Securing Elliptic Curve Cryptography with Random Permutation of Secret Key

Scalar multiplication is the basis of the widespread elliptic curve public key cryptography. Standard scalar multiplication is vulnerable to side-channel attacks that are able to infer the secret bit values by observing the power or delay traces. This work utilizes the arithmetic properties of scalar multiplication to propose two scalar multiplication algorithms to insulate ECC implementations from side-channel attacks. The two proposed designs rely on randomly permuting the ordering and storage locations of the different scalar multiplication values 2iG as well as the corresponding secret key bits ki. Statistical analysis and Python 3.9.13implementations confirm the validity of the two algorithms. Numerical results confirm that both designs produce the same results as the standard right-to-left scalar multiplication algorithm. Welch’s t-test as well as numerical simulations confirm the immunity of our proposed protocols to side-channel attacks.