Statistical Analysis of Pollard's Rho Attack on Elliptic Curve Cryptography

Abstract

Elliptic curve cryptography is a relatively new public-key cryptography mechanism which has been becoming more popular in recent years. Its usage has been increasing in various fields using different cryptographic protocols, such as Elliptic Curve Diffie-Hellman (ECDH), Elliptic Curve Digital Signature Algorithm (ECDSA) and the ElGamal encryption scheme. Several attacks have been developed to solve the elliptic curve discrete logarithm problem. One of the most practical generic attacks is the Pollard's Rho algorithm, which originates as an algorithm for prime factorisation. This paper will attempt to provide a statistical insight on how various factors, namely the private-public key pairs and parameters within the sequence used in Pollard's Rho algorithm, may affect the performance speed of the algorithm. This will be done using the ANOVA statistical test. which shows that from the perspective of the initial values and addends of the sequences, the Pollard's Rho algorithm is “random” enough.