STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Recent Progress and Prospects for Integer Factorisation Algorithms
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
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
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Let N = pq be an RSA modulus, i.e. the product of two large unknown primes of equal bit-size. In the X 9.31-1997 standard for public key cryptography, Section 4.1.2, there are a number of recommendations for the generation of the primes of an RSA modulus. Among them, the ratio of the primes shall not be close to the ratio of small integers. In this paper, we show that if the public exponent e satisfies an equation eX *** (N *** (ap + bq ))Y = Z with suitably small integers X , Y , Z , where $\frac{a}{b}$ is an unknown convergent of the continued fraction expansion of $\frac{q}{p}$, then N can be factored efficiently. In addition, we show that the number of such exponents is at least $N^{\frac{3}{4}-\varepsilon}$ where *** is arbitrarily small for large N .