Novel Trace Based Construction of the Parallel In Serial Out Multiplication for Elliptic Curve Digital Signature Algorithm Like Binary Extension Fields
The Gaussian normal bases (GNBs) recommended by the National Institute of Standards and Technology (NIST) for the five binary extension fields of the Elliptic Curve Digital Signature Algorithm (ECDSA) are self dual. Multiplication, is a complex, and critical, field operation for the hardware oriented implementations of field inversion an important operation in the elliptic curve based algorithms in the GNB representation. This paper, introduces a novel construction for the bit serial parallel in serial out (BS PISO) multiplication over the "NIST like" fields, based on the Trace mapping. The new formulations, are presented for the first time in literature as far as we know, and provide a new and simple understanding of the Trace based mathematical model behind such a BS PISO multiplication. In addition, derivation of existing formulations for the PISO GNB field multiplication, based on the new Trace based construction, is presented. A digit serial most significant digit first PISO field multiplication architecture is constructed, based on the new Trace based BS PISO formulations, and the corresponding theoretical space and time complexities are derived and compared to other counterparts. Moreover, post synthesis space and time readings are reported, based on Application specific integrated circuit (ASIC) realizations, using the NANGate 45nm open cell libraries.
2019 IEEE 9th Annual Computing and Communication Workshop and Conference (CCWC)