论文信息 - Finite-Field Arithmetic

Finite-Field Arithmetic

Finite fields are used in different types of computers and digital communication systems. Two well-known examples are error-correction codes and cryptography. The traditional way of implementing the corresponding algorithms is software, running on general-purpose processors or on digital-signal processors. Nevertheless, in some cases the time constraints cannot be met with instruction-set processors, and specific hardware must be considered.

[1] Alfred Menezes,et al. Guide to Elliptic Curve Cryptography , 2004, Springer Professional Computing.

[2] Chang Hoon Kim,et al. High-speed division architecture for GF(2/sup m/) , 2002 .

[3] Naofumi Takagi,et al. A VLSI Algorithm for Modular Division Based on the Binary GCD Algorithm(Special Section on Discrete Mathematics and Its Applications) , 1998 .

[4] Jean-Jacques Quisquater,et al. Efficient Modular Division Implementation: ECC over GF(p) Affine Coordinates Application , 2004, FPL.

[5] P. L. Montgomery. Modular multiplication without trial division , 1985 .

[6] Francisco Rodríguez-Henríquez,et al. Cryptographic Algorithms on Reconfigurable Hardware , 2010 .

[7] Jean-Pierre Deschamps. Hardware Implementation of Finite-Field Arithmetic , 2009 .

[8] Jean-Pierre Deschamps,et al. Modular Multiplication and Exponentiation Architectures for Fast RSA Cryptosystem Based on Digit Serial Computation , 2011, IEEE Transactions on Industrial Electronics.

[9] Alfred Menezes,et al. Handbook of Applied Cryptography , 2018 .

[10] G. Bioul,et al. Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems , 2006 .

[11] Donald E. Knuth,et al. The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .