Reduction of the Intruder Deduction Problem into Equational Elementary Deduction for Electronic Purse Protocols with Blind Signatures

Abstract

Abstract. The intruder deduction problem for an electronic purse protocol with blind signatures is considered. The algebraic properties of the protocol are modeled by an equational theory implemented as a convergent rewriting system which involves rules for addition, multiplication and exponentiation. The whole deductive power of the intruder is modeled as a sequent calculus that, modulo this rewriting system, deals with blind signatures. It is proved that the associative-commutative (AC) equality of the algebraic theory can be decided in polynomial time, provided a strategy to avoid distributivity law between the AC operators is adopted. Moreover, it is also shown that the intruder deduction problem can be reduced in polynomial time to the elementary deduction problem for this equational theory.

Elementary Deduction Problem for Locally Stable Theories with Normal Forms

“…By combining the techniques in [29] and [13], the IDP formulation for an Electronic Purse Protocol with blind signatures was proved to reduce in polynomial time to EDP for an AC-convergent theory containing three different AC operators and rules for exponentiation [26], extending the previous results. However, no algorithm was provided to decide EDP.…”

“…The rule (acut), called analytic cut is necessary to prove cut rule admissibility. A complete proof can be found in [26,29].…”

“…3. In [26], it was proved that deduction in S reduces polynomially to EDP in the case of the ACconvergent equational theory EP, which contains three different AC-symbols and rules for exponentiation and cannot be split into disjoint parts. As a consequence of the results mentioned in the above remark, we can state the following result: Corollary 2.…”

“…As an alternative approach, the intruder's deduction capability is modelled inside a sequent calculus modulo a rewriting system, following the approach of [9]. Then, the IDP is reduced in polynomial time to EDP.By combining the techniques in [29] and [13], the IDP formulation for an Electronic Purse Protocol with blind signatures was proved to reduce in polynomial time to EDP for an AC-convergent theory containing three different AC operators and rules for exponentiation [26], extending the previous results. However, no algorithm was provided to decide EDP.…”