High-performance and high-speed implementation of polynomial basis Itoh–Tsujii inversion algorithm over GF(2m)

• Published in: IET information security Vol. 11; no. 2; pp. 66 - 77
• Main Authors: Rashidi, Bahram, Rezaeian Farashahi, Reza, Sayedi, Sayed Masoud
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 01.03.2017
• Subjects: Algorithms; Computation; digit‐serial architecture; field multiplier; Field programmable gate arrays; field‐programmable gate array; flip‐flops; Hardware; hardware resources; High speed; Inversions; irreducible trinomials; ITA; k‐times squarer blocks; logic design; Multipliers; multiplying circuits; path delay; pentanomials; polynomial basis Itoh‐Tsujii inversion algorithm; Polynomials; registers; Research Article; tree structure; trees (mathematics); Virtex‐4 FPGA family; multiplying circuits; field multiplier; path delay; field programmable gate arrays; polynomials; tree structure; trees (mathematics); Virtex-4 FPGA family; k-times squarer blocks; field-programmable gate array; hardware resources; ITA; registers; digit-serial architecture; pentanomials; flip-flops; logic design; irreducible trinomials; polynomial basis Itoh-Tsujii inversion algorithm
• ISSN: 1751-8709; 1751-8717
• DOI: 10.1049/iet-ifs.2015.0461

In this study high-performance and high-speed field-programmable gate array (FPGA) implementations of polynomial basis Itoh–Tsujii inversion algorithm (ITA) over GF(2m) constructed by irreducible trinomials and pentanomials are presented. The proposed structures are designed by one field multiplier and k-times squarer blocks or exponentiation by 2k, where k is a small positive integer. The k-times squarer blocks have an efficient tree structure with low critical path delay, and the multiplier is based on a proposed high-speed digit-serial architecture with minimum hardware resources. Furthermore, to reduce the computation time of ITA, the critical path of the circuit is broken to finer path using several registers. The computation times of the structure on Virtex-4 FPGA family are 0.262, 0.192 and 0.271 µs for GF(2163), GF(2193) and GF(2233), respectively. The comparison results with other implementations of the polynomial basis Itoh–Tsujii inversion algorithm verify the improvement in the proposed architecture in terms of speed and performance.