Hardware Constructions for Error Detection of Number-Theoretic Transform Utilized in Secure Cryptographic Architectures

Polynomial multiplication is one of the most rigorous arithmetic construction of postquantum cryptosystems. Utilizing number-theoretic transformations, the product of such multiplication can be efficiently computed in quasi-linear time O(n.lgn). Error detection schemes of number-theoretic transform (NTT) architectures are essential to ensure correct mathematical operations, improved security, and thwart active side-channel attacks mounted through faults. NTT is not only significant to post-quantum cryptosystems, but the structure is also valuable to the already existing security protocols, e.g., signature schemes, hash functions, and the like. This paper, for the first time, introduces new error detection schemes of NTT architectures, successfully detecting both permanent and transient faults. Our schemes are based on recomputing with negated, scaled, and swapped operands. We have implemented the proposed schemes on the application-specific integrated circuit (ASIC). Performance and implementation metrics on this hardware platform show acceptable hardware overhead. As our schemes provide acceptable complexity and high efficiency, they can be utilized in compact hardware implementations of constrained applications, e.g., deeply embedded architectures.