Browsing by Author "Yayla, Oğuz"

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An Exhaustive Computer Search for Finding New Curves With Many Points Among Fibre Products of Two Kummer Covers Over $\\bbb{f}_5$ and $\\bbb{f}_7$
(2013) Özbudak, Ferruh; Temür, Burcu Gülmez; Yayla, Oğuz; Mathematics
In this paper we make an exhaustive computer search for finding new curves with many points among fibre products of 2 Kummer covers of the projective line over F5 and F7 . At the end of the search, we have 12 records and 6 new entries for the current Table of Curves with Many Points. In particular, we observe that the fibre product $y^3_1$ = $\\frac {5(x+2)(x +5)} {x}$, $y^3_2$ $\\frac {3x^2(x +5)} {x + 3}$ over F7 has genus 7 with 36 rational points. As this coincides with the Ihara bound, we conclude that the maximum number N7 (7) of F7 -rational points among all curves of genus 7 is 36. Our exhaustive search has been possible because of the methods given in the recent work by Özbudak and Temür (2012) for determining the number of rational points of such curves.
Threshold Structure-Preserving Signatures With Randomizable Key
(Science and Technology Publications, Lda, 2025) Ağırtaş, A.R.; Çelik, E.; Kocaman, S.; Sulak, F.; Yayla, Oğuz
Digital signatures confirm message integrity and signer identity, but linking public keys to identities can cause privacy concerns in anonymized settings. Signatures with randomizable keys can break this link, preserving verifiability without revealing the signer. While effective for privacy, complex cryptographic systems need to be modular structured for efficient implementation. Threshold structure-preserving signatures enable modular, privacy-friendly protocols. This work combines randomizable keys with threshold structure-preserving signatures to create a valid, modular, and unlinkable foundation for privacy-preserving applications. © 2025 by Paper published under CC license (CC BY-NC-ND 4.0).