A Proposal of Eliminating Fruitless Cycle for Efficient Pollard's Rho Method by Adding a Constant Rational Point

The security of elliptic curve cryptography is based on the ECDLP. The Pollard's rho method is known to be the most efficient attacking for ECDLP. In addition, the Pollard's rho method with skew Frobenius mapping, which is even more efficient version of the Pollard's rho method, however the number of fruitless cycle increases significantly. In this paper, the authors have succeeded in reducing them by adding an operation of addition and subtraction of constant rational points to Pollard's rho method with the skew Frobenius mapping.