Improvement of a convertible undeniable partially blind signature scheme

Undeniable signatures are the digital signatures that should be verified with the help of the signer. A signer may disavow a genuine document, if the signature is only verifiable with the aid of the signer under the condition that the signer is not honest. Undeniable signatures solve this problem by adding a new feature called the disavowal protocol in addition to the normal components of signature and verification. Disavowal protocol is able to prevent a dishonest signer from disavowing a valid signature. In some situations, an undeniable signature should be converted into a normal digital signature in order that the signature can be universally verified. Blind signatures are the digital signatures that help a user to get a signature on a message without revealing the content of the message to a signer. For the blind signatures, if the signer is able to make an agreement with the user, then the underlying signer may include some common information that is known to the user, then such signatures are partially blind signatures. Convertible undeniable partially blind signatures are of the features of undeniable signatures, blind signatures, convertible undeniable signatures, and partially blind signatures. Recently, a convertible undeniable partially blind signature scheme was presented. In this paper, we first analyse a security flaw of the convertible undeniable partially blind signature scheme. To address the security flaw, we present an improvement on the disavowal protocol. The improved scheme can prevent the signer from either proving that a given valid signature as invalid, or cheating the verifier

Practical fair anonymous undeniable signatures

We present a new model for undeniable signatures: fair-anonymous undeniable signatures. This protocol can not only preserve the privacy of the signer (i.e. anonymity) but also track the illegal utilization of the valid signatures. In addition, our model prevents the trusted centre from forging a valid signature for any signer

Design and Analysis of Opaque Signatures

Digital signatures were introduced to guarantee the authenticity and integrity of the underlying messages. A digital signature scheme comprises the key generation, the signature, and the verification algorithms. The key generation algorithm creates the signing and the verifying keys, called also the signer’s private and public keys respectively. The signature algorithm, which is run by the signer, produces a signature on the input message. Finally, the verification algorithm, run by anyone who knows the signer’s public key, checks whether a purported signature on some message is valid or not. The last property, namely the universal verification of digital signatures is undesirable in situations where the signed data is commercially or personally sensitive. Therefore, mechanisms which share most properties with digital signatures except for the universal verification were invented to respond to the aforementioned need; we call such mechanisms “opaque signatures”. In this thesis, we study the signatures where the verification cannot be achieved without the cooperation of a specific entity, namely the signer in case of undeniable signatures, or the confirmer in case of confirmer signatures; we make three main contributions. We first study the relationship between two security properties important for public key encryption, namely data privacy and key privacy. Our study is motivated by the fact that opaque signatures involve always an encryption layer that ensures their opacity. The properties required for this encryption vary according to whether we want to protect the identity (i.e. the key) of the signer or hide the validity of the signature. Therefore, it would be convenient to use existing work about the encryption scheme in order to derive one notion from the other. Next, we delve into the generic constructions of confirmer signatures from basic cryptographic primitives, e.g. digital signatures, encryption, or commitment schemes. In fact, generic constructions give easy-to-understand and easy-to-prove schemes, however, this convenience is often achieved at the expense of efficiency. In this contribution, which constitutes the core of this thesis, we first analyze the already existing constructions; our study concludes that the popular generic constructions of confirmer signatures necessitate strong security assumptions on the building blocks, which impacts negatively the efficiency of the resulting signatures. Next, we show that a small change in these constructionsmakes these assumptions drop drastically, allowing as a result constructions with instantiations that compete with the dedicated realizations of these signatures. Finally, we revisit two early undeniable signatures which were proposed with a conjectural security. We disprove the claimed security of the first scheme, and we provide a fix to it in order to achieve strong security properties. Next, we upgrade the second scheme so that it supports a iii desirable feature, and we provide a formal security treatment of the new scheme: we prove that it is secure assuming new reasonable assumptions on the underlying constituents

Universally Convertible Directed Signatures

Many variants of Chaum and van Antwerpen's undeniable signatures have been proposed to achieve specific properties desired in real-world applications of cryptography. Among them, directed signatures were introduced by Lim and Lee in 1993. Directed signatures differ from the well-known confirmer signatures in that the signer has the simultaneous abilities to confirm, deny and individually convert a signature. The universal conversion of these signatures has remained an open problem since their introduction in 1993. This paper provides a positive answer to this quest by showing a very efficient design for universally convertible directed signatures (UCDS) both in terms of computational complexity and signature size. Our construction relies on the so-called xyz-trick applicable to bilinear map groups. We define proper security notions for UCDS schemes and show that our construction is secure, in the random oracle model, under computational assumptions close to the CDH and DDH assumptions. Finally, we introduce and realize traceable universally convertible directed signatures where a master tracing key allows to link signatures to their direction

How to avoid repetitions in lattice-based deniable zero-knowledge proofs

Interactive zero-knowledge systems are a very important cryptographic primitive, used in many applications, especially when deniability (also known as non-transferability) is desired. In the lattice-based setting, the currently most efficient interactive zero-knowledge systems employ the technique of rejection sampling, which implies that the interaction does not always finish correctly in the first execution; the whole interaction must be re-run until abort does not happen. While repetitions due to aborts are acceptable in theory, in some practical applications it is desirable to avoid re-runs for usability reasons. In this work we present a generic technique that departs from an interactive zero-knowledge system (that might require multiple re-runs to complete the protocol) and obtains a 3-moves zero-knowledge system (without re-runs). The transformation combines the well-known Fiat-Shamir technique with a couple of initially exchanged messages. The resulting 3-moves system enjoys honest-verifier zero-knowledge and can be easily turned into a fully deniable proof using standard techniques. We show some practical scenarios where our transformation can be beneficial and we also discuss the results of an implementation of our transformation.Preprin

Further discussions on the security of a nominative signature scheme

A nominative signature scheme allows a nominator (or signer) and a nominee (or veri¯er) to jointly generate and publish a signature in such a way that only the nominee can verify the signature and if nec- essary, only the nominee can prove to a third party that the signature is valid. In a recent work, Huang and Wang proposed a new nominative signature scheme which, in addition to the above properties, only allows the nominee to convert a nominative signature to a publicly veri¯able one. In ACISP 2005, Susilo and Mu presented several algorithms and claimed that these algorithms can be used by the nominator to verify the validity of a published nominative signature, show to a third party that the signature is valid, and also convert the signature to a publicly veri¯able one, all without any help from the nominee. In this paper, we point out that Susilo and Mu\u27s attacks are actually incomplete and in- accurate. In particular, we show that there exists no e±cient algorithm for a nominator to check the validity of a signature if this signature is generated by the nominator and the nominee honestly and the Decisional Di±e-Hellman Problem is hard. On the other hand, we point out that the Huang-Wang scheme is indeed insecure, since there is an attack that allows the nominator to generate valid nominative signatures alone and prove the validity of such signatures to a third party

Short undeniable signatures:design, analysis, and applications

Digital signatures are one of the main achievements of public-key cryptography and constitute a fundamental tool to ensure data authentication. Although their universal verifiability has the advantage to facilitate their verification by the recipient, this property may have undesirable consequences when dealing with sensitive and private information. Motivated by such considerations, undeniable signatures, whose verification requires the cooperation of the signer in an interactive way, were invented. This thesis is mainly devoted to the design and analysis of short undeniable signatures. Exploiting their online property, we can achieve signatures with a fully scalable size depending on the security requirements. To this end, we develop a general framework based on the interpolation of group elements by a group homomorphism, leading to the design of a generic undeniable signature scheme. On the one hand, this paradigm allows to consider some previous undeniable signature schemes in a unified setting. On the other hand, by selecting group homomorphisms with a small group range, we obtain very short signatures. After providing theoretical results related to the interpolation of group homomorphisms, we develop some interactive proofs in which the prover convinces a verifier of the interpolation (resp. non-interpolation) of some given points by a group homomorphism which he keeps secret. Based on these protocols, we devise our new undeniable signature scheme and prove its security in a formal way. We theoretically analyze the special class of group characters on Z*n. After studying algorithmic aspects of the homomorphism evaluation, we compare the efficiency of different homomorphisms and show that the Legendre symbol leads to the fastest signature generation. We investigate potential applications based on the specific properties of our signature scheme. Finally, in a topic closely related to undeniable signatures, we revisit the designated confirmer signature of Chaum and formally prove the security of a generalized version

Efficient Deniable Authentication for Signatures, Application to Machine-Readable Travel Document

Releasing a classical digital signature faces to privacy issues. Indeed, there are cases where the prover needs to authenticate some data without making it possible for any malicious verifier to transfer the proof to anyone else. It is for instance the case for e-passports where the signature from the national authority authenticates personal data. To solve this problem, we can prove knowledge of a valid signature without revealing it. This proof should be non-transferable. We first study deniability for signature verification. Deniability is essentially a weaker form of non-transferability. It holds as soon as the protocol is finished (it is often called offline non-transferability). We introduce Offline Non-Transferable Authentication Protocol (ON-TAP) and we show that it can be built by using a classical signature scheme and a deniable zero-knowledge proof of knowledge. For that reason, we use a generic transform for Σ-protocols. Finally, we give examples to upgrade signature standards based on RSA or ElGamal into an ONTAP. Our examples are well-suited for implementation in e-passports

Strong Designated Verifier Signature Schemes with Undeniable Property and Their Applications

Most of the strong designated verifier signature (SDVS) schemes cannot tell the real signature generator when the signer and the designated verifier dispute on a signature. In other words, most of the SDVS schemes do not have the undeniability property. In this paper, we propose two SDVS schemes which hold the undeniability property, namely, strong designated verifier signature with undeniability property (SDVSUP). Our two schemes are called SDVSUP-1 and SDVSUP-2. In our two SDVSUP schemes, the signer not only can designate a verifier but also can designate an arbiter who can judge the signature when the signer and the designated verifier dispute on the signature. What is more, the judgment procedure can be performed by the arbiter alone without help from the signer or the designated verifier, which increases the judgment efficiency and reduces the complexity of signature confirmation. We also demonstrate a real instance of applying our SDVSUP scheme to electronic bidding system