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Pairings in local fields and cryptography. (English) Zbl 1369.11080

Summary: In this paper we present the results on the problem of explicit reciprocity law, as in the classical part of the field of algebraic numbers and their generalization to multidimensional fields and formal groups. The result is an explicit formula in the circular extension of the field of \(p\)-adic numbers is applied to the determination of a new public-key cryptosystems and electronic signatures.

MSC:

11S31 Class field theory; \(p\)-adic formal groups
94A60 Cryptography
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