Finite field parallel multiplier

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G06F 700

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052726614

ABSTRACT:
A finite field parallel multiplier in GF(q.sup.m) including a router for directing 2m-1 components in m groups of m single-component signal lines towards m computing circuits for performing multiply and add modulo-q. The router guides m components from a first finite field element along with an additional m-1 components generated from linear combinations of the m components of the first finite field element. Each of the computing circuits receives all of the components from the second finite field element and m components provided by one set of signal lines through the router. Each computing circuit generates a single component for the resultant finite field element. These resulting components may be input through a basis change circuit to obtain a result in the desired basis.

REFERENCES:
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patent: 5046037 (1991-09-01), Cognault et al.
C. C. Wang et al., "VLSI Architectures for Computing Multiplications and Inverses in GF (2.sup.M)." IEEE Trans. on Computers, vol. C-34, No. 8, pp. 709-717, Aug. 1985.
M. Morii et al., "Efficient Bit-Serial Multiplication and the Discrete-Time Wiener-Hopf Equation Over Finite Fields." IEEE Trnas. on Inform. Theory, vol. 35, No. 6, pp. 1177-1183, Nov. 1989.
E. R. Berlekamp, "Bit-Serial Reed-Solomon Encoders." IEEE Trans. on Inform. Theory, vol. IT-28, No. 6, pp. 869-874, Nov. 1982.
P. A. Scott et al., "A Fast VLSI Multiplier for GF (2.sup.M)." IEEE Journal on Selected Areas in Communications, vol. Sac-4, No. 1, pp. 62-65, Jan. 1986, plus additional 7 pages.

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