Security and Performance Analysis of Elliptic Curve Crypto System using Bitcoin Curves

This paper analysis an attack on crypto currency signatures generated by Elliptic Curve Digital Signature Algorithm (ECDSA). This attack is done on three different dimensions with leakage of nonce weak nonce and by using Lenstra–Lenstra–Lovasz (LLL) by considering various crypto currency curve parameters such as number of private keys, single nonce, multiple nonces, single signature, multiple signatures on varying bit sizes of length 64, 128, 256, 512 and 1024. This work demonstrates demonstrate leak-weak nonce method performs exponentially better over LLL to crack ECDSA. In addition to finding multiple vulnerabilities on ECDSA and to avoid leak-weak nonces we use T-of-N threshold signing algorithm based on GG20 where nonce k is distributed across N parties unlike having with one single party. This technique is implemented and evaluated considering group of N parties. This paper brings out the pitfalls of ECDSA, when it is used to sign crypto currency transactions.