Steganography is the art and science of embedding secret data in another medium to prevent the leakage of secret information. A VQ-based (vector quantization) steganographic method usually involves changes of the block values in the VQ images, which might cause serious distortion. As a result, many existing methods use closest pairs or clustering techniques to preserve an acceptable image quali...

Given an N x N array of OS and Is, the closest pair problem is to determine the minimum distance between any pair of ones. Let D be this minimum distance (or D = 2N if there are fewer than two Is). Two solutions to this problem are given, one requiring O(log( N) + D) time and the other O(log( N)). These solutions are for two types of parallel computers arranged in a pyramid fashion with the bas...

Blomer and Naewe[BN09] modified the randomized sieving algorithm of Ajtai, Kumar and Sivakumar[AKS01] to solve the shortest vector problem (SVP). The algorithm starts with $N = 2^{O(n)}$ randomly chosen vectors in the lattice and employs a sieving procedure to iteratively obtain shorter vectors in the lattice. The running time of the sieving procedure is quadratic in $N$. We study this problem ...

We study the algorithmic complexity of lattice problems based on the sieving technique due to Ajtai, Kumar, and Sivakumar [AKS01]. Given a k-dimensional subspace M ⊆ Rn and a full rank integer lattice L ⊆ Qn, the subspace avoiding problem SAP, defined by Blömer and Naewe [BN07], is to find a shortest vector in L \ M. We first give a 2O(n+k log k) time algorithm to solve the subspace avoiding pr...

Lattice based cryptography is claimed as a serious candidate for post quantum cryptography, it recently became an essential tool of modern cryptography. Nevertheless, if lattice based cryptography has made theoretical progresses, its chances to be adopted in practice are still low due to the cost of the computation. If some approaches like RSA and ECC have been strongly optimized in particular ...

A new type of signature scheme, called NTRUSign, based on solving the approximately closest vector problem in a NTRU lattice was proposed at CT-RSA’03. However no security proof against chosen messages attack has been made for this scheme. In this paper, we show that NTRUSign signature scheme contains the weakness of malleability. From this, one can derive new valid signatures from any previous...

The NTRU Signature Scheme (NSS) with enhanced document encoding and signature verification is described. Three areas of security are investigated: (1) It is proven (under a heuristic assumption) that direct forgery is equivalent to the solution of a closest vector problem, up to constant factor, in an NTRU convolution modular lattice. (2) The probability of forgery using partially preselected v...