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Bipartite GF (2m) Modular Multiplier Method

V.R.Venkatasubramani, M.Arunarumugam, R.Ragavendran, S.Bhuvaneswaran

This paper proposes a new modular multiplication method over GF(2m) that uses Least Significant Digit Multiplier and Hybrid Karatsuba Multiplier (HKM), which are state of the art field for secured Elliptic Curve Cryptography (ECC), according to NIST. The work suggests the operand multiplicand to be split into two parts that can be processed separately in parallel thereby increasing the computational speed. The lower part of the split multiplicand can be processed by calculating a product modulo p(α)of the multiplier using Least Significant Digit (LSD).The upper part of the split multiplicand can be processed using HKM by calculating a product modulo p(α) of the multiplier. A HKM requires least amount of space on a FPGA. The LSD provides excellent area-time trade-off. Complexity analysis comparison shows that the proposed scheme has better calculation speed and has more flexibility in making the compromise between area and time.