A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Cryptanalysis of Unbalanced RSA with Small CRT-Exponent
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Fast RSA-Type Cryptosystem Modulo pkq
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the RSA Schemes with Short Secret Exponent from Asiacrypt '99
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: 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
Deterministic Polynomial-Time Equivalence of Computing the RSA Secret Key and Factoring
Journal of 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
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
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
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
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
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
On the optimality of lattices for the coppersmith technique
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
On optimal bounds of small inverse problems and approximate GCD problems with higher degree
ISC'12 Proceedings of the 15th international conference on Information Security
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We introduce a "generalized small inverse problem (GSIP)" and present an algorithm for solving this problem. GSIP is formulated as finding small solutions of f(x0, x1, . . . , xn) = x0h(x1, . . . , xn) + C = 0(mod M) for an n-variate polynomial h, non-zero integers C and M. Our algorithm is based on lattice-based Coppersmith technique. We provide a strategy for construction of a lattice basis for solving f = 0, which are systematically transformed from a lattice basis for solving h = 0. Then, we derive an upper bound such that the target problem can be solved in polynomial time in log M in an explicit form. Since GSIPs include some RSA-related problems, our algorithm is applicable to them. For example, the small key attacks by Boneh and Durfee are refound automatically.