Flexible VLSI architectures for Galois field multipliers

• Published in: Integration (Amsterdam) Vol. 59; pp. 109 - 124
• Main Authors: Basiri M, Mohamed Asan, Shukla, Sandeep K.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2017; Elsevier BV
• Subjects: CMOS; Cryptography; ECC; Error correcting codes; Error correction; Error correction & detection; Galois field multiplier; Integrated circuits; Modular arithmetic; Montgomery multiplication; Multipliers; Studies; Vector processors; Very large scale integration; ECC; Modular arithmetic; Montgomery multiplication; Cryptography; Error correcting codes; Vector processors; Galois field multiplier
• ISSN: 0167-9260; 1872-7522
• DOI: 10.1016/j.vlsi.2017.06.009

Galois field (GF) multipliers play a major role in the engineering applications such as cryptography and error correcting codes. This paper proposes systolic vector m-bit GF(p) and GF(2m) multipliers (m=log2p), where four numbers of m2-bit GF multiplications can be done in parallel. Similarly, twelve and sixteen numbers of GF(2m4) and m4-bit GF(p) multiplications can be done in parallel respectively. Also, this paper proposes non vector flexible GF(2m) and m-bit GF(p) multipliers, where the m can be varied from 2 to the maximum allowable value. Our proposed systolic vector parallel GF(216) multiplier achieves 95.8% of improvement in throughput over reconfigurable bit serial design [7]. Similarly, the proposed systolic vector parallel 16-bit GF(p) multiplier achieves 82.5% of improvement in throughput over reconfigurable bit serial design [23] using 45nm CMOS technology. •Galois multipliers play a major role in the engineering applications such as cryptography and error correcting codes.•This paper proposes vector GF(2m) and m-bit GF(p) multipliers to perform more smaller multiplications in parallel.•Thus the proposed systolic GF(2m) and m-bit GF(p) multipliers can be used in SIMD applications.•Also, this paper proposes non vector flexible GF(2m) and m-bit GF(p) multipliers, where the m can be varied from 2 to max.•Also, this paper proposes dual field systolic vector multipliers in the same line of proposed GF(p) multipliers.