CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Finding Small Roots of Univariate Modular Equations Revisited
Proceedings of the 6th IMA International Conference on Cryptography and Coding
Approximate Integer Common Divisors
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Finding Small Solutions to Small Degree Polynomials
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Simplified OAEP for the RSA and Rabin Functions
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
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
Cryptanalysis of RSA with private key d less than N0.292
IEEE Transactions on Information Theory
Password authenticated key exchange using hidden smooth subgroups
Proceedings of the 12th ACM conference on Computer and communications security
Toward a Rigorous Variation of Coppersmith's Algorithm on Three Variables
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Factorization of Square-Free Integers with High Bits Known
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Deterministic Polynomial Time Equivalence between Factoring and Key-Recovery Attack on Takagi's RSA
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Deterministic polynomial time equivalence between factoring and key-recovery attack on Takagi's RSA
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Finding small roots of bivariate integer polynomial equations: a direct approach
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Small secret key attack on a variant of RSA (due to Takagi)
CT-RSA'08 Proceedings of the 2008 The Cryptopgraphers' Track at the RSA conference on Topics in cryptology
Solving generalized small inverse problems
ACISP'10 Proceedings of the 15th Australasian conference on Information security and privacy
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Multi-query computationally-private information retrieval with constant communication rate
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Inferring sequences produced by nonlinear pseudorandom number generators using coppersmith's methods
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
On the optimality of lattices for the coppersmith technique
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
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We present a new and flexible formulation of Coppersmith's method for finding small solutions of bivariate polynomials p(x,y) over the integers. Our approach allows to maximize the bound on the solutions of p(x,y) in a purely combinatorial way. We give various construction rules for different shapes of p(x,y)'s Newton polygon. Our method has several applications. Most interestingly, we reduce the case of solving univariate polynomials f(x) modulo some composite number N of unknown factorization to the case of solving bivariate polynomials over the integers. Hence, our approach unifies both methods given by Coppersmith at Eurocrypt 1996.