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Error correction is an effective way to mitigate fault attacks in cryptographic hardware. It is also an effective solution to soft errors in deep sub-micron technologies. To this end, we present a systematic method for designing single error correcting (SEC) and double error detecting (DED) finite field (Galoisfield) multipliers over GF(2m). The detection and correction are done on-line. We use multiple...
In this paper, we present a systematic method for the designing fault tolerant reversible arithmetic circuits for finite field or Galois fields of the form GF(2m). To tackle the problem of errors in computation, we propose error detection and correction using multiple parity prediction technique based on low density parity check (LDPC) code. For error detection and correction, we need additional garbage...
This paper discusses some new integer factoring methods involving cyclotomic polynomials. There are several polynomials f(X) known to have the following property: given a multiple of f(p), we can quickly split any composite number that has p as a prime divisor. For example -- taking f(X) to be X- 1 -- a multiple of p - 1 will suffice to easily factor any multiple of p, using an algorithm of Pollard...
An algorithm is presented which reduces the problem of finding the irreducible factors of a bivariate polynomial with integer coefficients in polynomial time in the total degree and the coefficient lengths to factoring a univariate integer polynomial. Together with A. Lenstra's, H. Lenstra's and L. Lovasz' polynomial-time factorization algorithm for univariate integer polynomials and the author's...
Deterministic exponential lower time bounds are obtained for analyzing monadic recursion schemes, multi-variable recursion schemes, and recursive programs. The lower bound for multivariable recursion schemes holds for any domain of interpretation with at least two elements. The lower bound for recursive programs holds for any recursive programming language with a nontrivial predicate test (i.e. a...
We show that there can be no computationally tractable description by linear inequalities of the polyhedron associated with any NP-complete combinatorial optimization problem unless NP = co-NP -- a very unlikely event. We also apply the ellipsoid method for linear programming to show that a combinatorial optimization problem is solvable in polynomial time if and only if it admits a small generator...
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