Methods and applications of error-free computation
Methods and applications of error-free computation
Exponentiation using canonical recoding
Theoretical Computer Science
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
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
On Computing Multiplicative Inverses in GF(2/sup m/)
IEEE Transactions on Computers
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
A Carry-Free Architecture for Montgomery Inversion
IEEE Transactions on Computers
A-Codes from Rational Functions over Galois Rings
Designs, Codes and Cryptography
Improvement to Montgomery Modular Inverse Algorithm
IEEE Transactions on Computers
Modular inverse algorithms without multiplications for cryptographic applications
EURASIP Journal on Embedded Systems
A fast inversion algorithm and low-complexity architecture over GF(2m)
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part II
Using an RSA accelerator for modular inversion
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded 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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The Montgomery inverse is used in cryptography for the computation of modular inverse of b modulo a, where a is a prime. We analyse existing algorithms from the point of view of their hardware implementation. We propose a new, hardware-optimal algorithm for the calculation of the classical modular inverse. The left-shift binary algorithm is shown to naturally calculate the classical modular inverse in fewer operations than the algorithm derived from the Montgomery inverse.