Proceedings on Advances in cryptology---CRYPTO '86
An FFT extension of the elliptic curve method of factorization
An FFT extension of the elliptic curve method of factorization
Modern computer algebra
Factorization of the tenth Fermat number
Mathematics of Computation
Tellegen's principle into practice
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The Middle Product Algorithm I
Applicable Algebra in Engineering, Communication and Computing
Fast Modular Reduction for Large Wordlengths via One Linear and One Cyclic Convolution
ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
A gmp-based implementation of schönhage-strassen's large integer multiplication algorithm
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
A New Protocol for Conditional Disclosure of Secrets and Its Applications
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Improved stage 2 to P ± 1 factoring algorithms
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
SPAKE: a single-party public-key authenticated key exchange protocol for contact-less applications
FC'10 Proceedings of the 14th international conference on Financial cryptograpy and data security
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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The Elliptic Curve Method for integer factorization (ECM) was invented by H. W. Lenstra, Jr., in 1985 [14]. In the past 20 years, many improvements of ECM were proposed on the mathematical, algorithmic, and implementation sides. This paper summarizes the current state-of-the-art, as implemented in the GMP-ECM software.