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Recent Advances in RSA Cryptography

Stefan Katzenbeisser Vienna University of Technology, Austria

Recent Advances in RSA Cryptography surveys the most important achievements of the last 22 years of research in RSA cryptography. Special emphasis is laid on the description and analysis of proposed attacks against the RSA cryptosystem. The first chapters introduce the necessary background information on number theory, complexity and public key cryptography. Subsequent chapters review factorization algorithms and specific properties that make RSA attractive for cryptographers. Most recent attacks against RSA are discussed in the third part of the book (among them attacks against low-exponent RSA, Hastad's broadcast attack, and Franklin-Reiter attacks). Finally, the last chapter reviews the use of the RSA function in signature schemes.

Recent Advances in RSA Cryptography is of interest to graduate level students and researchers who will gain an insight into current research topics in the field and an overview of recent results in a unified way.

Recent Advances in RSA Cryptography is suitable as a secondary text for a graduate level course, and as a reference for researchers and practitioners in industry.

  1. Mathematical background: Divisibility and the residue class ring Zn; Polynomials; Euler's totient fun ction and Zn*; Polynomial congruences and systems of linear congruences; Quadratic residues
  2. Computational complexity: Turing machines; Deterministic and nondeterministic machines; Decision probl ems and complexity classes; Reductions; completeness and oracle computations; co-NP; Efficient computati on and randomized complexity classes
  3. Public key cryptography: Public key cryptography; Permutation polynomials and RSA-type cryptosystems; Efficient implementation of RSA; One-way functions; On the complexity of an attack against RSA
  4. Factorization methods: Trial division and Fermat factorization; Monte-carlo factorization; Factor b ase methods; The continued fraction method; Quadratic sieve; Other Factorization Methods
  5. Properties of the RSA cryptosystem: Computing the decryption exponent; Partial decryption; Cycling attacks and s uperencryption; Incorrect keys; Partial information on RSA and hard-core predicates
  6. Low-exponent RSA: Wiener's attack; Lattice basis reduction; The attack of Boneh and Durfee; Low public exponents; Polynomially related messages; Partial key exposure
  7. Protocol and implementation attacks: Simple protocol attacks against RSA; Hastad's broadcast attack; Effective se curity of small RSA messages; Optimal Asymmetric Encryption; Faulty encryption; Timing attacks
  8. RSA Signatures: Attacks on RSA signatures with redundancy; Security of hash-and-sign signatu res; Provably secure RSA signatures; Undeniable signatures; Threshold signatures
  9. References
  10. Index

Kluwer Academic Publishers, Boston. Hardbound, ISBN 0-7923-7438-X. September 2001, 160 pp. EUR 110.00 / USD 99.50 / GBP 70.00.

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