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
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
Scalable VLSI Architecture for GF(p) Montgomery Modular Inverse Computation
ISVLSI '02 Proceedings of the IEEE Computer Society Annual Symposium on VLSI
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After a comprehensive study on the Montgomery modular inverse algorithm and its revised versions, two modified high radix algorithms are proposed which utilize higher radix to reduce iterations needed without increasing complexity much, thereby accelerating the process. The radix-4 algorithm can reduce the average number of iterations from 1.4n to 0.82n and a software experiment shows the speedup is about 11 percent and iterations are 41.5 percent less on average. The radix-8 algorithm can reduce the average number of iterations to 0.73n, but it is more complicated, which makes it suitable only for very large numbers (2,048 bits) in the experiment, where the speedup can be 13--18 percent. The proposed algorithms are suitable for software implementations on general-purpose microprocessors.