An Efficient Fault Detection Method for Elliptic Curve Scalar Multiplication Montgomery Algorithm

Abstract

Elliptical curve cryptography (ECC) is being used more and more in public key cryptosystems. Its main advantage is that, at a given security level, key sizes are much smaller compared to classical asymmetric cryptosystems like RSA. Smaller keys imply less power consumption, less cryptographic computation and require less memory. Besides performance, security is another major problem in embedded devices. Cryptosystems, like ECC, that are considered mathematically secure, are not necessarily considered safe when implemented in practice. An attacker can monitor these interactions in order to mount attacks called fault attacks. A number of countermeasures have been developed to protect Montgomery Scalar Multiplication algorithm against fault attacks. In this work, we proposed an efficient countermeasure premised on duplication scheme and the scrambling technique for Montgomery Scalar Multiplication algorithm against fault attacks. Our approach is simple and easy to hardware implementation. In addition, we perform injection-based error simulations and demonstrate that the error coverage is about 99.996%.