Oregon State University

Erkay Savas

Çetin K Koç

Alexandre F Tenca

Cetin K Koç

Tugrul Yanik

Scalable and unified multipliers for multiplication of cryptographic parameters represented as elements of either of the prime field (GF(p)) and the binary extension field (GF(2)) include processing elements arranged to execute in pipeline stages. The processing elements are configurable to perform operations corresponding to either the prime field or the binary extension field. In an example, the processing elements include a dual-field adder having a field-select input that permits selection of a field arithmetic. In a representative example, multipliers are implemented as integrated circuits having processing units that each receive a single bit of one operand and partial words of the remaining operand.

Scalable and unified multiplication methods and apparatus

Methods and apparatus for modular arithmetic operations with respect to a modulus p include representing operands as a series of s w-bit numbers, wherein Operations are executed word by word and a carry, borrow, or other bit or word is obtained from operations on most significant words of the operands. Depending on the value of this bit or word, an operation-specific correction factor is applied. Cryptographic systems include computer executable instructions for such methods. Bit-level operations are generally avoided and the methods and apparatus are applicable to systems based on, for example, public-key cryptographic algorithms defined over the finite field GF(p).

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Corvallis, OR, United States of America

Erkay Savas