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Explicit formulae and complexities of bit-parallel GF(2n) squarers for a new class of irreducible pentanomials xn + xn??1 + xk + x + 1, where n is odd and 1 < k < (n ?? 1)/2 are presented. The squarer is based on the generalised polynomial basis of GF(2n). Its gate delay matches the best results, whereas its XOR gate complexity is n + 1, which is only about two thirds of the current best results.
The Key Laboratory for Information System Security, Ministry of Education; Tsinghua National Laboratory for Information Science and Technology, School of Software, Tsinghua University, Beijing, People??s Republic of China
The Key Laboratory for Information System Security, Ministry of Education; Tsinghua National Laboratory for Information Science and Technology, School of Software, Tsinghua University, Beijing, People??s Republic of China