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The target of this article is to regard chosen issues of the topic of latest cryptology, established in 5 fairly autonomous yet similar subject matters: effective allotted computation modulo a shared mystery, multiparty computation, sleek cryptography, provable safeguard for public key schemes, and effective and safe public-key cryptosystems.
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Extra resources for Contemporary Cryptology (Advanced Courses in Mathematics - CRM Barcelona)
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Assume that a set of n players wants to establish whether a shared value a belongs to a set of (shared) integers b1 , . . , bm . A simple strategy to solve this problem is to check if there is a bj for which a ≡ bj mod p holds. To perform this check in a distributed way one may simply compute (for each bj ) the value a − bj mod p, multiply it with a jointly generated random element and check if the obtained result is zero or not. Unfortunately, however, this solution does not quite solve the problem in our setting.