Abstract
We describe a scalable and unified architecture for a Montgomery multiplication module which operates in both types of finite fields GF(p) and GF(2m). The unified architecture requires only slightly more area than that of the multiplier architecture for the field GF(p). The multiplier is scalable, which means that a fixed-area multiplication module can handle operands of any size, and also, the wordsize can be selected based on the area and performance requirements. We utilize the concurrency in the Montgomery multiplication operation by employing a pipelining design methodology. The upper limit on the precision of the scalable and unified Montgomery multiplier is dictated only by the available memory to store the operands and internal results, and the module is capable of performing infinite-precision Montgomery multiplication in both types of finite fields.
Readers should note that Oregon State University filed a patent application containing this work to the US Patent and Trademark Office.
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Savaš, E., Tenca, A.F., Koç, Ç.K. (2000). A Scalable and Unified Multiplier Architecture for Finite Fields GF(p) and GF(2m). In: Koç, Ç.K., Paar, C. (eds) Cryptographic Hardware and Embedded Systems — CHES 2000. CHES 2000. Lecture Notes in Computer Science, vol 1965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44499-8_22
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