Combinatorics with Copula for Code based Post-Quantum Cryptography
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Codes have been proposed as useful tools in designing cryptosystem that are safe against quantum computing. Despite the large public key size, decryption failure rate and attacks on its constructed trapdoors have been impediments to not only to its standardization but its eventual deployment in communication. The successful attacks on its trapdoors are due to the high probability in decoding codewords into syndromes of low rank through combinatoric schemes such as Decoding with Index/Information sets from Grassmannian support proposed in literature. Decoding with Marginals/Belief propagation especially with Raptor codes has not been exploited fully in post quantum cryptography which this paper has done with new results. The introduction of Grassmannian supoort during information set decoding, leads us to explore the concatenation of bipartite graph with Grassmannian graph into a novel concept termed boundary measurement. Finally, we transform conditional prob-ability function into Copula for dependency and estimation of the marginal using iterative expectation-maximization approach thereby limiting the probability of decryption failure in the process
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