*03:17* [Pub][ePrint]
Random Projections, Graph Sparsification, and Differential Privacy, by Jalaj Upadhyay
This paper initiates the study of preserving {\\em differential privacy} ({\\sf DP}) when the data-set is sparse. We study the problem of constructing efficient sanitizer that preserves {\\sf DP} and guarantees high utility for answering cut-queries on graphs. The main motivation for studying sparse graphs arises from the empirical evidences that social networking sites are sparse graphs. We also motivate and advocate the necessity to include the efficiency of sanitizers, in addition to the utility guarantee, if one wishes to have a practical deployment of privacy preserving sanitizers. We show that the technique of Blocki et al. (FOCS2012) ({\\sf BBDS}) can be adapted to preserve {\\sf DP} for answering cut-queries on sparse graphs, with an asymptotically efficient sanitizer than~{\\sf BBDS}. We use this as the base technique to construct an efficient sanitizer for arbitrary graphs. In particular, we use a preconditioning step that preserves the spectral properties (and therefore, size of any cut is preserved), and then apply our basic sanitizer. We first prove that our sanitizer preserves {\\sf DP} for graphs with high conductance. We then carefully compose our basic technique with the modified sanitizer to prove the result for arbitrary graphs. In certain sense, our approach is complementary to the Randomized sanitization for answering cut queries (Gupta, Roth, and Ullman, TCC 2012): we use graph sparsification, while Randomized sanitization uses graph densification.

Our sanitizers almost achieves the best of both the worlds with the same privacy guarantee, i.e., it is almost as efficient as the most efficient sanitizer and it has utility guarantee almost as strong as the utility guarantee of the best sanitization algorithm.

We also make some progress in answering few open problems by {\\sf BBDS}. We make a combinatorial observation that allows us to argue that the sanitized graph can also answer $(S,T)$-cut queries with same asymptotic efficiency, utility, and {\\sf DP} guarantee as our sanitization algorithm for $S, \\bar{S}$-cuts. Moreover, we achieve a better utility guarantee than Gupta, Roth, and Ullman (TCC 2012). We give further optimization by showing that fast Johnson-Lindenstrauss transform of Ailon and Chazelle~\\cite{AC09} also preserves {\\sf DP}.

*03:17* [Pub][ePrint]
The Special Number Field Sieve in $\\F _{p^{n}}$, Application to Pairing-Friendly Constructions, by Antoine Joux and Cécile Pierrot
In this paper, we study thediscrete logarithm problem in finite fields related to pairing-based

curves. We start with a precise analysis of the

state-of-the-art algorithms for computing discrete logarithms that

are suitable for finite fields related to pairing-friendly

constructions. To improve upon these algorithms, we extend the

Special Number Field Sieve to compute discrete logarithms in

$\\F_{p^{n}}$, where $p$ has an adequate sparse representation. Our

improved algorithm works for the whole range of applicability of the

Number Field Sieve.

*03:17* [Pub][ePrint]
Cryptanalysis of GOST R Hash Function, by Zongyue Wang, Hongbo Yu, Xiaoyun Wang
GOST R is the hash function standard of Russia. This paper presents some cryptanalytic results on GOST R. Using the rebound attack technique, we achieve collision attacks on the reduced round compression function. Result on up to 9.5 rounds is proposed, the time complexity is 2^{176} and the memory requirement is 2^{128} bytes. Based on the 9.5-round collision result, a limited birthday distinguisher is presented. Moreover, a method to construct k collisions on 512-bit version of GOST R is given which show the weakness of the structure used in GOST R. To the best of our knowledge, these are the first results on GOST R.

*03:17* [Pub][ePrint]
On Algebraic Immunity of $\\Tr(x^{-1})$ over $\\mathbb{F}_{2^n}, by Xiutao Feng
The trace inverse function $\\Tr(x^{-1})$ over the finite field $\\mathbb{F}_{2^n}$ is a class of very important Boolean functions in stream ciphers, which possesses many good properties, including high algebraic degree, high nonlinearity, ideal autocorrelation, etc. In this work we discuss properties of $\\Tr(x^{-1})$ in resistance to (fast) algebraic attacks.

As a result, we prove that the algebraic immunity of $\\Tr(x^{-1})$ arrives the upper bound

given by Y. Nawaz et al when $n\\ge4$, that is, $\\AI(\\Tr(x^{-1}))=\\ceil{2\\sqrt{n}}-2$, which shows that D.K. Dalai\' conjecture on the algebraic immunity

of $\\Tr(x^{-1})$ is correct for almost all positive integers $n$. What is more, we further demonstrate some weak properties of $\\Tr(x^{-1})$ in resistance to fast algebraic attacks.