovery Mechanism 215 2.2 Authentication Header (IPSec AH) 216 2.3 Cryptographic Address Generation (CGA SeND) 216 3 State of the Art 217 4 Proposed Model 218 5 CGA SEND and CGA AH Performance Analysis and Test 221 6 Conclusion 223 References 223 BI-NTRU Encryption Schemes: Two New Secure Variants of NTRU 226 1 Introduction 226 2 Preliminaries 228 2.1 Basic Definitions in Lattices 228 2.2 NTRU-Like Cryptosystems 231 3 BI-NTRU IND-CPA 232 3.1 BI-NTRU-Product 233 3.2 BI-NTRU-LPR 235 4 Conclusion 238 A Appendix 239 References 243 Author Index 246 Front Matter ....Pages i-xii Front Matter ....Pages 1-1 Hopficity of Modules and Rings (Survey) (L’Moufadal Ben Yakoub)....Pages 3-38 Functor \((\overline{S})^{-1}( )\) and Functorial Isomorphisms (Daouda Faye, Mohamed Ben Maaouia, Mamadou Sanghare)....Pages 39-50 On the Computation of Minimal Free Resolutions with Integer Coefficients (Soda Diop, Guy Mobouale Wamba, Andre Saint Eudes Mialebama Bouesso, Djiby Sow)....Pages 51-72 On the Splitting Field of Some Polynomials with Class Number One (Abdelmalek Azizi)....Pages 73-80 Front Matter ....Pages 81-81 Group Codes (Santos González, Victor Markov, Olga Markova, Consuelo Martínez)....Pages 83-96 Designing a Public Key Cryptosystem Based on Quasi-cyclic Subspace Subcodes of Reed-Solomon Codes (Thierry P. Berger, Cheikh Thiécoumba Gueye, Jean Belo Klamti, Olivier Ruatta)....Pages 97-113 Quantum Resistant Public Key Encryption Scheme polarRLCE (Jingang Liu, Yongge Wang, Zongxinag Yi, Dingyi Pei)....Pages 114-128 Security Evaluation Against Side-Channel Analysis at Compilation Time (Nicolas Bruneau, Charles Christen, Jean-Luc Danger, Adrien Facon, Sylvain Guilley)....Pages 129-148 Subliminal Hash Channels (George Teşeleanu)....Pages 149-165 Boolean Functions for Homomorphic-Friendly Stream Ciphers (Claude Carlet, Pierrick Méaux)....Pages 166-182 Jacobian Versus Infrastructure in Split Hyperelliptic Curves (Monireh Rezai Rad, Michael J. Jacobson Jr., Renate Scheidler)....Pages 183-203 Proposition of a Model for Securing the Neighbor Discovery Protocol (NDP) in IPv6 Environment (Bôa Djavph Yoganguina, Khadidiatou Wane ep Keîta, Idy Diop, Khaly Tall, Sidi Mouhamed Farssi)....Pages 204-215 BI-NTRU Encryption Schemes: Two New Secure Variants of NTRU (Michel Seck, Djiby Sow)....Pages 216-235 Back Matter ....Pages 237-237