polynomial basis

Galois Fields Elements Processing Units for Cryptographic Data Protection in Cyber-Physical Systems

Currently, elliptic curves are the mathematical basis for digital signature processing. Elliptic curve points processing is based on the performance of operations in Galois field GF(2m) in normal or polynomial bases. Characteristics of multipliers for these bases are different. In this paper, the time complexity of software multipliers for binary Galois fields GF(2m) and fields GF(dn) was investigated. Fields with approximately the same number of elements were investigated. Elements of these fields were represented in a polynomial basis.

Calculating Structural Complexity of Galois Fields Multipliers Based on Elementary Converters

Calculating structural complexity of Galois fields multiplier based on elementary converters is analyzed in paper. Structural complexity is determined by combing VHDL- SHmodels into a VHDL-SH model. Mastrovito multiplier and classic Galois fields multiplier were chosen for calculation results analysis. The order of the Galois field, which is considered in the article is ≤ 409.

Structural Complexity Calculation of Multipliers Based on Polynomial Basis of Galois Fields Elements Gf(2m)

The structural complexity of multipliers in polynomial basis for Galois field GF(2^m) is analyzed in paper. Mastrovito multiplication algorithm was chosen to determine the structural complexity of multiplication in Galois fields. The definition of structural complexity is calculated by combining the SH- and VHDL-models into a VHDL-SH model.