Blinded Montgomery Powering Ladder Protected Against the Jacobi Symbol Attack

Recently, many physical attack types (e.g., timing attacks, power consumption attacks, faultattacks) have been developed against cryptosystems, specifically against the modularexponentiation that is the core operation of many security systems. Indeed, there is a real need toeliminate the vulnerabilities of cryptosystems, such as RSA or the Elliptic Curve Cryptosystem,that make them susceptible to such attacks. In 2006, Boreale described a new type of physicalattack based in the Jacobi symbol concept, and later, Schmidt used the same concept as Borealeto break the security of the blinded Montgomery powering ladder. In this paper, a countermeasureagainst Schmidt's attack is presented to make the blinded Montgomery powering ladder resistantto the Jacobi symbol attack.