Oblivious Transfer Using Generalized Jacobian of Elliptic Curves
Volume 15, Issue 2, July 2023, Pages 260-273
https://doi.org/10.22042/isecure.2023.336301.779
Maryam Rezaei Kashi, Mojtaba Bahramian
Abstract 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.
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.
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 $OT$, $OT^1_2$, $OT^t_k$.
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.