On the Theory and Practice of Personal Digital Signatures

(Full version of a PKC 2009 paper) We take a step towards a more realistic modeling of personal digital signatures, where a human user, his mobile equipment, his PC and a server are all considered as independent players in the protocol, and where only the human user is assumed incorruptible. We then propose a protocol for issuing digital signatures on behalf of the user. This protocol is proactively UC-secure assuming at most one player is corrupted in every operational phase. In more practical terms, this means that one can securely sign using terminals (PC’s) that are not necessarily trusted, as long as the mobile unit and the PC are not both corrupted at the same time. In other words, our solution cannot be broken by phising or key-logging via the PC. The protocol allows for mobile units with very small computing power by securely outsourcing computation to the PC and also allows usage of any PC that can communicate properly. Finally, we report on the results of a prototype implementation of our solution

Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting

The problem of generating an RSA composite in a distributed manner without leaking its factorization is particularly challenging and useful in many cryptographic protocols. Our first contribution is the first non-generic fully simulatable protocol for distributively generating an RSA composite with security against malicious behavior. Our second contribution is complete Paillier [Pai99] threshold encryption scheme in the two-party setting with security against malicious behavior. Furthermore, we describe how to extend our protocols to the multiparty setting with dishonest majority. Our RSA key generation is comprised of the following: (i) a distributed protocol for generation of an RSA composite, and (ii) a biprimality test for verifying the validity of the generated composite. Our Paillier threshold encryption scheme uses the RSA composite as public key and is comprised of: (i) a distributed generation of the corresponding secret-key shares and, (ii) a distributed decryption protocol for decrypting according to Paillier

Formal Treatment of Privacy-Enhancing Credential Systems

Privacy-enhancing attribute-based credentials (PABCs) are the core ingredient to privacy-friendly authentication systems, allowing users to obtain credentials on attributes and prove possession of these credentials in an unlinkable fashion while revealing only a subset of the attributes. To be useful in practice, however, PABCs typically need additional features such as i) revocation, ii) pooling prevention by binding credentials to users\u27 secret keys, iii) pseudonyms as privacy-friendly user public keys, iv) proving equality of attributes without revealing their values, v) or advanced issuance where attributes can be blindly carried over into new credentials. Provably secure solutions exist for most of these features in isolation, but it is unclear how they can be securely combined into a full-fledged PABC system, or even which properties such a system would aim to fulfill. We provide a formal treatment of PABC systems supporting the mentioned features by defining their syntax and security properties, resulting in the most comprehensive definitional framework for PABCs so far. Unlike previous efforts, our definitions are not targeted at one specific use-case; rather, we try to capture generic properties that can be useful in a variety of scenarios. We believe that our definitions can also be used as a starting point for diverse application-dependent extensions and variations of PABCs. We present and prove secure a generic and modular construction of a PABC system from simpler building blocks, allowing for a plug-and-play composition based on different instantiations of the building blocks. Finally, we give secure instantiations for each of the building blocks, including in particular instantiations based on CL- and Brands-signatures which are the core of the Idemix and U-Prove protocols

Efficient Threshold Zero-Knowledge with Applications to User-Centric Protocols

In this paper, we investigate on threshold proofs, a framework for distributing the prover’s side of interactive proofs of knowledge over multiple parties. Interactive proofs of knowledge (PoK) are widely used primitives of cryptographic protocols, including important user-centric protocols, such as identification schemes, electronic cash (e-cash), and anonymous credentials. We present a security model for threshold proofs of knowledge and develop threshold versions of well-known primitives such as range proofs, zero-knowledge proofs for preimages of homomorphisms (which generalizes PoKs of discrete logarithms, representations, p-th roots, etc.), as well as OR statements. These building blocks are proven secure in our model. Furthermore, we apply the developed primitives and techniques in the context of user-centric protocols. In particular, we construct distributed-user variants of Brands ’ e-cash system and the bilinear anonymous credential scheme by Camenisch and Lysyanskaya. Distributing the user party in such protocols has several practical advantages: First, the security of a user can be increased by sharing secrets and computations over multiple devices owned by the user. In this way, losing control of a single device does not result in a security breach. Second, this approach also allows groups of users to jointly control an application (e.g., a joint e-cash account), not giving a single user full control. The distributed versions of the protocols we propose in this paper are relatively efficient (when compared to a general MPC approach). In comparison to the original protocols only the prover’s (or user’s) side is modified while the other side stays untouched. In particular, it is oblivious to the other party whether it interacts with a distributed prover (or user) or one as defined in the original protocol