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Information Protection Based on Extraction of Square Roots of Gaussian Integers
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International Journal of Communications, Network and System Sciences·Volume 04 (2011)·Pages 133–138·Published 10 March 2011·DOI10.4236/ijcns.2011.43016
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Abstract
A cryptosystem based on computation of square roots of complex integers modulo composite <i>n</i> is described in this paper. This paper provides an algorithm extracting a square root of Gaussian integer. Various properties of square roots and a method for finding Gaussian generators are demonstrated. The generators can be instrumental in constructing other cryptosystems. It is shown how to significantly reduce average complexity of decryption per each block of ciphertext.
KeywordsPublic Key CryptosystemsSquare-Root ExtractionGaussian IntegersGaussian GeneratorMultiplicative InverseSquare Root AlgorithmInformation HidingAmbiguity of Recovery
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