Oblivious Transfer Using Generalized Jacobian of Elliptic Curves

Oblivious transfer (OT ) is one of the essential tools in cryptography, in which a sender sends a message to a receiver with a probability between 0 and 1. In contrast, the sender remains oblivious that the receiver has received the message. t-out-of-k oblivious transfer (OT t) is a variant of OT schemes in which a sender transfers k messages to a receiver, but the receiver can only learn t of them. Moreover, the sender remains oblivious to which secrets the receiver has extracted. In this paper, We offer several novel protocols for secure communication using elliptic curve cryptography. First, we propose a new type of Diffie-Hellman key exchange protocol that utilizes the generalized Jacobian of elliptic curves. Next, we introduce simple and secure two-round algorithms for several variants of OT schemes, including OT , OT21, and OTkt. The security of our proposed protocols relies on the intractability assumption of solving the discrete logarithm problem. Furthermore, in our OT schemes, it is unnecessary to map the messages to the points on the elliptic curve, which reduces the computational overhead and improves the efficiency of the protocols.