The zheng-seberry public key cryptosystem and signcryption

In 1993 Zheng-Seberry presented a public key cryptosystem that was considered efficient and secure in the sense of indistinguishability of encryptions (IND) against an adaptively chosen ciphertext adversary (CCA2). This thesis shows the Zheng-Seberry scheme is not secure as a CCA2 adversary can break the scheme in the sense of IND. In 1998 Cramer-Shoup presented a scheme that was secure against an IND-CCA2 adversary and whose proof relied only on standard assumptions. This thesis modifies this proof and applies it to a modified version of the El-Gamal scheme. This resulted in a provably secure scheme relying on the Random Oracle (RO) model, which is more efficient than the original Cramer-Shoup scheme. Although the RO model assumption is needed for security of this new El-Gamal variant, it only relies on it in a minimal way

Contributions to Lattice–based Cryptography

Post–quantum cryptography (PQC) is a new and fast–growing part of Cryptography. It focuses on developing cryptographic algorithms and protocols that resist quantum adversaries (i.e., the adversaries who have access to quantum computers). To construct a new PQC primitive, a designer must use a mathematical problem intractable for the quantum adversary. Many intractability assumptions are being used in PQC. There seems to be a consensus in the research community that the most promising are intractable/hard problems in lattices. However, lattice–based cryptography still needs more research to make it more efficient and practical. The thesis contributes toward achieving either the novelty or the practicality of lattice– based cryptographic systems

Faster computation of the Tate pairing

This paper proposes new explicit formulas for the doubling and addition step in Miller's algorithm to compute the Tate pairing. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the first geometric interpretation of the group law on Edwards curves by presenting the functions which arise in the addition and doubling. Computing the coefficients of the functions and the sum or double of the points is faster than with all previously proposed formulas for pairings on Edwards curves. They are even competitive with all published formulas for pairing computation on Weierstrass curves. We also speed up pairing computation on Weierstrass curves in Jacobian coordinates. Finally, we present several examples of pairing-friendly Edwards curves.Comment: 15 pages, 2 figures. Final version accepted for publication in Journal of Number Theor

Identification and Privacy: Zero-Knowledge is not Enough

At first glance, privacy and zero-knowledgeness seem to be similar properties. A scheme is private when no information is revealed on the prover and in a zero-knowledge scheme, communications should not leak provers\u27 secrets. Until recently, privacy threats were only partially formalized and some zero-knowledge (ZK) schemes have been proposed so far to ensure privacy. We here explain why the intended goal is not reached. Following the privacy model proposed by Vaudenay at Asiacrypt 2007, we then reconsider the analysis of these schemes and thereafter introduce a general framework to modify identification schemes leading to different levels of privacy. Our new protocols can be useful, for instance, for identity documents, where privacy is a great issue. Furthermore, we propose efficient implementations of zero-knowledge and private identification schemes based on modifications of the GPS scheme. The security and the privacy are based on a new problem: the Short Exponent Strong Diffie-Hellman (SESDH) problem. The hardness of this problem is related to the hardness of the Strong Diffie-Hellman (SDH) problem and to the hardness of the Discrete Logarithm with Short Exponent (DLSE) problem. The security and privacy of these new schemes are proved in the random oracle paradigm

Contextualizing Alternative Models of Secret Sharing

A secret sharing scheme is a means of distributing information to a set of players such that any authorized subset of players can recover a secret and any unauthorized subset does not learn any information about the secret. In over forty years of research in secret sharing, there has been an emergence of new models and extended capabilities of secret sharing schemes. In this thesis, we study various models of secret sharing and present them in a consistent manner to provide context for each definition. We discuss extended capabilities of secret sharing schemes, including a comparison of methods for updating secrets via local computations on shares and an analysis of approaches to reproducing/repairing shares. We present an analysis of alternative adversarial settings which have been considered in the area of secret sharing. In this work, we present a formalization of a deniability property which is inherent to some classical secret sharing schemes. We provide new, game-based definitions for different notions of verifiability and robustness. By using consistent terminology and similar game-based definitions, we are able to demystify the subtle differences in each notion raised in the literature

Dynamic Threshold Public-Key Encryption

The original publication is available at www.springerlink.comInternational audienceThis paper deals with threshold public-key encryption which allows a pool of players to decrypt a ciphertext if a given threshold of authorized players cooperate. We generalize this primitive to the dynamic setting, where any user can dynamically join the system, as a possible recipient; the sender can dynamically choose the authorized set of recipients, for each ciphertext; and the sender can dynamically set the threshold t for decryption capability among the authorized set. We first give a formal security model, which includes strong robustness notions, and then we propose a candidate achieving all the above dynamic properties, that is semantically secure in the standard model, under a new non-interactive assumption, that fits into the general Diffie-Hellman exponent framework on groups with a bilinear map. It furthermore compares favorably with previous proposals, a.k.a. threshold broadcast encryption, since this is the first threshold public-key encryption, with dynamic authorized set of recipients and dynamic threshold that provides constant-size ciphertexts

Group key exchange protocols withstanding ephemeral-key reveals

When a group key exchange protocol is executed, the session key is typically extracted from two types of secrets; long-term keys (for authentication) and freshly generated (often random) values. The leakage of this latter so-called ephemeral keys has been extensively analyzed in the 2-party case, yet very few works are concerned with it in the group setting. We provide a generic {group key exchange} construction that is strongly secure, meaning that the attacker is allowed to learn both long-term and ephemeral keys (but not both from the same participant, as this would trivially disclose the session key). Our design can be seen as a compiler, in the sense that it builds on a 2-party key exchange protocol which is strongly secure and transforms it into a strongly secure group key exchange protocol by adding only one extra round of communication. When applied to an existing 2-party protocol from Bergsma et al., the result is a 2-round group key exchange protocol which is strongly secure in the standard model, thus yielding the first construction with this property

On Session Key Construction in Provably-Secure Key Establishment Protocols: Revisiting Chen & Kudla (2003) and McCullagh & Barreto (2005) ID-Based Protocols

We examine the role of session key construction in provably- secure key establishment protocols. We revisit an ID-based key establishment protocol due to Chen & Kudla (2003) and an ID-based protocol 2P-IDAKA due to McCullagh & Barreto (2005). Both protocols carry proofs of security in a weaker variant of the Bellare & Rogaway (1993) model where the adversary is not allowed to make any Reveal query. We advocate the importance of such a (Reveal) query as it captures the known-key security requirement. We then demonstrate that a small change to the way that session keys are constructed in both protocols results in these protocols being secure without restricting the adversary from asking the Reveal queries in most situations. We point out some errors in the existing proof for protocol 2P-IDAKA, and provide proof sketches for the improved Chen & Kudla\u27s protocol. We conclude with a brief discussion on ways to construct session keys in key establishment protocols