Simplified bit parallel systolic multipliers for special class of galois field (2m) with testability

This study presents a simplified structure of bit parallel systolic multiplier over Galois fields (GFs) over the set GF(2m) suitable for cryptographic hardware implementation. A redundant standard basis representation with the irreducible all one polynomial is considered. The systolic multiplier consists of (m+1)² identical cells, each consisting of one two-input AND gate, one two-input XOR gate and two one-bit latches. This architecture is well suited to very large-scale integration implementation because of its regularity modular structure and unidirectional data flow. The proposed multipliers have clock cycle latency of (m +1). This architecture has a total reduction of m² D-flip-flops compared to earlier bit parallel systolic multiplication architecture. As the finite-field multiplier is one of the complex blocks in cryptographic hardware and need secure testability to avoid unwanted access into the on-chip security blocks, the authors also introduce an on-chip testing scheme. The authors propose a test generation technique for detecting stuck-at fault (SAF), transition delay fault (TDF), stuck-open fault (SOF) and path delay faults (PDFs) at the gate and cell level in the systolic architecture. The authors also show that realistic sequential cell fault can be detected only by 12 single input change test vectors in the complete systolic multiplier over GF(2m). The proposed technique derives test vectors from the cell expressions of systolic multipliers without any requirement of an automatic test pattern generation tool. The complete systolic architecture is C-testable for SAF, TDF, SOF and PDF with only 12 constant tests. The test vectors are independent of the multiplier size. The test set provides 100% single SAF, TDF, SOF and PDF coverage.