A digital signature on cubic Pell Cryptosystem CP256-1299 - Abu, Nur Azman; Nitaj, Abderrahmane; Kamel Ariffin, Muhammad Rezal (International Association of Computer Science and Information Technology, 2025)
Elliptic curves have proven to be a suitable foundation for cryptosystems, with Elliptic Curve Cryptosystems (ECC) offering strong security with smaller key sizes. Recent advancements in ECC design aim to create more efficient and secure curves. In this paper, we introduce a new digital signature scheme, named CP256-1299. It is a 256-bit scheme based on a cubic Pell curve where the arithmetic operations are efficient and straightforward. In previous works, cubic Pell curves have been used to design public key cryptosystems. Our main motivation in proposing the new digital signature algorithm is to exploit the effectiveness of the arithmetic of cubic Pell curves, while maintaining reasonable keys and high security. We compare our new scheme to three widely-used digital signature algorithms based on ECC, namely ED25519, SECP256K1 and SECP256R1. It turns out that our cubic Pell curve based digital signature algorithm is designed to operate with a larger periodic order while maintaining at least similar computational requirements to most popular elliptic curve cryptosystems. Our new scheme is also suitable to support a central bank digital currency.