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
Implementing elliptic curve cryptography
Implementing elliptic curve cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Montgomery Multiplier and Squarer for a Class of Finite Fields
IEEE Transactions on Computers
Mesh Algorithms for Multiplication and Division
HiPC '01 Proceedings of the 8th International Conference on High Performance Computing
A Scalable and Unified Multiplier Architecture for Finite Fields GF(p) and GF(2m)
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
New Algorithm for Classical Modular Inverse
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Scalable and Unified Hardware to Compute Montgomery Inverse in GF(p) and GF(2)
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Hardware architectures for public key cryptography
Integration, the VLSI Journal
Efficient scalable VLSI architecture for Montgomery inversion in GF(p)
Integration, the VLSI Journal
Subtraction-free almost montgomery inverse algorithm
Information Processing Letters
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
On the implementation of the discrete Fourier transform in the encrypted domain
IEEE Transactions on Information Forensics and Security
An RNS implementation of an Fpelliptic curve point multiplier
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Subtraction-free Almost Montgomery Inverse algorithm
Information Processing Letters
Finite field arithmetic for cryptography
IEEE Circuits and Systems Magazine
A complete modular resultant algorithm targeted for realization on graphics hardware
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Efficient multi-bit shifting algorithm in multiplicative inversion problems
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part II
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part IV
Modular resultant algorithm for graphics processors
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
Accelerating inverse of GF(2n) with precomputation
ISPEC'10 Proceedings of the 6th international conference on Information Security Practice and Experience
Computing resultants on Graphics Processing Units: Towards GPU-accelerated computer algebra
Journal of Parallel and Distributed Computing
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We modify an algorithm given by Kaliski to compute the Montgomery inverse of an integer modulo a prime number. We also give a new definition of the Montgomery inverse, and introduce efficient algorithms for computing the classical modular inverse, the Kaliski-Montgomery inverse, and the new Montgomery inverse. The proposed algorithms are suitable for software implementations on general-purpose microprocessors.