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$F(X) =(A\\times X)Mod(2^r)Div(2^s)$ .\\\\* Mod is modulo operation , Div is integer division operation , A , r and s are known natural numbers while $( r > s )$ .\\\\* In this paper it is also proven that this problem is equivalent to SAT problem which is NP complete .
lightweight cryptographic design. Many lightweight block ciphers have
been proposed, targeted mostly at hardware applications. Typically software performance has not been a priority, and consequently software
performance for many of these algorithms is unexceptional. SIMON and
SPECK are lightweight block cipher families developed by the U.S. National Security Agency for high performance in constrained hardware and software environments. In this paper, we discuss software performance and demonstrate how to achieve high performance implementations of SIMON and SPECK on the AVR family of 8-bit microcontrollers. Both ciphers compare favorably to other lightweight block ciphers on this platform. Indeed, SPECK seems to have better overall performance than any existing block cipher --- lightweight or not.
Since any ideal is a module over the ring of Boolean polynomials, the change of the basis is uniquely determined by invertible matrix over the ring.
Algorithms for invertible simplifying and complicating the basis of Boolean ideal that fixes the size of basis are proposed. Algorithm of simplification optimizes the choose of pairs of polynomials during the Groebner basis computation, and eliminates variables without using resultants.
But how to optimally extract all the information contained in all possible $d$-tuples of points?
In this article, we introduce preprocessing tools that answer this question.
We first show that maximizing the higher-order CPA coefficient is equivalent to finding the maximum of the covariance.
We apply this equivalence to the problem of trace dimensionality reduction by linear combination of its samples.
Then we establish the link between this problem and the Principal Component Analysis. In a second step we present the optimal solution for the problem of maximizing the covariance.
We also theoretically and empirically compare these methods.
We finally apply them on real measurements, publicly available under the DPA Contest v4, to evaluate how the proposed techniques improve the second-order CPA (2O-CPA).
We use a fuzzy commitment scheme so the extracted key is chosen by definition to have uniformly random bits. The biometric source is used as the noise term in the LPN problem. A key idea in our construction is to use additional `confidence\' information produced by the source for polynomial-time key recovery even under high-noise settings, i.e., $\\Theta(m)$ errors, where $m$ is the number of biometric bits. The confidence information is never exposed and is used as a noise-avoiding trapdoor to exponentially reduce key recovery complexity. Previous computational fuzzy extractors were unable to correct $\\Theta(m)$ errors or would run in exponential time in $m$.
A second key result is that we relax the requirement on the noise in the LPN problem, which relaxes the requirement on the biometric source. Through a reduction argument, we show that in the LPN problem, correlation in the bits generated by the biometric source can be viewed as a bias on the bits, which affects the security parameter, but not the security of the overall construction.
Using a silicon Physical Unclonable Function (PUF) as a concrete example, we show how keys can be extracted securely and efficiently even under extreme environmental variation.
same time as that of the ciphertext or some future time. Furthermore, a ciphertext attached to a certain time can be updated to a new one attached to a future time using only public information. The SUE schemes available in the literature are either (a) fully secure but developed in a composite order bilinear group setting under highly non-standard assumptions or (b) designed in prime order bilinear groups but only selectively secure. This paper presents the first fully secure SUE scheme in prime order bilinear groups under standard assumptions, namely, the Decisional Linear and the Decisional Bilinear Diffie-Hellman assumptions. As pointed out by Freeman (EUROCRYPT 2010)and Lewko (EUROCRYPT 2012), the communication and storage, as well as, computational efficiency of prime order bilinear groups are much higher compared to that of composite order bilinear groups with an equivalent level of security. Consequently, our SUE scheme is highly cost-effective than the existing fully secure SUE.