Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page

Pairing-based identification schemes

We propose four different identification schemes that make use of bilinear pairings, and prove their security under certain computational assumptions. Each of the schemes is more efficient and/or more secure than any known pairing-based identification scheme

Supporting Non-membership Proofs with Bilinear-map Accumulators

In this short note, we present an extension of Nguyen\u27s bilinear-map based accumulator scheme to support \emph{non-membership witnesses} and corresponding \emph{non-membership proofs}, i.e., cryptographic proofs that an element has not been accumulated to a given set. This complements the non-membership proofs developed by Li \emph{et al.} for the RSA accumulator, making the functionality of the bilinear-map accumulator equivalent to that of the RSA accumulator. Our non-membership extension of Nguyen\u27s scheme makes use of the $q$-Strong Diffie-Hellman assumption the security of the original scheme is based on

Signcryption schemes with threshold unsigncryption, and applications

The final publication is available at link.springer.comThe goal of a signcryption scheme is to achieve the same functionalities as encryption and signature together, but in a more efficient way than encrypting and signing separately. To increase security and reliability in some applications, the unsigncryption phase can be distributed among a group of users, through a (t, n)-threshold process. In this work we consider this task of threshold unsigncryption, which has received very few attention from the cryptographic literature up to now (maybe surprisingly, due to its potential applications). First we describe in detail the security requirements that a scheme for such a task should satisfy: existential unforgeability and indistinguishability, under insider chosen message/ciphertext attacks, in a multi-user setting. Then we show that generic constructions of signcryption schemes (by combining encryption and signature schemes) do not offer this level of security in the scenario of threshold unsigncryption. For this reason, we propose two new protocols for threshold unsigncryption, which we prove to be secure, one in the random oracle model and one in the standard model. The two proposed schemes enjoy an additional property that can be very useful. Namely, the unsigncryption protocol can be divided in two phases: a first one where the authenticity of the ciphertext is verified, maybe by a single party; and a second one where the ciphertext is decrypted by a subset of t receivers, without using the identity of the sender. As a consequence, the schemes can be used in applications requiring some level of anonymity, such as electronic auctions.Peer ReviewedPostprint (author's final draft

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

Two-sources Randomness Extractors for Elliptic Curves

This paper studies the task of two-sources randomness extractors for elliptic curves defined over finite fields $K$, where $K$ can be a prime or a binary field. In fact, we introduce new constructions of functions over elliptic curves which take in input two random points from two differents subgroups. In other words, for a ginven elliptic curve $E$ defined over a finite field $\mathbb{F}_q$ and two random points $P \in \mathcal{P}$ and $Q\in \mathcal{Q}$, where $\mathcal{P}$ and $\mathcal{Q}$ are two subgroups of $E(\mathbb{F}_q)$, our function extracts the least significant bits of the abscissa of the point $P\oplus Q$ when $q$ is a large prime, and the $k$-first $\mathbb{F}_p$ coefficients of the asbcissa of the point $P\oplus Q$ when $q = p^n$, where $p$ is a prime greater than $5$. We show that the extracted bits are close to uniform. Our construction extends some interesting randomness extractors for elliptic curves, namely those defined in \cite{op} and \cite{ciss1,ciss2}, when $\mathcal{P} = \mathcal{Q}$. The proposed constructions can be used in any cryptographic schemes which require extraction of random bits from two sources over elliptic curves, namely in key exchange protole, design of strong pseudo-random number generators, etc

Anonymous Single-Sign-On for n designated services with traceability

Anonymous Single-Sign-On authentication schemes have been proposed to allow users to access a service protected by a verifier without revealing their identity which has become more important due to the introduction of strong privacy regulations. In this paper we describe a new approach whereby anonymous authentication to different verifiers is achieved via authorisation tags and pseudonyms. The particular innovation of our scheme is authentication can only occur between a user and its designated verifier for a service, and the verification cannot be performed by any other verifier. The benefit of this authentication approach is that it prevents information leakage of a user's service access information, even if the verifiers for these services collude which each other. Our scheme also supports a trusted third party who is authorised to de-anonymise the user and reveal her whole services access information if required. Furthermore, our scheme is lightweight because it does not rely on attribute or policy-based signature schemes to enable access to multiple services. The scheme's security model is given together with a security proof, an implementation and a performance evaluation.Comment: 3

Keyword-Based Delegable Proofs of Storage

Cloud users (clients) with limited storage capacity at their end can outsource bulk data to the cloud storage server. A client can later access her data by downloading the required data files. However, a large fraction of the data files the client outsources to the server is often archival in nature that the client uses for backup purposes and accesses less frequently. An untrusted server can thus delete some of these archival data files in order to save some space (and allocate the same to other clients) without being detected by the client (data owner). Proofs of storage enable the client to audit her data files uploaded to the server in order to ensure the integrity of those files. In this work, we introduce one type of (selective) proofs of storage that we call keyword-based delegable proofs of storage, where the client wants to audit all her data files containing a specific keyword (e.g., "important"). Moreover, it satisfies the notion of public verifiability where the client can delegate the auditing task to a third-party auditor who audits the set of files corresponding to the keyword on behalf of the client. We formally define the security of a keyword-based delegable proof-of-storage protocol. We construct such a protocol based on an existing proof-of-storage scheme and analyze the security of our protocol. We argue that the techniques we use can be applied atop any existing publicly verifiable proof-of-storage scheme for static data. Finally, we discuss the efficiency of our construction.Comment: A preliminary version of this work has been published in International Conference on Information Security Practice and Experience (ISPEC 2018