Optimisation heuristics for cryptology

The aim of the research presented in this thesis is to investigate the use of various optimisation heuristics in the fields of automated cryptanalysis and automated cryptographic function generation. These techniques were found to provide a successful method of automated cryptanalysis of a variety of the classical ciphers. Also, they were found to enhance existing fast correlation attacks on certain stream ciphers. A previously proposed attack of the knapsack cipher is shown to be flawed due to the absence of a suitable solution evaluation mechanism. Finally, a new approach for finding highly nonlinear Boolean functions is introduced.

[1]  J. D. Golic.  Computation of low-weight parity-check polynomials , 1996 .

[2]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[3]  Nicholas J. Patterson,et al.  The covering radius of the (215, 16) Reed-Muller code is at least 16276 , 1983, IEEE Trans. Inf. Theory.

[4]  D. G. N. Hunter,et al.  Experiments with Relaxation Algorithms for Breaking Simple Substitution Ciphers , 1983, Comput. J..

[5]  Gustavus J. Simmons,et al.  Contemporary Cryptology: The Science of Information Integrity , 1994 .

[6]  Colin R. Reeves,et al.  Improving the Efficiency of Tabu Search for Machine Sequencing Problems , 1993 .

[7]  Ed Dawson,et al.  A Comparison of Fast Correlation Attacks , 1996, FSE.

[8]  Ernest F. Brickell,et al.  Solving Low Density Knapsacks , 1983, CRYPTO.

[9]  Mitsuru Matsui,et al.  Linear Cryptanalysis Method for DES Cipher , 1994, EUROCRYPT.

[10]  Celso C. Ribeiro,et al.  Location and sizing of offshore platforms for oil exploration , 1992 .

[11]  Ronald L. Rivest,et al.  A Knapsack Type Public Key Cryptosystem Based On Arithmetic in Finite Fields , 1984, CRYPTO.

[12]  Reihaneh Safavi-Naini,et al.  Automated Cryptanalysis of Substitution Ciphers , 1993, Cryptologia.

[13]  Douglas R. Stinson,et al.  Cryptography: Theory and Practice , 1995 .

[14]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[15]  Henry Beker,et al.  Cipher Systems: The Protection of Communications , 1982 .

[16]  Paolo Brandimarte,et al.  Routing and scheduling in a flexible job shop by tabu search , 1993, Ann. Oper. Res..

[17]  Robert A. J. Matthews.  An Empirical Method for Finding the Keylength of periodic Ciphers , 1988, Cryptologia.

[18]  Jennifer Seberry,et al.  Advances in Cryptology — AUSCRYPT '90 , 1990, Lecture Notes in Computer Science.

[19]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[20]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[21]  B. Sankur,et al.  Applications of Walsh and related functions , 1986 .

[22]  Jovan Dj. Golic,et al.  Convergence of a Bayesian Iterative Error-Correction Procedure on a Noisy Shift register Sequence , 1992, EUROCRYPT.

[23]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[24]  Martina Gorges-Schleuter,et al.  ASPARAGOS An Asynchronous Parallel Genetic Optimization Strategy , 1989, ICGA.

[25]  James L. Massey,et al.  A spectral characterization of correlation-immune combining functions , 1988, IEEE Trans. Inf. Theory.

[26]  David J. C. MacKay,et al.  A Free Energy Minimization Framework for Inference Problems in modulo 2 Arithmetic , 1994, FSE.

[27]  Joos Vandewalle,et al.  A critical analysis of the security of knapsack public-key algorithms , 1984, IEEE Trans. Inf. Theory.

[28]  David Connolly.  Knapsack Problems: Algorithms and Computer Implementations , 1991 .

[29]  Adi Shamir,et al.  A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem , 1984, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[30]  Abraham P. Punnen,et al.  Categorized Assignment Scheduling: a Tabu Search Approach , 1993 .

[31]  Robert A. J. Matthews,et al.  The Use of Genetic Algorithms in Cryptanalysis , 1993, Cryptologia.

[32]  Thomas Siegenthaler,et al.  Decrypting a Class of Stream Ciphers Using Ciphertext Only , 1985, IEEE Transactions on Computers.

[33]  Ed Dawson,et al.  Discrete Optimisation and Fast Correlation Attacks , 1995, Cryptography: Policy and Algorithms.

[34]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[35]  J. Wesley Barnes,et al.  A tabu search experience in production scheduling , 1993, Ann. Oper. Res..

[36]  John M. Carroll,et al.  The Automated Cryptanalysis of Polyalphabetic Ciphers , 1987, Cryptologia.

[37]  Donald E. Brown,et al.  A Parallel Genetic Heuristic for the Quadratic Assignment Problem , 1989, ICGA.

[38]  C. Adams,et al.  DESIGNING S-BOXES FOR CIPHERS RESISTANT TO DIFFERENTIAL CRYPTANALYSIS ( Extended , 1993 .

[39]  Jovan Dj. Golic,et al.  A Comparison of Cryptanalytic Principles Based on Iterative Error-Correction , 1991, EUROCRYPT.

[40]  Nicholas J. Patterson,et al.  Correction to 'The covering radius of the (215, 16) Reed-Muller code is at least 16276' (May 83 354-356) , 1990, IEEE Trans. Inf. Theory.

[41]  Matthew J. Weiner,et al.  Efficient DES Key Search , 1994 .

[42]  Thomas P. Jakobsen,et al.  A Fast Method for the Cryptanalysis of Substitution Ciphers , 1995 .

[43]  Martin E. Hellman,et al.  Hiding information and signatures in trapdoor knapsacks , 1978, IEEE Trans. Inf. Theory.

[44]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[45]  Azriel Rosenfeld,et al.  Breaking substitution ciphers using a relaxation algorithm , 1979, CACM.

[46]  Fred W. Glover,et al.  A user's guide to tabu search , 1993, Ann. Oper. Res..

[47]  SpillmanRichard,et al.  Use of a genetic algorithm in the cryptanalysis of simple substitution ciphers , 1993 .

[48]  Peter B. Gibbons,et al.  The construction of subsquare free Latin squares by simulated annealing , 1992, Australas. J Comb..

[49]  Miodrag V. Zivkovic.  On two probabilistic decoding algorithms for binary linear codes , 1991, IEEE Trans. Inf. Theory.

[50]  S. M. Jennings,et al.  Multiplexed Sequences: Some Properties of the Minimum Polynomial , 1982, EUROCRYPT.

[51]  Mitsuru Matsui,et al.  On Correlation Between the Order of S-boxes and the Strength of DES , 1994, EUROCRYPT.

[52]  Joseph B. Mazzola,et al.  A tabu-search heuristic for the flexible-resource flow shop scheduling problem , 1993, Ann. Oper. Res..

[53]  John C. King.  An Algorithm for the Complete Automated Cryptanalysis of Periodic Polyalphabetic Substitution Ciphers , 1994, Cryptologia.

[54]  Yoshikazu Fukuyama,et al.  Parallel genetic algorithm for generation expansion planning , 1996 .

[55]  Richard Spillman,et al.  Cryptanalysis of Knapsack Ciphers Using Genetic Algorithms , 1993, Cryptologia.

[56]  C. G. Giinther.  ALTERNATING STEP GENERATORS CONTROLLED BY DE BRUIJN SEQUENCES , 1988 .

[57]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[58]  Fred Glover,et al.  Tabu Search: A Tutorial , 1990 .

[59]  Éric D. Taillard,et al.  Solving real-life vehicle routing problems efficiently using tabu search , 1993, Ann. Oper. Res..

[60]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[61]  Heinz Mühlenbein,et al.  Parallel Genetic Algorithms, Population Genetics, and Combinatorial Optimization , 1989, Parallelism, Learning, Evolution.

[62]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[63]  Jovan Dj. Golic,et al.  A Fast Iterative Algorithm For A Shift Register Initial State Reconstruction Given The Nosiy Output Sequence , 1990, AUSCRYPT.

[64]  James L. Massey,et al.  Shift-register synthesis and BCH decoding , 1969, IEEE Trans. Inf. Theory.

[65]  G. Athithan,et al.  An Automated Approach to Solve Simple Substitution Ciphers , 1993, Cryptologia.

[66]  Eli Biham,et al.  Differential cryptanalysis of DES-like cryptosystems , 1990, Journal of Cryptology.

[67]  Fred Piper,et al.  Stream Ciphers , 1982, EUROCRYPT.

[68]  Ed Dawson,et al.  Optimisation, Fitness and the Knapsack Cipher , 1994 .

[69]  Willi Meier,et al.  Nonlinearity Criteria for Cryptographic Functions , 1990, EUROCRYPT.

[70]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[71]  Dennis R. Bahler,et al.  An Implementation of Probabilistic Relaxation in the Cryptanalysis of Simple Substitution Ciphers , 1992, Cryptologia.

[72]  Kencheng Zeng,et al.  On the Linear Syndrome Method in Cryptanalysis , 1988, CRYPTO.

[73]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .