Abuse-Free Optimistic Contract Signing Using RSA for Multiuser Systems

Published Online May 2017 in MECS

• B.    Background

We are interested in the notion of abuse-freeness as defined in [1]. A protocol is abuse-free if no group of signer can prove that he holds the power to complete or abort the contract signature. Garay et al. introduce a new cryptographic object called Private Contract Signature in [1] based on ElGa- mal cryptosystem [2] and use it to define a two- party contract signing and a three-party contract signing. These constructions are proven to be fair, optimistic and abuse-free. In [3] an optimistic protocol for exchanging fairly signatures was proposed by Asokan et al.. Mukhamedov et al. proposed another optimistic MPCS for any number of signers in [4] also base on private contract signatures. Wang proposed an abuse-free, optimistic two-party contract signing in [5] using RSA and trapdoor commitment schemes [6]. Kordy et al. proved an equivalence between a mathematical sequence and the fairness of an MPCS protocol in [7], it is based on private contract signature. The obtained protocol is abuse-free, optimistic, fair and efficient because it reaches the lower bounds in terms of bandwidth and message complexity determined by Garay et al. in [8]. In [9] Mauw et al. extend the work of Kordy et al. using a labeled DAG instead of a linear sequence, and achieving as well an optimistic abuse- free fair and efficient MPCS.

• C.    Objectives

A common point to optimistic MPCS is that at some point, a commitment is exchanged before sending the signature. This paper focuses on finding an MPCS protocol which is abuse-free, optimistic and fair for any number of signers. A secondary objective is its efficiency, i.e. it has to be usable in practice without heavy computation and should stick to the RSA industry standard.

• D.    Results

In this paper, we find an alternative to Private Contract Signatures [1] using the newly discovered Certificatebased verifiably encrypted RSA signature scheme defined in [10]. We then propose an variation of the MPCS defined in [7] using this new scheme.

• II.    Related Work

We conducted a systematic review about optimistic abuse-free contract signing. Juan et el [1] used El Gamal on the Private Contract Signature object. Although the protocol [1] proposed is fair, optimistic and abuse-free, it is applicable for a maximum of 3 signers. Also, El Gamal is not today’s industry standard. Barbara et el. [7]

converted a sequence of signers to a protocol specification, which made protocols be handled equally by Trusted Third Party (TTP). Also, Barbara et el. [7] did not prove the abuse-free property. Juan et el. [8] proposed a protocol that works for more than three signers. The problem with article [8] is that it was proven unfair if there are more than four signers. Sjouke et el. proposed a protocol, but the abuse-free property was not established. Also, the author uses El Gamal, which is not today’s industry standard. In [11], the author used BLS instead of El Gamal encryption scheme and proposed a protocol which is fair, abuse-free and also optimistic. The shortcoming in article proposed by Gao et el. is that it is only applicable for two signers. Wang et el. [5], used trapdoor commitment scheme with RSA keys to propose the protocol with abuse-freeness, optimism and fairness but it is only applicable for two signers. Villar et el. [12] used partial signature scheme with a variant of Boneh-Boyen which is also fair, abuse- free and optimistic but applicable only for two signers. Juan et el.,Wang et el.,Gao et el.,Li et el., Chen et el., Villar et el., [1], [5], [8], [11], [13], [14], [12] have successfully proven existence of abuse- freeness and therefore we can say that contract signing protocols can be be abuse-free. Juan et el., Barbara et el., Sjouke et el.,Li et el.,Villar et el, [1], [8], [7], [9], [13], [12] in their articles used Private contract signature objects which have limitations either concerning with properties or number of signers, therefore Private Contract signature may not be a solution for us. From articles written by Juan et el. and Li et el., [8], [13] we can say that contract signing protocols can have properties like abuse-freeness, optimism, fairness and can also have multiple signers but if number of signers are greater than or equal to four in Juan et el.’s [8] article, the fairness property might be broken. Also in Li et el.’s article [13] El Gamal is used which is not an industry standard. From explanations given by Wang et el. and Villar et el. [5], [14] we can say that RSA is compatible with some contract signing mechanisms used today and that gives us confidence in our research. We mainly focused on the different cryptographic primitives used rather than the protocols or their efficiency. In table 1, we summarized the results of reviewed literature. We highlighted some gaps in the current protocols, and we will strive to address one in further research.

Table 1. Results overview