Speeding Fermat's factoring method
Mathematics of Computation
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Fast RSA-Type Cryptosystem Modulo pkq
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
An Attack on RSA Given a Small Fraction of the Private Key Bits
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
On the Design of RSA with Short Secret Exponent
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: 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
Low Secret Exponent RSA Revisited
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Estimating the Prime-Factors of an RSA Modulus and an Extension of the Wiener Attack
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
Low-exponent RSA with related messages
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
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
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Another look at small RSA exponents
CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
RSA with balanced short exponents and its application to entity authentication
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
New attacks on RSA with small secret CRT-Exponents
PKC'06 Proceedings of the 9th international conference on Theory and Practice of 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
Dual RSA and Its Security Analysis
IEEE Transactions on Information Theory
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Given an integer N=pq, which is a product of two primes, it is difficult to determine the prime factors p and q efficiently. However, for the suitable size of a number N, Fermat's algorithm is one of the most simple method for solving it. In this paper, a method called EPF for estimating the prime factors of a composite number is proposed. We use the technique of continued fractions to output two integers, pE+qE and pE·qE, which are close to p+q and p·q, respectively. Furthermore, we show that EPF can be adopted to reduce the loop count in Fermat's algorithm before factoring a composite number. The effect depends on the size of the prime factor. We believe that there are still other applications as well wherein EPF can be used.