Pollard's rho attack on ECDLP and Threshold Schemes
K. P. Vidya · Monte Carlo Methods and Applications · 2007
A threshold secret sharing scheme is one in which a piece of information is shared among a group of t persons such that, any k number of them for k ≤ t pool in their shares to recover the secret. In this paper, we propose a suitable technique for a (2, t )-threshold scheme that is based on a cryptanalytic attack of the Elliptic Curve Discrete Logarithm Problem (ECDLP). This scheme can be used in applications where two or more persons among a group of t ≥ 2 may combine to carry out a critical action such as, opening the door to the bank vault. We illustrate the application of our scheme to ATM cards.