Iranian Society of Cryptology The ISC International Journal of Information Security 2008-2045 15 2 2023 07 01 Oblivious Transfer Using Generalized Jacobian of Elliptic Curves 260 273 172258 10.22042/isecure.2023.336301.779 EN Maryam Rezaei Kashi Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran Mojtaba Bahramian Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran Journal Article 2022 04 06 ‎Oblivious transfer is one of the important tools in cryptography‎, ‎in which a sender sends a message to a receiver with a probability between 0 and 1‎, ‎while the sender remains oblivious that the receiver has received the message‎.<br />‎A flavor of $OT$ schemes is chosen $t$-out-of-$k$ oblivious transfer ($OT^t_k$)‎. ‎In an $OT^t_k$ scheme‎, ‎a sender transfers $k$ messages to a receiver‎, ‎the receiver can learn only $t$ of them‎, ‎and the sender remains oblivious to which secrets are extracted by the receiver‎. <br />‎In this paper‎, ‎we first propose a type of Diffie-Hellman key exchange protocol using the generalized Jacobian of elliptic curves‎. ‎Next‎, ‎we introduce simple‎, ‎secure two-round algorithms for $OT$‎, ‎$OT^1_2$‎, ‎$OT^t_k$‎.<br />‎The security of proposed protocols is based on the intractability assumption of solving discrete logarithm problem; furthermore‎, ‎in our $OT$ schemes‎, ‎it is not necessary to map the messages to the points on the elliptic curve‎. https://www.isecure-journal.com/article_172258_fa14b69b64c01cc8257b477574da8242.pdf