ACE: A VLSI chip for Galois field GF(2(m)) based exponentiation

Finite or Galois fields are used in numerous applications like error correcting codes, digital signal processing and cryptography. These applications often require computing exponentiations in GF(2(m)) which is a very computationally intensive operation, The methods proposed in the literature achieve exponentiation by iterative methods using repeated multiplications and the hardware implementations use a number of Galois field multipliers in parallel resulting in expensive hardware. In this paper, we present a new algorithm based on a pattern matching technique for computing exponentiations in GF(2(m)), for values of m less than or equal to 8. A systolic array processor architecture was,developed by the authors for performing multiplication and division in GF(2(m)) in [13], A similar strategy is proposed in this paper for achieving exponentiation at the rate of a new result every clock cycle. A prototype VLSI chip called ACE implementing the proposed architecture for Galois field GF(2(4)) has been designed and verified using CMOS 2 mu m technology. The chip can yield a computational rate of 40 million exponentiations per second.