Strengthening Megrelishvili Protocol Against Man-in-the-Middle Attack

Abstract

In this paper we study the security aspect of Megrelishvili protocol—a linear algebra-based variant of the Diffie-Hellman key agreement. We demonstrate that the conventional version of this protocol is vulnerable to the man-in-the-middle attack. Hence, to avert such attack, we propose an authenticated version of this protocol using an embedded digital signature scheme. The scheme is constructed using the hardness assumption of the Megrelishvili vector-matrix problem (MVMP)—the underlying computational problem for the security of the conventional Megrelishvili protocol. We prove the correctness of the signature scheme and argue that our proposed protocol is secure against the man-in-the-middle attack provided that the MVMP is intractable.