The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
Dual-Field Arithmetic Unit for GF(p) and GF(2m)
CHES '02 Revised Papers from the 4th 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
New hardware algorithms and designs for montgomery modular inverse computation in galois fields gf(p) and gf(2n)
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
Modular inverse algorithms without multiplications for cryptographic applications
EURASIP Journal on Embedded Systems
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We present the hardware architecture of an arithmetic unit intended for computing basic operations over a Galois field GF(p). The arithmetic unit supports addition, subtraction, multiplication, and multiplicative inverse modulo a prime p. To compute the multiplicative inverse, we use the promising left-shifting algorithm that is based on the extended Euclidean algorithm. We discuss the potential applications of the arithmetic unit, including elliptic curve cryptography.