C&O 685 project topics

C&O 685 - Project Topics

Links: Crypto seminars at Waterloo, LNCS, Journal of Cryptology, eprint.

Primality testing
- M. Agrawal, N. Kayal and N. Saxena, "Primes is in P", Annals of Mathematics, Volume 160, No. 2, 2004, 781-793.
  This paper proves that the problem of determining whether a number n is prime or composite can be solved in deterministic polynomial time.
Integer factorization. Special-purpose hardware for accelerating linear algebra
- A. Lenstra, A. Shamir, J. Tomlinson and E. Tromer, Analysis of Bernstein's factorization circuit, Proceedings of ASIACRYPT 2002, 2002, 1-26.
- M. Wiener, The full cost of cryptanalytic attacks, Journal of Cryptology, 17 (2004), 105-124.
Integer factorization. Optical hardware for accelerating sieving
- A. Shamir, Factoring large numbers with the TWINKLE device, Proceedings of CHES '99, 1999, 2-12.
- A. Lenstra and A. Shamir, Analysis and optimization of the TWINKLE factoring device, Proceedings of EUROCRYPT 2000, 2000, 35-52.
Integer factorization. Special-purpose hardware for accelerating sieving
- A. Shamir and E. Tromer, On the cost of factoring RSA-1024, RSA CryptoBytes, volume 6, number 2, 2003, 10-19.
- A. Shamir and E. Tromer, Factoring large numbers with the TWIRL device, Proceedings of CRYPTO 2003, 2003, 1-26.
- A. Lenstra, E. Tromer, A. Shamir, W. Kortsmit, B. Dodson, J. Hughes and P. Leyland, Factoring estimates for a 1024-bit RSA modulus, Proceedings of ASIACRYPT 2003, 2003, 55-74.
Integer factorization. The elliptic curve factoring algorithm
- R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer-Verlag, 2001.
Integer factorization. The number field sieve factoring algorithm
- R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer-Verlag, 2001.
Integer factorization. Factoring integers of a special form
- D. Boneh, G. Durfee and N. Howgrave-Graham, Factoring p^rq for large r, Crypto '99.
RSA security. Finding cube roots modulo n may be easier than factoring
- D. Boneh and R. Venkatesan, Breaking RSA may not be equivalent to factoring, EUROCRYPT '98, pages 59-71.
RSA security. Finding cube roots modulo n may be as hard as factoring
- D. Brown, Breaking RSA may be as difficult as factoring, 2005.
RSA signature schemes. Chosen-message attacks on some RSA signature schemes
- J. Coron, D. Naccache, Y. Desmedt, A. Odlyzko and J. Stern, Index calculation attacks on RSA signature schemes, Designs, Codes and Cryptography, 38 (2006), 41-53.
RSA-like signature schemes. Provably-secure and fast Rabin-Williams signature sheme
- D. Bernstein Proving tight security for standard Rabin-Williams signatures.
Discrete logarithm problem. Parallelizing Pollard's rho algorithm
- P. van Oorschot and M. Wiener, Parallel collision search with cryptanalytic applications, Journal of Cryptology, volume 12 (1999), pages 1-28.
Discrete logarithm problem. Coppersmith's algorithm for computing logarithms in F_2^m^*
- D. Coppersmith, Fast evaluation of logarithms in fields of characteristic two, IEEE Transactions on Information Theory, volume 30 (1984), pages 587-594.
- R. Thome, Computation of discrete logarithms in F_2⁶⁰⁷, Proceedings of Asiacrypt 2001, 2001, 107-124.
Discrete logarithm problem. The Gaussian integer method (and sieving).
- R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer-Verlag, 2001.
Diffie-Hellman problem. Towards the equivalence of the Diffie-Hellman and discrete logarithm problems
- U. Maurer, Towards the equivalence of breaking the Diffie-Hellman protocol and computing discrete logarithms, Proceedings of Crypto '94, 1994, pages 271-281.
Diffie-Hellman problem. Equivalence of the Diffie-Hellman and discrete logarithm problems for elliptic curves
- D. Boneh and R. Lipton, Algorithms for black-box fields and their applications to cryptography, Proceedings of Crypto '96, 1996, pages 283-297.
DSA. Attack on DSA
- N. Howgrave-Graham and N. Smart, Lattice attacks on digital signature schemes, Designs, Codes and Cryptography, volume 23 (2001), pages 283-290.
Discrete log signature scheme.
- E. Goh and S. Jarecki, A signature scheme as secure as the Diffie-Hellman problem, Proceedings of Eurocrypt 2003, 2003, pages 401-415.
A critique of the random oracle model.
- M. Bellare, A. Boldyreva and A. Palacio, An uninstantiable random-oracle-model scheme for a hybrid encryption problem, full version of paper that appeared in the Proceedings of Eurocrypt 2004.
Pairing-based cryptography.
- D. Boneh and X. Boyen, Short signatures without random oracles, full version of paper that appeared in the Proceedings of Eurocrypt 2004.
Pairing-based cryptography.
- D. Boneh, X. Boyen and H. Shacham, Short group signatures, full version of paper that appeared in the Proceedings of Crypto 2004.
Pairing-based cryptography.
- D. Boneh, G. Di Crescenzo, R. Ostrovsky and G. Persiano, Public key encryption with keyword search, full version of paper that appeared in the Proceedings of Eurocrypt 2004.