37 research outputs found
Refinements of Miller's Algorithm over Weierstrass Curves Revisited
In 1986 Victor Miller described an algorithm for computing the Weil pairing
in his unpublished manuscript. This algorithm has then become the core of all
pairing-based cryptosystems. Many improvements of the algorithm have been
presented. Most of them involve a choice of elliptic curves of a \emph{special}
forms to exploit a possible twist during Tate pairing computation. Other
improvements involve a reduction of the number of iterations in the Miller's
algorithm. For the generic case, Blake, Murty and Xu proposed three refinements
to Miller's algorithm over Weierstrass curves. Though their refinements which
only reduce the total number of vertical lines in Miller's algorithm, did not
give an efficient computation as other optimizations, but they can be applied
for computing \emph{both} of Weil and Tate pairings on \emph{all}
pairing-friendly elliptic curves. In this paper we extend the Blake-Murty-Xu's
method and show how to perform an elimination of all vertical lines in Miller's
algorithm during Weil/Tate pairings computation on \emph{general} elliptic
curves. Experimental results show that our algorithm is faster about 25% in
comparison with the original Miller's algorithm.Comment: 17 page
Analysing the IOBC Authenticated Encryption Mode
Abstract. The idea of combining a very simple form of added plaintext redundancy with a special mode of data encryption to provide data in-tegrity is an old one; however, despite its wide deployment in protocols such as Kerberos, it has largely been superseded by provably secure au-thenticated encryption techniques. In this paper we cryptanalyse a block cipher mode of operation called IOBC, possibly the only remaining en-cryption mode designed for such use that has not previously been ana-lyzed. We show that IOBC is subject to known-plaintext-based forgery attacks with a complexity of around 2n=3, where n is the block cipher block length.
Post-quantum cryptography
Cryptography is essential for the security of online communication, cars and implanted medical devices. However, many commonly used cryptosystems will be completely broken once large quantum computers exist. Post-quantum cryptography is cryptography under the assumption that the attacker has a large quantum computer; post-quantum cryptosystems strive to remain secure even in this scenario. This relatively young research area has seen some successes in identifying mathematical operations for which quantum algorithms offer little advantage in speed, and then building cryptographic systems around those. The central challenge in post-quantum cryptography is to meet demands for cryptographic usability and flexibility without sacrificing confidence.</p
Two-Face: New Public Key Multivariate Schemes
We present here new multivariate schemes that can be seen as HFE generalization having a property called `Two-Face\u27.
Particularly, we present five such families of algorithms named `Dob\u27, `Simple Pat\u27, `General Pat\u27, `Mac\u27, and `Super Two-Face\u27. These families have connections between them, some of them are refinements or generalizations of others. Notably, some of these schemes can be used for public key encryption, and some for public key signature. We introduce also new multivariate quadratic permutations that may have interest beyond cryptography
Failure of the Point Blinding Countermeasure Against Fault Attack in Pairing-Based Cryptography
Article published in the proceedings of the C2SI conference, May 2015.Pairings are mathematical tools that have been proven to be very useful in the construction of many cryptographic protocols. Some of these protocols are suitable for implementation on power constrained devices such as smart cards or smartphone which are subject to side channel attacks. In this paper, we analyse the efficiency of the point blinding countermeasure in pairing based cryptography against side channel attacks. In particular,we show that this countermeasure does not protect Miller's algorithm for pairing computation against fault attack. We then give recommendation for a secure implementation of a pairing based protocol using the Miller algorithm
Computing Optimal Ate Pairings on Elliptic Curves with Embedding Degree and
Much attention has been given to efficient computation of pairings on elliptic curves with even embedding degree since the advent of pairing-based cryptography. The existing few works in the case of odd embedding degrees require some improvements.
This paper considers the computation of optimal ate pairings on elliptic curves of embedding degrees k=9, 15 \mbox{ and } 27 which have twists of order three. Mainly, we provide a detailed arithmetic and cost estimation of operations in the tower extensions field of the corresponding extension fields. A good selection of parameters
enables us to improve the theoretical cost for the Miller step and the final exponentiation using the lattice-based method comparatively to the previous few works that exist in these cases. In particular for and we obtained an improvement, in terms of operations in the base field, of up to and respectively in the computation of the final exponentiation.
Also, we obtained that elliptic curves with embedding degree present faster results than BN curves at the -bit security levels.
We provided a MAGMA implementation in each case to ensure the correctness of the formulas used in this work
Efficient Elliptic Curve Diffie-Hellman Computation at the 256-bit Security Level
In this paper we introduce new Montgomery and Edwards form elliptic curve targeted at the 256-bit security level.
To this end, we work with three primes, namely , and . While has been considered earlier in the literature, and are new. We define a pair of birationally equivalent Montgomery and Edwards form curves over all the three primes. Efficient 64-bit assembly implementations targeted at Skylake and later generation Intel processors have been made for the shared secret computation phase of the Diffie-Hellman key agreement protocol for the new Montgomery curves. Curve448 of the Transport Layer Security, Version 1.3 is a Montgomery curve which provides security at the 224-bit security level. Compared to the best publicly available 64-bit implementation of Curve448, the new Montgomery curve over leads to a - slowdown and the new Montgomery curve over leads to a - slowdown; on the other hand, 29 and 30.5 extra bits of security respectively are gained. For designers aiming for the 256-bit security level, the new curves over and provide an acceptable trade-off between security and efficiency
Attribute-based encryption with granular revocation
National Research Foundation (NRF) Singapor
Analysis of Step-Reduced SHA-256
This is the first article analyzing the security of SHA-256 against fast collision search which considers the recent attacks by Wang et al. We show the limits of applying techniques known so far to SHA-256. Next we introduce a new type of perturbation vector which circumvents the identified limits. This new technique is then applied to the unmodified SHA-256. Exploiting the combination of Boolean functions and modular
addition together with the newly developed technique allows us to derive collision-producing characteristics for step-reduced SHA-256, which was not possible before. Although our results do not threaten the security of SHA-256, we show that the low probability of a single local collision may give rise to a false sense of security