186 research outputs found
Resolution of Linear Algebra for the Discrete Logarithm Problem Using GPU and Multi-core Architectures
In cryptanalysis, solving the discrete logarithm problem (DLP) is key to
assessing the security of many public-key cryptosystems. The index-calculus
methods, that attack the DLP in multiplicative subgroups of finite fields,
require solving large sparse systems of linear equations modulo large primes.
This article deals with how we can run this computation on GPU- and
multi-core-based clusters, featuring InfiniBand networking. More specifically,
we present the sparse linear algebra algorithms that are proposed in the
literature, in particular the block Wiedemann algorithm. We discuss the
parallelization of the central matrix--vector product operation from both
algorithmic and practical points of view, and illustrate how our approach has
contributed to the recent record-sized DLP computation in GF().Comment: Euro-Par 2014 Parallel Processing, Aug 2014, Porto, Portugal.
\<http://europar2014.dcc.fc.up.pt/\>
A Formal Study of the Privacy Concerns in Biometric-Based Remote Authentication Schemes
With their increasing popularity in cryptosystems, biometrics have attracted more and more attention from the information security community. However, how to handle the relevant privacy concerns remains to be troublesome. In this paper, we propose a novel security model to formalize the privacy concerns in biometric-based remote authentication schemes. Our security model covers a number of practical privacy concerns such as identity privacy and transaction anonymity, which have not been formally considered in the literature. In addition, we propose a general biometric-based remote authentication scheme and prove its security in our security model
New efficient and secure protocols for verifiable signature sharing and other applications
Quantum resource estimates for computing elliptic curve discrete logarithms
We give precise quantum resource estimates for Shor's algorithm to compute
discrete logarithms on elliptic curves over prime fields. The estimates are
derived from a simulation of a Toffoli gate network for controlled elliptic
curve point addition, implemented within the framework of the quantum computing
software tool suite LIQ. We determine circuit implementations for
reversible modular arithmetic, including modular addition, multiplication and
inversion, as well as reversible elliptic curve point addition. We conclude
that elliptic curve discrete logarithms on an elliptic curve defined over an
-bit prime field can be computed on a quantum computer with at most qubits using a quantum circuit of at most Toffoli gates. We are able to classically simulate the
Toffoli networks corresponding to the controlled elliptic curve point addition
as the core piece of Shor's algorithm for the NIST standard curves P-192,
P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to
recent resource estimates for Shor's factoring algorithm. The results also
support estimates given earlier by Proos and Zalka and indicate that, for
current parameters at comparable classical security levels, the number of
qubits required to tackle elliptic curves is less than for attacking RSA,
suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added.
ASIACRYPT 201
Threshold password-authenticated key exchange
Abstract. In most password-authenticated key exchange systems there is a single server storing password verification data. To provide some resilience against server compromise, this data typically takes the form of a one-way function of the password (and possibly a salt, or other public values), rather than the password itself. However, if the server is compromised, this password verification data can be used to perform an offline dictionary attack on the userâs password. In this paper we propose an efficient password-authenticated key exchange system involving a set of servers, in which a certain threshold of servers must participate in the authentication of a user, and in which the compromise of any fewer than that threshold of servers does not allow an attacker to perform an offline dictionary attack. We prove our system is secure in the random oracle model under the Decision Diffie-Hellman assumption against an attacker that may eavesdrop on, insert, delete, or modify messages between the user and servers, and that compromises fewer than that threshold of servers.
Discrete Logarithm in GF(2809) with FFS
International audienceThe year 2013 has seen several major complexity advances for the discrete logarithm problem in multiplicative groups of small- characteristic finite fields. These outmatch, asymptotically, the Function Field Sieve (FFS) approach, which was so far the most efficient algorithm known for this task. Yet, on the practical side, it is not clear whether the new algorithms are uniformly better than FFS. This article presents the state of the art with regard to the FFS algorithm, and reports data from a record-sized discrete logarithm computation in a prime-degree extension field
(One) Failure Is Not an Option:Bootstrapping the Search for Failures in Lattice-Based Encryption Schemes
Lattice-based encryption schemes are often subject to the possibility of decryption failures, in which valid encryptions are decrypted incorrectly. Such failures, in large number, leak information about the secret key, enabling an attack strategy alternative to pure lattice reduction. Extending the failure boosting\u27\u27 technique of D\u27Anvers et al. in PKC 2019, we propose an approach that we call directional failure boosting\u27\u27 that uses previously found failing ciphertexts\u27\u27 to accelerate the search for new ones. We analyse in detail the case where the lattice is defined over polynomial ring modules quotiented by and demonstrate it on a simple Mod-LWE-based scheme parametrized Ă la Kyber768/Saber. We show that, using our technique, for a given secret key (single-target setting), the cost of searching for additional failing ciphertexts after one or more have already been found, can be sped up dramatically. We thus demonstrate that, in this single-target model, these schemes should be designed so that it is hard to even obtain one decryption failure. Besides, in a wider security model where there are many target secret keys (multi-target setting), our attack greatly improves over the state of the art
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