Secrecy by witness-functions under equational theories

Abstract

Abstract-In this paper, we use the witness-functions to analyze cryptographic protocols for secrecy under nonempty equational theories. The witness-functions are safe metrics used to compute security. An analysis with a witness-function consists in making sure that the security of every atomic message does not decrease during its lifecycle in the protocol. The analysis gets more difficult under nonempty equational theories. Indeed, the intruder can take advantage of the algebraic properties of the cryptographic primitives to derive secrets. These properties arise from the use of mathematical functions, such as multiplication, addition, exclusive-or or modular exponentiation in the cryptosystems and the protocols. Here, we show how to use the witness-functions under nonempty equational theories and we run an analysis on the Needham-Schroeder-Lowe protocol under the cipher homomorphism. This analysis reveals that although this protocol is proved secure under the perfect encryption assumption, its security collapses under the homomorphic primitives. We show how the witness-functions help to illustrate an attack scenario on it and we propose an amended version to fix it.

Cryptographic protocol for multipart missions involving two independent and distributed decision levels in a military context

“…An example of algebraic properties may be the homomorphic property [37], [38] where {m 1 .m 2 } k is equivalent to {m 1 } k . {m 2 } k under the equational theory [34], [39], [40].…”

“…In an upcoming work, we are going to give the formal proof of the security properties assured by the proposed protocol using our recent theory called the theory of witness-functions [29]. This theory proposes a series of functions that have been successfully experimented on lots protocols and were powerful either in detecting security flaws or in proving security properties inside cryptographic protocols [30]- [34]. Originally, they were designed to prove secrecy inside protocols by proving that the level of security of every atomic message exchanged in the protocol does not decrease during its life cycle.…”