A New Cryptosystem Based On Hidden Order Groups

Let $G_1$ be a cyclic multiplicative group of order $n$. It is known that the Diffie-Hellman problem is random self-reducible in $G_1$ with respect to a fixed generator $g$ if $\phi(n)$ is known. That is, given $g, g^x\in G_1$ and having oracle access to a `Diffie-Hellman Problem' solver with fixed generator $g$, it is possible to compute $g^{1/x} \in G_1$ in polynomial time (see theorem 3.2). On the other hand, it is not known if such a reduction exists when $\phi(n)$ is unknown (see conjuncture 3.1). We exploit this ``gap'' to construct a cryptosystem based on hidden order groups and present a practical implementation of a novel cryptographic primitive called an \emph{Oracle Strong Associative One-Way Function} (O-SAOWF). O-SAOWFs have applications in multiparty protocols. We demonstrate this by presenting a key agreement protocol for dynamic ad-hoc groups.Comment: removed examples for multiparty key agreement and join protocols, since they are redundan

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

An Identity-Based Group Signature with Membership Revocation in the Standard Model

Group signatures allow group members to sign an arbitrary number\ud of messages on behalf of the group without revealing their\ud identity. Under certain circumstances the group manager holding a\ud tracing key can reveal the identity of the signer from the\ud signature. Practical group signature schemes should support\ud membership revocation where the revoked member loses the\ud capability to sign a message on behalf of the group without\ud influencing the other non-revoked members. A model known as\ud \emph{verifier-local revocation} supports membership revocation.\ud In this model the trusted revocation authority sends revocation\ud messages to the verifiers and there is no need for the trusted\ud revocation authority to contact non-revoked members to update\ud their secret keys. Previous constructions of verifier-local\ud revocation group signature schemes either have a security proof in the\ud random oracle model or are non-identity based. A security proof\ud in the random oracle model is only a heuristic proof and\ud non-identity-based group signature suffer from standard Public Key\ud Infrastructure (PKI) problems, i.e. the group public key is not\ud derived from the group identity and therefore has to be certified.\ud \ud \ud In this work we construct the first verifier-local revocation group\ud signature scheme which is identity-based and which has a security proof in the standard model. In\ud particular, we give a formal security model for the proposed\ud scheme and prove that the scheme has the\ud property of selfless-anonymity under the decision Linear (DLIN)\ud assumption and it is fully-traceable under the\ud Computation Diffie-Hellman (CDH) assumption. The proposed scheme is based on prime order bilinear\ud groups

Full-resilient memory-optimum multi-party non-interactive key exchange

Multi-Party Non-Interactive Key Exchange (MP-NIKE) is a fundamental cryptographic primitive in which users register into a key generation centre and receive a public/private key pair each. After that, any subset of these users can compute a shared key without any interaction. Nowadays, IoT devices suffer from a high number and large size of messages exchanged in the Key Management Protocol (KMP). To overcome this, an MP-NIKE scheme can eliminate the airtime and latency of messages transferred between IoT devices. MP-NIKE schemes can be realized by using multilinear maps. There are several attempts for constructing multilinear maps based on indistinguishable obfuscation, lattices and the Chinese Remainder Theorem (CRT). Nevertheless, these schemes are inefficient in terms of computation cost and memory overhead. Besides, several attacks have been recently reported against CRT-based and lattice-based multilinear maps. There is only one modular exponentiation-based MP-NIKE scheme in the literature which has been claimed to be both secure and efficient. In this article, we present an attack on this scheme based on the Euclidean algorithm, in which two colluding users can obtain the shared key of any arbitrary subgroup of users. We also propose an efficient and secure MP-NIKE scheme. We show how our proposal is secure in the random oracle model assuming the hardness of the root extraction modulo a composite number

Pairing-based cryptosystems and key agreement protocols.

For a long time, pairings on elliptic curves have been considered to be destructive in elliptic curve cryptography. Only recently after some pioneering works, particularly the well-known Boneh-Franklin identity-based encryption (IBE), pairings have quickly become an important tool to construct novel cryptographic schemes. In this thesis, several new cryptographic schemes with pairings are proposed, which are both efficient and secure with respect to a properly defined security model, and some relevant previous schemes are revisited. IBE provides a public key encryption mechanism where a public key can be an arbitrary string such as an entity identifier and unwieldy certificates are unnecessary. Based on the Sakai-Kasahara key construction, an IBE scheme which is secure in the Boneh-Franklin IBE model is constructed, and two identity-based key encapsulation mechanisms are proposed. These schemes achieve the best efficiency among the existing schemes to date. Recently Al-Riyami and Paterson introduced the certificateless public key encryption (CL-PKE) paradigm, which eliminates the need of certificates and at the same time retains the desirable properties of IBE without the key escrow problem. The security formulation of CL-PKE is revisited and a strong security model for this type of mechanism is defined. Following a heuristic approach, three efficient CL-PKE schemes which are secure in the defined strong security model are proposed. Identity-based two-party key agreement protocols from pairings are also investigated. The Bellare-Rogaway key agreement model is enhanced and within the model several previously unproven protocols in the literature are formally analysed. In considering that the user identity may be sensitive information in many environments, an identity-based key agreement protocol with unilateral identity privacy is proposed

Report and Trace Ring Signatures

We introduce report and trace ring signature schemes, balancing the desire for signer anonymity with the ability to report malicious behaviour and subsequently revoke anonymity. We contribute a formal security model for report and trace ring signatures that incorporates established properties of anonymity, unforgeability and traceability, and captures a new notion of reporter anonymity. We present a construction of a report and trace ring signature scheme, proving its security and analysing its efficiency, comparing with the state of the art in the accountable ring signatures literature. Our analysis demonstrates that our report and trace scheme is efficient, particularly for the choice of cryptographic primitives that we use to instantiate our construction. We contextualise our new primitive with respect to related work, and highlight, in particular, that report and trace ring signature schemes protect the identity of the reporter even after tracing is complete