A group signature scheme based on the integer factorization and the subgroup discrete logarithm problems

8 pagesGroup signature schemes allow a user, belonging to a speci c group of users, to sign a message in an anonymous way on behalf of the group. In general, these schemes need the collaboration of a Trusted Third Party which, in case of a dispute, can reveal the identity of the real signer. A new group signature scheme is presented whose security is based on the Integer Factorization Problem (IFP) and on the Subgroup Discrete Logarithm Problem (SDLP).This work has been partially supported by the \Fundaci on Memoria D. Samuel Sol orzano Barruso" under the Project FS/7-2010.Peer reviewe

A group signature scheme based on the integer factorization and the subgroup discrete logarithm problems

8 pagesGroup signature schemes allow a user, belonging to a speci c group of users, to sign a message in an anonymous way on behalf of the group. In general, these schemes need the collaboration of a Trusted Third Party which, in case of a dispute, can reveal the identity of the real signer. A new group signature scheme is presented whose security is based on the Integer Factorization Problem (IFP) and on the Subgroup Discrete Logarithm Problem (SDLP).This work has been partially supported by the \Fundaci on Memoria D. Samuel Sol orzano Barruso" under the Project FS/7-2010.Peer reviewe

Group signatures in practice

10 páginas, 2 figuras, 1 tabla. International Joint Conference. CISIS’15 and ICEUTE’15Group signature schemes allow a user to sign a message in an anonymous way on behalf of a group. In general, these schemes need the collaboration of a Key Generation Center or a Trusted Third Party, which can disclose the identity of the actual signer if necessary (for exam- ple, in order to settle a dispute). This paper presents the results obtained after implementing a group signature scheme using the Integer Factoriza- tion Problem and the Subgroup Discrete Logarithm Problem, which has allowed us to check the feasibility of the scheme when using big numbers.This work has been partially supported under the framework of the international cooperation program managed by National Research Foundation of Korea (NRF- 2013K2A1A2053670) and by Comunidad de Madrid (Spain) under the project S2013/ICE-3095-CM (CIBERDINE).Peer reviewe

Lattice-based Blind Signatures

Motivated by the need to have secure blind signatures even in the presence of quantum computers, we present two efficient blind signature schemes based on hard worst-case lattice problems. Both schemes are provably secure in the random oracle model and unconditionally blind. The first scheme is based on preimage samplable functions that were introduced at STOC 2008 by Gentry, Peikert, and Vaikuntanathan. The scheme is stateful and runs in 3 moves. The second scheme builds upon the PKC 2008 identification scheme of Lyubashevsky. It is stateless, has 4 moves, and its security is based on the hardness of worst-case problems in ideal lattices

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

Enhancing Privacy Protection:Set Membership, Range Proofs, and the Extended Access Control

Privacy has recently gained an importance beyond the field of cryptography. In that regard, the main goal behind this thesis is to enhance privacy protection. All of the necessary mathematical and cryptographic preliminaries are introduced at the start of this thesis. We then show in Part I how to improve set membership and range proofs, which are cryptographic primitives enabling better privacy protection. Part II shows how to improve the standards for Machine Readable Travel Documents (MRTDs), such as biometric passports. Regarding set membership proofs, we provide an efficient protocol based on the Boneh-Boyen signature scheme. We show that alternative signature schemes can be used and we provide a general protocol description that can be applied for any secure signature scheme. We also show that signature schemes in our design can be replaced by cryptographic accumulators. For range proofs, we provide interactive solutions where the range is divided in a base u and the u-ary digits are handled by one of our set membership proofs. A general construction is also provided for any set membership proof. We additionally explain how to handle arbitrary ranges with either two range proofs or with an improved solution based on sumset representation. These efficient solutions achieve, to date, the lowest asymptotical communication load. Furthermore, this thesis shows that the first efficient non-interactive range proof is insecure. This thesis thus provides the first efficient and secure non-interactive range proof. In the case of MRTDs, two standards exist: one produced by the International Civil Aviation Organization (ICAO) and the other by the European Union, which is called the Extended Access Control (EAC). Although this thesis focuses on the EAC, which is supposed to solve all privacy concerns, it shows that both standards fail to provide complete privacy protection. Lastly, we provide several solutions to improve them