Cryptanalysis of RSA and Its Variants (Chapman & Hall/CRC Cryptography and Network Security Series v. 3)
By: M. Jason Hinek (author), Douglas R. Stinson (series_editor)Hardback
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Thirty years after RSA was first publicized, it remains an active research area. Although several good surveys exist, they are either slightly outdated or only focus on one type of attack. Offering an updated look at this field, Cryptanalysis of RSA and Its Variants presents the best known mathematical attacks on RSA and its main variants, including CRT-RSA, multi-prime RSA, and multi-power RSA. Divided into three parts, the book first introduces RSA and reviews the mathematical background needed for the majority of attacks described in the remainder of the text. It then brings together all of the most popular mathematical attacks on RSA and its variants. For each attack presented, the author includes a mathematical proof if possible or a mathematical justification for attacks that rely on assumptions. For the attacks that cannot be proven, he gives experimental evidence to illustrate their practical effectiveness. Focusing on mathematical attacks that exploit the structure of RSA and specific parameter choices, this book provides an up-to-date collection of the most well-known attacks, along with details of the attacks.
It facilitates an understanding of the cryptanalysis of public-key cryptosystems, applications of lattice basis reduction, and the security of RSA and its variants.
M. Jason Hinek is an adjunct research fellow in the iCORE Information Security Lab at the University of Calgary. He earned his Ph.D. in computer science from the University of Waterloo, where his research focused on the security of variants of RSA.
PRELIMINARIES The RSA Cryptosystem Public-Key Cryptography The RSA Cryptosystem The Security of RSA Efficiency of RSA RSA Signature Scheme Variants of RSA Some Notation, Mathematics, and Techniques Some Notation Some Mathematics Results Integer Factorization Continued Fractions Lattices Solving Linear Equations Coppersmith's Methods On Attacks and Proofs CRYPTANALYSIS OF RSA Some Early Attacks Common Modulus Attack Hastad's Broadcast Attack Cycling Attacks Small Public Exponent Attacks Stereotyped Message Attack Related Message Attacks Random Padding Attack Leaking Information Small Private Exponent Attacks Wiener's Continued Fraction Attack Boneh and Durfee's Lattice Attacks Effectiveness of the Attacks Partial Key Exposure Attacks Factoring with a Hint Partially Known Private Exponent: MSBs Partially Known Private Exponent: LSBs Partially Known Primes Key Reconstruction with Random Errors More Small Private Exponent Attacks Common Modulus Attack Common Private Exponent Attack CRYPTANALYSIS OF VARIANTS OF RSA CRT-RSA CRT-RSA Small CRT-Exponent Attacks Partial Key Exposure Attacks Key Reconstruction with Random Errors Multi-Prime RSA Multi-Prime RSA Factoring the Modulus Small Private Exponent Attacks Partial Key Exposure Attacks Common Modulus Attacks CRT Attacks Multi-Power RSA Takagi's Scheme Factoring the Modulus Small Private Exponent Attacks Partial Key Exposure Attacks Common Modulus Attack Multi-Exponent RSA Common Prime RSA Common Prime RSA Factoring the Modulus Small Private Exponent Attacks Small CRT-Exponent Attacks Dual RSA Dual RSA Small Public Exponent Small Private Exponent Dual CRT-RSA Efficiency and Comparison Appendix A: Distribution of g = gcd(p - 1, q - 1) Appendix B: Geometrically Progressive Matrices Appendix C: Some AlgorithmsFurther Reading Bibliography Index Additional Notes appear at the end of each chapter.
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- ID: 9781420075182
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