Modular multiplication processing apparatus

Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed

Reexamination Certificate

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Reexamination Certificate

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07904498

ABSTRACT:
A modular multiplication processing apparatus is provided that can process modular multiplication of data exceeding a bit length which a coprocessor can process, by using the coprocessor based upon Montgomery multiplication In the modular multiplication processing apparatus, data to be subjected to modular multiplication is decomposed, and the decomposed data elements are transformed into a form suitable for Montgomery multiplication, respectively. Further, after respective data elements are transformed to have sizes that can be inputted into a coprocessor, Montgomery multiplication is repeatedly performed in the coprocessor. A remainder of Montgomery multiplication of an original bit length is restored from the obtained remainder.

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A. Menezes, et al., “Multiple-Precision Modular Arithmetic”, Handbook of Applied Cryptography, pp. 559-603, 1997.
W. Fischer, et al., “Increasing the Bitlength of a Crypto-Coprocessor”, CHES 2002, vol. 2523 of Lecture Notes in Computer Science, Springer-Verlag, pp. 71-81, 2003.
B. Chevallier-Mames, et al., “Faster Double-Size Modular Multiplication from Euclidean Multipliers”, CHES 2003, vol. 2779 of Lecture Notes in Computer Science, Springer-Verlag, pp. 214-227, 2003.
M. Kaihara, et al., “Bipartite Modular Multiplication”, CHES 2005, vol. 3659 of Lecture Notes in Computer Science, Springer-Verlag, pp. 201-210, 2005.

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