On using RSA with low exponent in a public key network
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Finding Small Roots of Univariate Modular Equations Revisited
Proceedings of the 6th IMA International Conference on Cryptography and Coding
Rational Points Near Curves and Small Nonzero |x3-y2| via Lattice Reduction
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Approximate Integer Common Divisors
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Finding a small root of a univariate modular equation
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Finding a small root of a bivariate integer equation; factoring with high bits known
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
The Two Faces of Lattices in Cryptology
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Toward a Rigorous Variation of Coppersmith's Algorithm on Three Variables
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Algebraic Cryptanalysis of CTRU Cryptosystem
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Implicit Factoring: On Polynomial Time Factoring Given Only an Implicit Hint
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
On the provable security of an efficient RSA-Based pseudorandom generator
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
On the modular inversion hidden number problem
Journal of Symbolic Computation
A tool kit for finding small roots of bivariate polynomials over the integers
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
On the optimality of lattices for the coppersmith technique
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Small private-exponent attack on RSA with primes sharing bits
ISC'07 Proceedings of the 10th international conference on Information Security
| Hi-index | 0.00 |
This talk is a brief survey of recent results and ideas concerning the problem of finding a small root of a univariate polynomial mod N, and the companion problem of finding a small solution to a bivariate equation over Z. We start with the lattice-based approach from [2,3], and speculate on directions for improvement.