• A proposed digital signature scheme enhancing the chaotic characteristics through the use of a dynamic S-box, in comparison with standard ECDSA, while simultaneously reducing computation time by eliminating modular multiplicative inverse operations during signing and verification. • A methodology is presented for assessing signature quality by constructing images from concatenated signatures and evaluating their chaotic properties, intra-signature and inter-signature, using established cryptographic metrics. Digital signatures are essential for ensuring data integrity and authentication. One widely used standard is the Elliptic Curve Digital Signature Algorithm (ECDSA), due to its security based on the hardness of the elliptic curve discrete logarithm problem. Despite its advantages, ECDSA entails a significant computational cost, primarily due to the modular inverse operation. This motivates the development of more efficient elliptic-curve-based signature schemes. Existing lightweight variants often reduce computational complexity, while this work additionally considers the chaotic behavior of the signature. In this paper, we introduce DSAECDH e , a digital signature scheme instantiated in this work over an elliptic curve of order q ≈ 2 1024 , while remaining applicable to different prime parameter sizes. For reducing computational cost, the scheme avoids performing modular inverse calculations during signing and verification. To preserve chaotic behavior, a dynamic substitution box is incorporated, generated from the product of the hash of the message and the transcendental number e . To validate the randomness properties of the number e , entropy and correlation metrics are computed over 100 color images generated from bit-blocks of its decimal expansion. To evaluate the statistical properties of intra-signature and inter-signature information, concatenated signatures are mapped to 512 × 512 images and analyzed using entropy, correlation coefficients, the discrete Fourier transform, and the chi-square goodness-of-fit test. In addition, the NIST SP 800-22 test suite is applied, and main attack vectors to EUF-CMA are analyzed.
Silva-García et al. (Sun,) studied this question.