Certificate Transparency with Enhancements and Short Proofs

Browsers can detect malicious websites that are provisioned with forged or fake TLS/SSL certificates. However, they are not so good at detecting malicious websites if they are provisioned with mistakenly issued certificates or certificates that have been issued by a compromised certificate authority. Google proposed certificate transparency which is an open framework to monitor and audit certificates in real time. Thereafter, a few other certificate transparency schemes have been proposed which can even handle revocation. All currently known constructions use Merkle hash trees and have proof size logarithmic in the number of certificates/domain owners. We present a new certificate transparency scheme with short (constant size) proofs. Our construction makes use of dynamic bilinear-map accumulators. The scheme has many desirable properties like efficient revocation, low verification cost and update costs comparable to the existing schemes. We provide proofs of security and evaluate the performance of our scheme.Comment: A preliminary version of the paper was published in ACISP 201

Type 2 Structure-Preserving Signature Schemes Revisited

Abstract. Abe, Groth, Ohkubo and Tibouchi recently presented structure-preserving signature schemes using Type 2 pairings. The schemes are claimed to enjoy the fastest signature verification. By properly accounting for subgroup membership testing of group elements in signatures, we show that the schemes are not as efficient as claimed. We presen

Extended Tower Number Field Sieve with Application to Finite Fields of Arbitrary Composite Extension Degree

We propose a generalization of exTNFS algorithm recently introduced by Kim and Barbulescu (CRYPTO 2016). The algorithm, exTNFS, is a state-of-the-art algorithm for discrete logarithm in $\mathbb{F}_{p^n}$ in the medium prime case, but it only applies when $n=\eta\kappa$ is a composite with nontrivial factors $\eta$ and $\kappa$ such that $\gcd(\eta,\kappa)=1$. Our generalization, however, shows that exTNFS algorithm can be also adapted to the setting with an arbitrary composite $n$ maintaining its best asymptotic complexity. We show that one can solve discrete logarithm in medium case in the running time of $L_{p^n}(1/3, \sqrt[3]{48/9})$ (resp. $L_{p^n}(1/3, 1.71)$ if multiple number fields are used), where $n$ is an \textit{arbitrary composite}. This should be compared with a recent variant by Sarkar and Singh (Asiacrypt 2016) that has the fastest running time of $L_{p^n}(1/3, \sqrt[3]{64/9})$ (resp. $L_{p^n}(1/3, 1.88)$) when $n$ is a power of prime 2. When $p$ is of special form, the complexity is further reduced to $L_{p^n}(1/3, \sqrt[3]{32/9})$. On the practical side, we emphasize that the keysize of pairing-based cryptosystems should be updated following to our algorithm if the embedding degree $n$ remains composite

A New Family of Pairing-Friendly elliptic curves

International audienceThere have been recent advances in solving the finite extension field discrete logarithm problem as it arises in the context of pairing-friendly elliptic curves. This has lead to the abandonment of approaches based on supersingular curves of small characteristic, and to the reconsideration of the field sizes required for implementation based on non-supersingular curves of large characteristic. This has resulted in a revision of recommendations for suitable curves, particularly at a higher level of security. Indeed for a security level of 256 bits, the BLS48 curves have been suggested, and demonstrated to be superior to other candidates. These curves have an embedding degree of 48. The well known taxonomy of Freeman, Scott and Teske only considered curves with embedding degrees up to 50. Given some uncertainty around the constants that apply to the best discrete logarithm algorithm, it would seem to be prudent to push a little beyond 50. In this note we announce the discovery of a new family of pairing friendly elliptic curves which includes a new construction for a curve with an embedding degree of 54

Who let the DOGS out: Anonymous but Auditable communications using Group Signature schemes with Distributed Opening

Over the past two decades, group signature schemes have been developed and used to enable authenticated and anonymous peer-to-peer communications. Initial protocols rely on two main authorities, Issuer and Opener, which are given substantial capabilities compared to (regular) participants, such as the ability to arbitrarily identify users. Building efficient, fast, and short group signature schemes has been the focus of a large number of research contributions. However, only a few dealt with the major privacy-preservation challenge of group signatures; this consists in providing user anonymity and action traceability while not necessarily relying on a central and fully trusted authority. In this paper, we present DOGS, a privacy-preserving Blockchain-supported group signature scheme with a distributed Opening functionality. In DOGS, participants no longer depend on the Opener entity to identify the signer of a potentially fraudulent message; they instead collaborate and perform this auditing process themselves. We provide a high-level description of the DOGS scheme and show that it provides both user anonymity and action traceability. Additionally, we prove how DOGS is secure against message forgery and anonymity attacks

Solving discrete logarithms on a 170-bit MNT curve by pairing reduction

Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances are built over finite fields of large characteristic and their security relies on the fact that the embedding field of the underlying curve is relatively large. How large is debatable. The aim of our work is to sustain the claim that the combination of degree 3 embedding and too small finite fields obviously does not provide enough security. As a computational example, we solve the DLP on a 170-bit MNT curve, by exploiting the pairing embedding to a 508-bit, degree-3 extension of the base field.Comment: to appear in the Lecture Notes in Computer Science (LNCS

Exponentiating in Pairing Groups

We study exponentiations in pairing groups for the most common security levels and show that, although the Weierstrass model is preferable for pairing computation, it can be worthwhile to map to alternative curve representations for the non-pairing group operations in protocols

Secure Key Encapsulation Mechanism with Compact Ciphertext and Public Key from Generalized Srivastava code

Code-based public key cryptosystems have been found to be an interesting option in the area of Post-Quantum Cryptography. In this work, we present a key encapsulation mechanism (KEM) using a parity check matrix of the Generalized Srivastava code as the public key matrix. Generalized Srivastava codes are privileged with the decoding technique of Alternant codes as they belong to the family of Alternant codes. We exploit the dyadic structure of the parity check matrix to reduce the storage of the public key. Our encapsulation leads to a shorter ciphertext as compared to DAGS proposed by Banegas et al. in Journal of Mathematical Cryptology which also uses Generalized Srivastava code. Our KEM provides IND-CCA security in the random oracle model. Also, our scheme can be shown to achieve post-quantum security in the quantum random oracle model

Public cloud data auditing with practical key update and zero knowledge privacy

Data integrity is extremely important for cloud based storage services, where cloud users no longer have physical possession of their outsourced files. A number of data auditing mechanisms have been proposed to solve this problem. However, how to update a cloud user\u27s private auditing key (as well as the authenticators those keys are associated with) without the user\u27s re-possession of the data remains an open problem. In this paper, we propose a key-updating and authenticator-evolving mechanism with zero-knowledge privacy of the stored files for secure cloud data auditing, which incorporates zero knowledge proof systems, proxy re-signatures and homomorphic linear authenticators. We instantiate our proposal with the state-of-the-art Shacham-Waters auditing scheme. When the cloud user needs to update his key, instead of downloading the entire file and re-generating all the authenticators, the user can just download and update the authenticators. This approach dramatically reduces the communication and computation cost while maintaining the desirable security. We formalize the security model of zero knowledge data privacy for auditing schemes in the key-updating context and prove the soundness and zero-knowledge privacy of the proposed construction. Finally, we analyze the complexity of communication, computation and storage costs of the improved protocol which demonstrates the practicality of the proposal

More results on Shortest Linear Programs

At the FSE conference of ToSC 2018, Kranz et al. presented their results on shortest linear programs for the linear layers of several well known block ciphers in literature. Shortest linear programs are essentially the minimum number of 2-input xor gates required to completely describe a linear system of equations. In the above paper the authors showed that the commonly used metrics like d-xor/s-xor count that are used to judge the ``lightweightedness\u27\u27 do not represent the minimum number of xor gates required to describe a given MDS matrix. In fact they used heuristic based algorithms of Boyar/Peralta and Paar to find implementations of MDS matrices with even fewer xor gates than was previously known. They proved that the AES mixcolumn matrix can be implemented with as little as 97 xor gates. In this paper we show that the values reported in the above paper are not optimal. By suitably including random bits in the instances of the above algorithms we can achieve implementations of almost all matrices with lesser number of gates than were reported in the above paper. As a result we report an implementation of the AES mixcolumn matrix that uses only 95 xor gates. In the second part of the paper, we observe that most standard cell libraries contain both 2 and 3-input xor gates, with the silicon area of the 3-input xor gate being smaller than the sum of the areas of two 2-input xor gates. Hence when linear circuits are synthesized by logic compilers (with specific instructions to optimize for area), most of them would return a solution circuit containing both 2 and 3-input xor gates. Thus from a practical point of view, reducing circuit size in presence of these gates is no longer equivalent to solving the shortest linear program. In this paper we show that by adopting a graph based heuristic it is possible to convert a circuit constructed with 2-input xor gates to another functionally equivalent circuit that utilizes both 2 and 3-input xor gates and occupies less hardware area. As a result we obtain more lightweight implementations of all the matrices listed in the ToSC paper