A generalization of the binary GCD algorithm
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Journal of Algorithms
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Low-Cost Double-Size Modular Exponentiation or How to Stretch Your Cryptoprocessor
PKC '99 Proceedings of the Second International Workshop on Practice and Theory in Public Key Cryptography
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CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
New Algorithm for Classical Modular Inverse
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Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
The RSA cryptography processor
EUROCRYPT'87 Proceedings of the 6th annual international conference on Theory and application of cryptographic techniques
Affine precomputation with sole inversion in elliptic curve cryptography
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Improved precomputation scheme for scalar multiplication on elliptic curves
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Fast point quadrupling on elliptic curves
Proceedings of the Third Symposium on Information and Communication Technology
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We present a very simple new algorithm for modular inversion. Modular inversion can be done by the extended Euclidean algorithm. We substitute the extended Euclidean algorithm by a standard (non-extended) Euclidean algorithm that works on integers of approximately double the length of the modulus. This substitution can be very useful on smart card coprocessors, since in some cases computations with longer numbers than necessary can be done at no extra cost. Many smart card coprocessors have been designed for the RSA algorithm of, say, 1024 bits length. On the other hand, elliptic curve algorithms work with much smaller numbers, and modular inversion is a much more important primitive in elliptic curve cryptography than in RSA cryptography. On one smart card coprocessor the new algorithm is more than twice as fast as the classical algorithm.