Partial Recomputation Fault Detection Architecture for Multiple-Precision Montgomery Modular Multiplication

Detection of soft errors and faults are one of the most critical factors in ensuring the reliability of algorithm implementations. Multiplication, as a fundamental and computationally intensive operation, is particularly vulnerable to such errors. Given its widespread use in cryptography and coding applications, detecting these errors is crucial. For example, in hash functions, even a single-bit change in the input can completely alter the output (ideally, each bit of the output changes with a probability of 12). Montgomery multiplication as an efficient multiplication method is an integral part of numerous cryptographic applications expanding both classical and post quantum cryptography. For that reason, this paper introduces a fault detection method for the multiple-precision Montgomery modular multiplication algorithm based on partial recomputation. Through extensive simulations and implementations, we demonstrate that our approach efficiently detects both permanent and transient errors with a high success rate, while imposing modest area and time overhead on the system.