Improved Deterministic Usage of the Elliptic Curve Digital Signature Algorithm with Scrypt

In this paper, we propose an improved deterministic usage of the Elliptic Curve Digital Signature Algorithm (ECDSA) with the key derivation function scrypt. In particular, the scrypt function generates a batch of random bits where the random bits needed for the signing process are selected. As a certain number of bits is chosen from a bigger set, the reuse of the secret random number for each signing process is avoided, which is against fault and side-channel attacks. Numerical results are provided for five different-length messages and seventeen private keys considered as inputs for deterministic ECDSA and our proposed method. The random quality assessment using a statistical test suite of the National Institute of Standards and Technology (NIST) shows that our proposed method generates higher-quality random bit sequences, which can be seen clearly with one- and two-million-bit lengths respectively.