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Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
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Efficient Bit-Parallel Multiplier for Irreducible Pentanomials Using a Shifted Polynomial Basis
IEEE Transactions on Computers
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IEEE Transactions on Computers
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CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
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Low complexity bit-parallel multipliers based on a class of irreducible pentanomials
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Efficient bit-parallel multipliers over finite fields GF(2m)
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New bit parallel multiplier with low space complexity for all irreducible trinomials over GF(2n)
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Low latency systolic montgomery multiplier for finite field GF(2m) based on pentanomials
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
New efficient bit-parallel polynomial basis multiplier for special pentanomials
Integration, the VLSI Journal
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This paper considers the design of bit-parallel dedicated finite field multipliers using standard basis. An explicit algorithm is proposed for efficient construction of Mastrovito product matrix, based on which we present a systematic design of Mastrovito multiplier applicable to $GF(2^m)$ generated by an arbitrary irreducible polynomial. This design effectively exploits the spatial correlation of elements in Mastrovito product matrix to reduce the complexity. Using a similar methodology, we propose a systematic design of modified Mastrovito multiplier, which is suitable for $GF(2^m)$ generated by high-Hamming weight irreducible polynomials. For both original and modified Mastrovito multipliers, the developed multiplier architectures are highly modular, which is desirable for VLSI hardware implementation. Applying the proposed algorithm and design approach, we study the Mastrovito multipliers for several special irreducible polynomials, such as trinomial and equally-spaced-polynomial, and the obtained complexity results match the best known results. Moreover, we have discovered several new special irreducible polynomials which also lead to low-complexity Mastrovito multipliers.