Novel GF(2m)GF2m Digit-Serial PISO Multipliers for the Self-Dual Gaussian Normal Bases

Security protocols such as Transport Layer Security implement the Elliptic curve digital signature algorithm (ECDSA) over different binary extension fields defined by the National Institute of Standards and Technology (NIST). Specifically, such multiple cipher-suite support is a security recommendation. Binary extension field arithmetic processors are expensive, especially if more than one field is supported. In this context, this article introduces a novel lightweight digit-serial parallel-in-serial-out (DS-PISO) design for versatile multiplication (DS-VPISO) targeting the NIST-like fields in resource constrained embedded systems where the crypto module allocation is limited. The proposed DS-VPISO multiplier offers competitive area (up to 40 percent area savings) compared to existing multiple field multiplier schemes based on results conducted on bit-serial implementations using Intel's Field programmable gate arrays. The article first presents a DS-PISO self-dual Gaussian normal basis multiplication architecture based on the trace mapping. After this, the article extends the new trace based DS-PISO multiplier to construct an architecture for the first versatile DS-PISO multiplication (DS-VPISO) targeting NIST's binary fields. The latter extension to versatile multiplication is based on novel architectures for versatile cyclic shifts and versatile multiplication by normal elements.

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