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
Håstad’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.
Biography
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.
I enjoyed reading the book because the author is always caring about the different references that he used to write the text. This allows the reader to go further in his understanding of what is presented. … I was pleased by the way the author presented all the different attacks and variant of RSA. I would recommend this book for people who would like to know more about the RSA and more precisely about the difficulties of attacking this cryptosystem with mathematical techniques. … this book can be used as a base for building a complete course on RSAs cryptanalysis.
—Antoine Rojat, SIGACT News, December 2011I can honestly recommend this book. It is written straightforward and is therefore easy to read. Every step is explained and original sources are given, so if you want to look deeper into the background of a certain problem, you can easily do that. … a substantiated overview over the current state of cryptanalysis of RSA. …
—IACR book reviews, January 2010
