An improvement of both security and reliability for elliptic curve scalar multiplication Montgomery algorithm

Elliptic curve cryptosystems (ECC) are well suited to devices with limited memory and processing capabilities, such as smart cards, as well as devices with limited power, such as wireless handheld devices. This is because, for considerably smaller key sizes, elliptic curves over huge finite fields provide the same level of security as other cryptosystems like RSAECC-based circuits are vulnerable to physical attacks aimed at getting the secret key, despite its security. Fault injection attacks are a sort of physical attack that involves inserting a fault into a circuit during a cryptographic operation to alter its behavior. In this regard, we introduce a new fault detection approach based on time redundancy for the Montgomery Elliptic Curve Scalar Multiplication algorithm. We divided the ECC design into three blocks with registers placed between them. When compared to the original Montgomery ECSM algorithm, our solution takes roughly 11.65% more occupied slices overhead but yields a frequency gain of 51.27%.