Improved Deterministic Usage of the Elliptic Curve Digital Signature Algorithm with Scrypt
Dang Ninh Tran, Ba Linh Vu, Xuan Nguyen Tien · 2023
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.