High-Speed Area-Efficient Hardware Architecture for the Efficient
Detection of Faults in a Bit-Parallel Multiplier Utilizing the Polynomial
Basis of GF(2m)
The utilization of finite field multipliers is pervasive in contemporary
digital systems, with hardware implementation for bit parallel operation often
necessitating millions of logic gates. However, various digital design issues,
whether natural or stemming from soft errors, can result in gate malfunction,
ultimately leading to erroneous multiplier outputs. Thus, to prevent
susceptibility to error, it is imperative to employ an effective finite field
multiplier implementation that boasts a robust fault detection capability. This
study proposes a novel fault detection scheme for a recent bit-parallel
polynomial basis multiplier over GF(2m), intended to achieve optimal fault
detection performance for finite field multipliers while simultaneously
maintaining a low-complexity implementation, a favored attribute in
resource-constrained applications like smart cards. The primary concept behind
the proposed approach is centered on the implementation of a BCH decoder that
utilizes re-encoding technique and FIBM algorithm in its first and second
sub-modules, respectively. This approach serves to address hardware complexity
concerns while also making use of Berlekamp-Rumsey-Solomon (BRS) algorithm and
Chien search method in the third sub-module of the decoder to effectively
locate errors with minimal delay. The results of our synthesis indicate that
our proposed error detection and correction architecture for a 45-bit
multiplier with 5-bit errors achieves a 37% and 49% reduction in critical path
delay compared to existing designs. Furthermore, the hardware complexity
associated with a 45-bit multiplicand that contains 5 errors is confined to a
mere 80%, which is significantly lower than the most exceptional BCH-based
fault recognition methodologies, including TMR, Hamming's single error
correction, and LDPC-based procedures within the realm of finite field
multiplication.Comment: 9 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:2209.1338