Title: An efficient composable 1-out-of-2 oblivious transfer scheme using vector decomposition

Authors: I. Praveen; S.S. Aravind Vishnu; M. Sethumadhavan

Addresses: Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, Tamil Nadu, India ' Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, Tamil Nadu, India ' TIFAC CORE in Cyber Security, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, Tamil Nadu, India

Abstract: A k-out-of-n oblivious transfer scheme is the interaction between a receiver and a sender where the sender possesses the messages m₁, m₂, … m_n. The receiver needs to access k messages out of the n messages. The scheme is a mechanism in which the receiver obtains no more than the messages m₁, m₂, … m_k which the receiver queried for with the indices 1, 2, … k being oblivious to the sender. We put forward a 1-out-of-2 oblivious transfer scheme. The security of our scheme is based on a decisional subspace assumption, decisional linear assumption and the computational infeasibility of vector decomposition problem a.k.a vector decomposition problem (VDP) assumption. Our scheme uses points on an elliptic curve as the ciphertext. Further, we prove the security of the proposed construction in the universal composability framework by using F_CRS - hybrid model.

Keywords: oblivious transfer; vector decomposition problem; public key cryptography; bilinear pairings; elliptic curve cryptography; hyperelliptic curves; distortion eigenvector space; universal composability.

DOI: 10.1504/IJAIP.2024.137190

International Journal of Advanced Intelligence Paradigms, 2024 Vol.27 No.2, pp.178 - 194

Received: 15 Jun 2019
Accepted: 20 Aug 2020
Published online: 05 Mar 2024 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article