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Unified dual-field multiplier in GF(P) and GF(2k)

Unified dual-field multiplier in GF(P) and GF(2k)

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  • Author(s): C.W. Chiou 1 ; C.-Y. Lee 2 ; J.-M. Lin 3
    • View affiliations
    • Affiliations: 1: Department of Computer Science and Information Engineering, Ching Yun University, Chung-Li, Taiwan, Republic of China
      2: Department of Computer Information and Network Engineering, Lunghwa University of Science and Technology, Taoyuan County, Taiwan, Republic of China
      3: Department of Information Engineering and Computer Science, Feng Chia University, Taichung City, Taiwan, Republic of China
  • Source: Volume 3, Issue 2, June 2009, p. 45 – 52
    DOI:  10.1049/iet-ifs.2007.0030 , Print ISSN 1751-8709, Online ISSN 1751-8717
© The Institution of Engineering and Technology
Published

A scalable unified multiplier for both prime fields GF(P) and binary extension fields GF(2k), where P=2m−1 and GF(2k) is generated by an irreducible all one polynomial. The proposed unified dual-field multiplier uses the LSB-first bit-serial architecture for multiplication in GF(P) and GF(2k) other than the Montgomery multiplication algorithm, which has been employed by most existing dual-field multipliers. The proposed unified dual-field multiplier costs little space and time complexities. The new multiplier is scalable for operands of any size while other existing dual-field multipliers are only scalable for operands with multiples of m. Furthermore, the proposed multiplier has simplicity, regularity, modularity and concurrency and is very suitable to be implement in VLSI.

Inspec keywords: Galois fields; computational complexity; public key cryptography; polynomials; digital arithmetic

Other keywords: Montgomery multiplication algorithm; GF(2k)-binary extension field; Galois field; scalable unified dual-field multiplier; time complexity; elliptic curve cryptography; LSB-first bit-serial architecture; GF(P)-prime field; polynomial generation

Subjects: Data security; Cryptography theory; Algebra; Cryptography; Computational complexity; Algebra

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