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Using an RSA Accelerator for Modular Inversion
"... Abstract. 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 (nonextended) Euclidean algorithm that works on integers of approximately double the length of the ..."
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Abstract. 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 (nonextended) 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. Key Words: smart card coprocessor, modular inversion, Euclidean algorithm. 1
JebeleanWeber’s Algorithm without Spurious Factors
"... Tudor Jebelean and Ken Weber introduced an algorithm for finding (a,b)pairs satisfying au + bv ≡ 0 (mod k), with 0 < a, b  < √ k. It is based on Sorenson’s “kary reduction ” This algorithm does not preserve the GCD’s and its related GCD algorithm has an O(n 2) time bit complexity in the worst ..."
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Tudor Jebelean and Ken Weber introduced an algorithm for finding (a,b)pairs satisfying au + bv ≡ 0 (mod k), with 0 < a, b  < √ k. It is based on Sorenson’s “kary reduction ” This algorithm does not preserve the GCD’s and its related GCD algorithm has an O(n 2) time bit complexity in the worst case. We present a modified version which avoids this problem. We show that a slightly modified GCD algorithm has an O(n 2 / log n) running time in the worst case, where n is the number of bits of the larger input.
A Sublinear Time Parallel GCD Algorithm for the EREW PRAM
, 2009
"... We present a parallel algorithm that computes the greatest common divisor of two integers of n bits in length that takes O(n log log n / logn) expected time using n 6+ǫ processors on the EREW PRAM parallel model of computation. We believe this to be the first sublinear time algorithm on the EREW PRA ..."
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We present a parallel algorithm that computes the greatest common divisor of two integers of n bits in length that takes O(n log log n / logn) expected time using n 6+ǫ processors on the EREW PRAM parallel model of computation. We believe this to be the first sublinear time algorithm on the EREW PRAM for this problem.