*06:17*[Forum] [2014 Reports] 2014/377 by Orr

This looks like a paper of "how to tranform secret key algorithm into public key one using obfuscation". Take AES-X, and obfuscate. From: 2014-02-06 05:46:14 (UTC)

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This looks like a paper of "how to tranform secret key algorithm into public key one using obfuscation". Take AES-X, and obfuscate. From: 2014-02-06 05:46:14 (UTC)

2014-05-30

This paper presents a new projective coordinate system and new explicit algorithms which together boost the speed of arithmetic in the divisor class group of genus 2 curves. The proposed formulas generalise the use of Jacobian coordinates on elliptic curves, and their application improves the speed of performing cryptographic scalar multiplications in Jacobians of genus 2 curves over prime fields by an approximate factor of 1.25x. For example, on a single core of an Intel Core i7-3770M (Ivy Bridge), we show that replacing the previous best formulas with our new set improves the cost of generic scalar multiplications from 243,000 to 195,000 cycles, and drops the cost of specialised GLV-style scalar multiplications from 166,000 to 129,000 cycles.

We propose Chaskey: a very efficient Message Authentication Code (MAC) algorithm for 32-bit microcontrollers. It is intended for applications that require 128-bit security, yet cannot implement standard MAC algorithms because of stringent requirements on speed, energy consumption, or code size. Chaskey is a permutation-based MAC algorithm that uses the Addition-Rotation-XOR (ARX) design methodology. We formally prove that Chaskey is secure in the standard model, based on the security of an underlying Even-Mansour block cipher. Chaskey is designed to perform well on a wide range of 32-bit microcontrollers. Our benchmarks show that on the ARM Cortex-M3/M4, our Chaskey implementation reaches a speed of 7.0 cycles/byte, compared to 89.4 cycles/byte for AES-128-CMAC. For the ARM Cortex-M0, our benchmark results give 16.9 cycles/byte and 136.5 cycles/byte for Chaskey and AES-128-CMAC respectively.

We present a new method for building pairs of HFE polynomials of high degree, such that the map constructed with such a pair is easy to invert. The inversion is accomplished using a low degree polynomial of Hamming weight three, which is derived from a special reduction via Hamming weight three polynomials produced by these two HFE polynomials. This allows us to build new candidates for multivariate trapdoor functions in which we use the pair of HFE polynomials to fabricate the core map. We performed the security analysis for the case where the base field is $GF(2)$ and showed that these new trapdoor functions have high degrees of regularity, and therefore they are secure against the direct algebraic attack. We also give theoretical arguments to show that these new trapdoor functions over $GF(2)$ are secure against the MinRank attack as well.

The modification of message that meets the sufficient conditions for

collision is found in the last step of differential attack proposed

by Wang et all. (2005) on MD4 hash algorithm. Here we show how this

attack phase, finding a collision starting from the list of

sufficient conditions for the collision, can be implemented using a

combination of two algorithms - evolutionary algorithm and hill

climbing. Hybridization of evolutionary algorithm and hill climbing

is a well-known technique for improving solutions, but it isn\'t

applied to this domain (at least by information that author has

collected).

In this work we introduce a large polynomial arithmetic library optimized for Nvidia GPUs to support fully homomorphic encryption schemes. To realize the large polynomial arithmetic library we convert the polynomial with large coefficients using the Chinese Remainder Theorem into many polynomials with small coefficients, and then carry out modular multiplications in the residue space using a custom developed discrete Fourier transform library. We further extend the library to support the homomorphic evaluation operations, i.e. addition, multiplication, and relinearization, in an NTRU based somewhat homomorphic encryption library. Finally, we put the library to use to evaluate homomorphic evaluation of two block ciphers: Prince and AES, which show 2.57 times and 7.6 times speedup, respectively, over an Intel Xeon software implementation.

Motivated by theoretical and practical interest, the challenging task of designing crypto- graphic protocols having only black-box access to primitives has generated various breakthroughs in the last decade. Despite such positive results, even though nowadays we know black-box constructions for secure two-party and multi-party computation even in constant rounds, there still are in Cryptography several constructions that critically require non-black-box use of primitives in order to securely realize some fundamental tasks. As such, the study of the gap between black-box and non-black-box constructions still includes major open questions.

In this work we make progress towards filling the above gap. We consider the case of black- box constructions for computations requiring that even the size of the input of a player remains hidden. We show how to commit to a string of arbitrary size and to prove statements over the bits of the string. Both the commitment and the proof are succinct, hide the input size and use standard primitives in a black-box way. We achieve such a result by giving a black-box construction of an extendable Merkle tree that relies on a novel use of the \"MPC in the head\" paradigm of Ishai et al. [STOC 2007].

We show the power of our new techniques by giving the first black-box constant-round public-coin zero knowledge argument for NP.

To achieve this result we use the non-black-box simulation technique introduced by Barak [FOCS 2001], the PCP of Proximity introduced by Ben-Sasson et al. [STOC 2004], together with a black-box public-coin witness indistinguishable universal argument that we construct along the way.

Additionally we show the first black-box construction of a generalization of zero-knowledge sets introduced by Micali et al. [FOCS 2003]. The generalization that we propose is a strengthening that requires both the size of the set and the size of the elements of the set to remain private.

Big data and its applications are attracting more and more research interests in recent years. As the new generation distributed computing platform, cloud computing is believed to be the most potent platform. With the data no longer under users\' direct control, data security in cloud computing is becoming one of the most obstacles of the proliferation of cloud. In order to improve service reliability and availability, storing multiple replicas along with original datasets is a common strategy for cloud service providers. Public data auditing schemes allow users to verify their outsourced data storage without having to retrieve the whole dataset. However, existing data auditing techniques suffers from efficiency and security problems. First, for dynamic datasets with multiple replicas, the communication overhead for update verification is very large, because verification for each update requires O(logn) communication complexity and update of all replicas. Second, to the best of our knowledge, there is no existing integrity verification schemes can provide public auditing and authentication of block indices at the same time. Without authentication of block indices, the server can build a valid proof based on data blocks other than the block client requested to verify. In order to address these problems, in this paper, we present a novel public auditing scheme named MuR-DPA. The new scheme incorporated a novel authenticated data structure based on the Merkle hash tree, which we name as MR-MHT. For support of full dynamic data updates, authentication of block indices and efficient verification of updates for multiple replicas at the same time, the level values of nodes in MR-MHT are generated in a top-down order, and all replica blocks for each data block are organized into a same replica sub-tree. Compared to existing integrity verification and public auditing schemes, theoretical analysis and experimental results show that the MuR-DPA scheme can not only incur much less communication overhead for both update and verification of datasets with multiple replicas, but also provide enhanced security against dishonest cloud service providers.

We revisit ``the randomized iterate\'\' technique that was originally used by Goldreich, Krawczyk, and Luby (SICOMP 1993) and refined by Haitner, Harnik and Reingold (CRYPTO 2006) in constructing pseudorandom generators (PRGs) from regular one-way functions (OWFs). We abstract out a technical lemma with connections to several recent work on cryptography with imperfect randomness, which provides an arguably simpler and more modular proof for the Haitner-Harnik-Reingold PRGs from regular OWFs.

We extend the approach to a more general construction of PRGs with seed length $O(n{\\log}n)$ from a broader class of OWFs. More specifically, consider an arbitrary one-way function $f$ whose range is divided into sets $\\Y_1$, $\\Y_2$, $\\ldots$, $\\Y_n$ where each $\\Y_i\\eqdef\\{y:2^{i-1}\\le|f^{-1}(y)|

A universal one-way hash function (UOWHF) is a compressing function for which finding a second preimage is infeasible. The seminal work of Rompel (STOC 1990) that one-way functions (OWFs) imply UOWHFs is one of the most important founding results of modern cryptography. The current best known UOWHF construction from any one-way function(on $n$-bit input) by Haitner et al. (Eurocrypt 2010) requires output and key length $\\tilO(n^7)$, which is far from practical.

On the other hand, special structured OWFs typically give rise to much more efficient (and almost practical) UOWHFs. Naor and Yung (STOC 1989) gave an optimal construction of UOWHFs of key and output lengths both linear in $n$ by making a single call to any one-way permutation. De Santis and Yung (Eurocrypt 1990), Barhum and Maurer (Latincrypt 2012), and Ames, Gennaro, and Venkitasubramaniam (Asiacrypt 2012) further extended the work to more generalized settings, namely, 1-to-1 and regular one-way functions. However, the best known constructions still require key length $O(n\\cdot\\log{n})$ even for 1-to-1 one-way functions, and need to make $O(\\omega(1 {\\cdot}\\log{n})$ calls to any known regular one-way functions, or even $\\tilO(n)$ adaptive calls if one wants linear output length at the same time.

In this paper, we first introduce a technical lemma about universal hashing with nice symmetry to the leftover hash lemma, which might be of independent interest. That is, if one applies universal hash function $h:\\bit{n}\\rightarrow\\bit{a+d}$ to any random variable $X$ of min-entropy $a$, then $h$ will be 1-to-1 on $X$ except for a $2^{-d}$ fraction. We also generalize the construction of Naor and Yung (that was optimal only for one-way permutations) to 1-to-1 and almost regular one-way functions, and significantly extend their analysis. The above yields the following results.

\\begin{itemize}

\\item For any 1-to-1 one-way function, we give an optimal construction of UOWHFs with key and output length $\\Theta(n)$ by making a single call to the underlying OWF.

\\item For any known-(almost-)regular one-way function with known hardness, we give another optimal construction of UOWHFs with key and output length $\\Theta(n)$ and a single call to the one-way function.

\\item For any known-(almost-)regular one-way function, we give a construction of UOWHFs with key and output length $O(\\omega(1){\\cdot}n)$ and by making $\\omega(1)$ non-adaptive calls to the one-way function.

\\end{itemize}

where the first two constructions enjoy optimal parameters simultaneously and the third one is nearly optimal up to any(efficiently computable) super-constant factor $\\omega(1)$, e.g., $\\log\\log\\log{n}$ or even less. Furthermore, the constructions enjoy optimal shrinkages by matching the upper bound of Gennaro et al. (SICOMP 2005).

Traditional cryptographic hash functions allow one to easily check whether the original plain-texts are equal or not, given a pair of hash values. Probabilistic hash functions extend this concept where given a probabilistic hash of a value and the value itself, one can efficiently check whether the hash corresponds to the given value. However, given distinct probabilistic hashes of the same value it is not possible to check whether they correspond to the same value. In this work we introduce a new cryptographic primitive called \\emph{relational hash} using which, given a pair of (relational) hash values, one can determine whether the original plain-texts were related or not. We formalize various natural security notions for the relational hash primitive - one-wayness, unforgeability and oracle simulatibility.

We develop a relational hash scheme for discovering linear relations among bit-vectors (elements of $\\FF_2^n$) and $\\FF_p$-vectors. Using these linear relational hash schemes we develop relational hashes for detecting proximity in terms of hamming distance. These proximity relational hashing scheme can be adapted to a privacy preserving biometric authentication scheme.

We also introduce the notion of \\emph{relational encryption}, which is a regular semantically secure public key encryption for any adversary which only has access to the public key. However, a semi-trusted entity can be given a relational key using which it can discover relations among ciphertexts, but still cannot decrypt and recover the plaintexts.