Algebraic Techniques for Rectification of Finite Field Circuits

This paper addresses the rectification of faulty finite field arithmetic circuits by computing patch functions at internal nets using techniques from polynomial algebra. Contemporary approaches that utilize SAT solving and Craig interpolation are infeasible in rectifying arithmetic circuits. Given candidate nets, prior algebra-based techniques can ascertain whether the circuit admits multi-fix rectification at these nets but cannot compute patch functions. We show how the algebraic computing model facilitates the exploration of admissible rectification functions, collectively, for the nets. This model also enables the exploitation of don’t care conditions for the synthesis and realization of the patches. Experimental results on large operand width finite field benchmarks, as used in cryptography, substantiate our approach.