The accelerated integer GCD algorithm
ACM Transactions on Mathematical Software (TOMS)
A double-digit Lehmer-Euclid algorithm for finding the GCD of long integers
Journal of Symbolic Computation - Special issue on design and implementation of symbolic computation systems
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
Handbook of Applied Cryptography
Handbook of Applied Cryptography
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
New Algorithm for Classical Modular Inverse
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
From Euclid's GCD to Montgomery Multiplication to the Great Divide
From Euclid's GCD to Montgomery Multiplication to the Great Divide
Anonymous ticketing for NFC-Enabled mobile phones
INTRUST'11 Proceedings of the Third international conference on Trusted Systems
Arithmetic unit for computations in GF(p) with the left-shifting multiplicative inverse algorithm
ARCS'13 Proceedings of the 26th international conference on Architecture of Computing Systems
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Hardware and algorithmic optimization techniques are presented to the left-shift, right-shift, and the traditional Euclidean-modular inverse algorithms. Theoretical arguments and extensive simulations determined the resulting expected running time. On many computational platforms these turn out to be the fastest known algorithms for moderate operand lengths. They are based on variants of Euclidean-type extended GCD algorithms. On the considered computational platforms for operand lengths used in cryptography, the fastest presented modular inverse algorithms need about twice the time of modular multiplications, or even less. Consequently, in elliptic curve cryptography delaying modular divisions is slower (affine coordinates are the best) and the RSA and ElGamal cryptosystems can be accelerated.