A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
On Some Attacks on Multi-prime RSA
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
A Generalized Takagi-Cryptosystem with a modulus of the form prqs
INDOCRYPT '00 Proceedings of the First International Conference on Progress 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
Revisiting Wiener's Attack --- New Weak Keys in RSA
ISC '08 Proceedings of the 11th international conference on Information Security
A new RSA vulnerability using continued fractions
AICCSA '08 Proceedings of the 2008 IEEE/ACS International Conference on Computer Systems and Applications
Cryptanalysis of RSA and Its Variants
Cryptanalysis of RSA and Its Variants
Converse results to the wiener attack on RSA
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Cryptanalysis of RSA with private key d less than N0.292
IEEE Transactions on Information Theory
Cryptanalysis of short RSA secret exponents
IEEE Transactions on Information Theory
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We show that the attack of de Weger on RSA using continued fractions extends to Multi-Prime RSA. Let (n,e) be a Multi-Prime RSA public-key with private key d, where n=p1p2⋯pr is a product of r distinct balanced (roughly of the same bit size) primes, and p1 p2 pr. We show that if pr−p1=nα, 0 α≤1/r, r≥3 and $2d^2+1