A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Low Secret Exponent RSA Revisited
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
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
Another generalization of Wiener's attack on RSA
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Cryptanalysis of RSA with private key d less than N0.292
IEEE Transactions on Information Theory
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Consider RSA with N = pq , q p q , public encryption exponent e and private decryption exponent d . We concentrate on thecases when e ( = N α )satisfies eX - ZY = 1, given |N -Z | = N τ . Using the ideaof Boneh and Durfee (Eurocrypt 1999, IEEE-IT 2000) we show that theLLL algorithm can be efficiently applied to get Z when|Y | = N v and γ Z = ψ (p , q , u ,v ) = (p - u )(q - v ).Further, we consider Z = ψ (p ,q , u , v ) = N - pu -v to provide a new class of weak keys in RSA. This ideadoes not require any kind of factorization as used in Nitaj's work.A very conservative estimate for the number of such weak exponentsis N 0.75 - ε , whereε 0 is arbitrarily small for suitably largeN .