International Association for Cryptologic Research

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2014-10-12
00:17 [Pub][ePrint]

Cayley hash functions are based on a simple idea of using a pair of

(semi)group elements, $A$ and $B$, to hash the 0 and 1 bit, respectively, and then to hash an arbitrary bit string in the natural way, by using multiplication of elements in the (semi)group. In this paper, we focus on hashing with $2 \\times 2$ matrices over $F_p$. Since there are many known pairs of $2 \\times 2$ matrices over $Z$ that generate a free monoid, this yields numerous pairs of matrices over $F_p$, for a sufficiently large prime $p$, that are candidates for collision-resistant hashing. However, this trick can backfire\", and lifting matrix entries to $Z$ may facilitate finding a collision. This lifting attack\" was successfully used by Tillich and Z\\\'emor in the special case where two matrices $A$ and $B$ generate (as a monoid) the whole monoid $SL_2(\\Z_+)$. However, in this paper we show that the situation with other, similar\", pairs of matrices from $SL_2(Z)$ is different, and the lifting attack\" can (in some cases) produce collisions in the {\\it group} generated by $A$ and $B$, but not in the positive {\\it monoid}. Therefore, we argue that for these pairs of matrices, there are no known attacks at this time that would affect security of the corresponding hash functions. We also give explicit lower bounds on the length of collisions for hash functions corresponding to some particular pairs of matrices from $SL_2(F_p)$.

00:17 [Pub][ePrint]

Decomposing a divisor over a suitable factor basis in the Jacobian of a hyperelliptic curve is a crucial step in an

index calculus algorithm for the discrete log problem in the Jacobian. For small genus curves, in the year 2000, Gaudry had proposed

a suitable factor basis and a decomposition method. In this work, we provide a new method for decomposition over the same factor

basis. The advantage of the new method is that it admits a sieving technique which removes smoothness checking of polynomials

required in Gaudry\'s method. Also, the total number of additions in the Jacobian required by the new method is less than

that required by Gaudry\'s method. The new method itself is quite simple and we present some example decompositions and timing

results of our implementation of the method using Magma.

00:17 [Pub][ePrint]

The main bottleneck affecting the efficiency of all known fully homomorphic encryption (FHE) schemes is Gentry\'s bootstrapping procedure, which is required to refresh noisy ciphertexts and keep computing on encrypted data. Bootstrapping in the latest implementation of FHE, the HElib library of Halevi and Shoup (Crypto 2014), requires about half an hour. We present a new method to homomorphically compute simple bit operations, and refresh (bootstrap) the resulting output, which runs on a personal computer in just about half a second. We present a detailed technical analysis of the scheme (based on the worst-case hardness of standard lattice problems) and report on the performance of our prototype implementation.

00:17 [Pub][ePrint]

Multi-precision squaring is a crucial operation for implementation of Elliptic Curve Cryptography. Particularly, when it comes to embedded processors, the operation should be designed carefully to execute expensive ECC operation on resource constrained devices. In order to bridge the gap between high overheads and limited computation capabilities, we present optimized Karatsuba squaring method for embedded processors. Traditional squaring computation can be divided into two sub-squaring and one sub-multiplication parts. Firstly we compute the multiplication part with the fastest Karatsuba multiplication and then remaining two squaring parts are conducted with the fastest sliding block doubling squaring. Proposed method sets the new speed records for multi-precision squaring, improving the execution time by up to 8.49% comparing to the best known works.

00:17 [Pub][ePrint]

This paper resolves an open problem raised by Blocki {\\it et al.} (FOCS 2012), i.e., whether other variants of the Johnson-Lindenstrauss transform preserves differential privacy or not? We prove that a general class of random projection matrices that satisfies the Johnson-Lindenstrauss lemma also preserves differential privacy. This class of random projection matrices requires only $n$ Gaussian samples and $n$ Bernoulli trials and allows matrix-vector multiplication in $O(n \\log n)$ time. In this respect, this work unconditionally improves the run time of Blocki {\\it et al.} (FOCS 2012) without using the graph sparsification trick of Upadhyay (ASIACRYPT 2013). For the metric of measuring randomness, we stick to the norm used by earlier researchers who studied variants of the Johnson-Lindenstrauss transform and its applications, i.e., count the number of random samples made. In concise, we improve the sampling complexity by quadratic factor, and the run time of cut queries by an $O(n^{o(1)})$ factor and that of covariance queries by an $O(n^{0.38})$ factor.

Our proof for both the privacy and utility guarantee uses several new ideas. In order to improve the dimension bound, we use some known results from the domain of statistical model selection. This makes our proof short and elegant, relying just on one basic concentration inequality. For the privacy proof, even though our mechanism closely resembles that of Blocki {\\it et al.} (FOCS 2012) and Upadhyay (ASIACRYPT 2013), we cannot use their proof idea. This is because the projection matrices we are interested in introduces non-trivial correlations between any two rows of the published matrix, and, therefore, we cannot invoke the composition theorem of Dwork, Rothblum and Vadhan (STOC 2009). We argue that the published matrix is not $r$-multivariate distribution; rather one matrix-variate distribution. We compute the distribution of the published matrix and then prove it preserves differential privacy.

2014-10-10
15:17 [Pub][ePrint]

Often S-boxes are the only nonlinear component in a block cipher and as such play an important role in ensuring its resistance to cryptanalysis. Cryptographic properties and constructions of S-boxes have been studied for many years. The most common techniques for constructing S-boxes are: algebraic constructions, pseudo-random generation and a variety of heuristic approaches. Among the latter are the genetic algorithms. In this paper, a genetic algorithm working in a reversed way is proposed. Using the algorithm we can rapidly and repeatedly generate a large number of strong bijective S-boxes of each dimension from $(8 \\times 8)$ to $(16 \\times 16)$, which have sub-optimal properties close to the ones of S-boxes based on finite field inversion, but have more complex algebraic structure and possess no linear redundancy.

15:17 [Pub][ePrint]

As intended by its name, Physically Unclonable Functions (PUFs) are considered as an ultimate solution to deal with insecure stor- age, hardware counterfeiting, and many other security problems. How- ever, many different successful attacks have already revealed vulnera- bilities of certain digital intrinsic PUFs. Although settling-state-based PUFs, such as SRAM PUFs, can be physically cloned by semi-invasive and fully-invasive attacks, successful attacks on timing-based PUFs were so far limited to modeling attacks. Such modeling requires a large sub- set of challenge-response-pairs (CRP) to successfully model the targeted PUF. In order to provide a final security answer, this paper proves that all arbiter-based (i.e. controlled and XOR-enhanced) PUFs can be com- pletely and linearly characterized by means of photonic emission analy- sis. Our experimental setup is capable of measuring every PUF-internal delay with a resolution of 6 picoseconds. Due to this resolution we in- deed require only the theoretical minimum number of linear independent equations (i.e. physical measurements) to directly solve the underlying inhomogeneous linear system. Moreover, we neither require to know the actual PUF challenges nor the corresponding PUF responses for our physical delay extraction. On top of that devastating result, we are also able to further simplify our setup for easier physical measurement han- dling. We present our practical results for a real arbiter PUF implemen- tation on a Complex Programmable Logic Device (CPLD) from Altera manufactured in a 180 nanometer process.

15:17 [Pub][ePrint]

Public key infrastructures (PKIs) enable users to look up and verify one another\'s public keys based on identities.

Current approaches to PKIs are vulnerable because they do not offer sufficiently strong guarantees of \\emph{identity retention}; that is, they do not effectively prevent one user from registering a public key under another\'s already-registered identity.

In this paper, we leverage the consistency guarantees provided by cryptocurrencies such as Bitcoin and Namecoin to build a PKI that ensures identity retention.

Our system, called Certcoin, has no central authority and thus requires the use of secure distributed dictionary data structures to provide efficient support for key lookup.

12:30 [Job][Update]

This is a permanent research and teaching position in one of UK\\\'s top research-led universities. The Security and Privacy group undertakes research in all fields related to information and cyber security, privacy, cryptography, etc.

12:20 [Job][New]

The Laboratory of Cryptology and Computer Security (LoCCS) at the CS Department of Shanghai Jiao Tong University invites applications for several tenure-track faculty positions in the area of cryptology, in particular (but not limited to), authenticated encryptions, leakage-resilient cryptography, side-channel attacks, obfuscation. Candidates with a proven track record (especially publications at top venues) are encouraged to apply. Salaries will be globally competitive and commensurate with candidates\' accomplishments and experience. Shanghai Jiao Tong University is a member of China\'s C9 League and she has one of the country\'s best CS schools.

06:17 [Pub][ePrint]

Performance monitors are provided in modern day computers for observing various features of the underlying microarchitectures. However the combination of underlying micro-architectural features and performance counters lead to side-channels which can be exploited for attacking cipher implementations. In this paper, to the best of our knowledge we study for the first time, the combination of branch-predictor algorithms and performance counters to demonstrate a fault attack on the popular square-and-multiply based exponentiation algorithm, used in the RSA. The attacks exploiting branching event like branch taken can be foiled by Montgomery Ladder based implementation of the exponentiation algorithm, while attacks based on branch miss are more devastating. We demonstrate the power of the attack exploiting branch misses from performance monitors by formalizing a fault attack model, where the adversary is capable of performing a bit flip at a desired bit position of the secret exponent. The paper characterizes the branch predictors using the popular two-bit predictor and formulates the dependence on the number of branch misses on the fault induced. This characterization is exploited to develop an iterative attack algorithm where knowledge of the previously determined key-bits and the difference of branch misses (as gathered from the performance counters) are utilised to determine the next bit. The attack has been validated on several standard Intel platforms, and puts to threat several implementations of exponentiation algorithms ranging from standard square-and-multiply, Montgomery Ladder to RSA-CRT and which are often used as side-channel counter measures. The attacks show that using the fault attack model featuring branch predictors one can attack implementations of exponentiation: both square and multiply, and Montgomery ladder, which forms the central algorithm for several standard public key ciphers.