In this article, using Fontaine＇s ФГ-module theory, we give a new proof of Coleman＇s explicit reciprocity law, which generalizes that of Artin-Hasse, Iwasawa and Wiles, by giving a complete formula for the norm re...In this article, using Fontaine＇s ФГ-module theory, we give a new proof of Coleman＇s explicit reciprocity law, which generalizes that of Artin-Hasse, Iwasawa and Wiles, by giving a complete formula for the norm residue symbol on Lubin-Tate groups. The method used here is different from the classical ones and can be used to study the Iwasawa theory of crystalline representations.展开更多
In this paper we introduce a cryptosystem based on the quotient groups of the group of rational points of an elliptic curve defined over p-adic number field. Some additional parameters are taken in this system, which ...In this paper we introduce a cryptosystem based on the quotient groups of the group of rational points of an elliptic curve defined over p-adic number field. Some additional parameters are taken in this system, which have an advantage in performing point multiplication while keeping the security of ECC over finite fields. We give a method to select generators of the cryptographic groups, and give a way to represent the elements of the quotient groups with finitely bounded storage by establishing a bijection between these elements and their approximate coordinates. The addition formula under this representation is also presented.展开更多
基金This paper is supported partially by the 973 Program
文摘In this article, using Fontaine＇s ФГ-module theory, we give a new proof of Coleman＇s explicit reciprocity law, which generalizes that of Artin-Hasse, Iwasawa and Wiles, by giving a complete formula for the norm residue symbol on Lubin-Tate groups. The method used here is different from the classical ones and can be used to study the Iwasawa theory of crystalline representations.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60763009 and 10531060) the National 863 Project (Grant No.2007AA701315)
文摘In this paper we introduce a cryptosystem based on the quotient groups of the group of rational points of an elliptic curve defined over p-adic number field. Some additional parameters are taken in this system, which have an advantage in performing point multiplication while keeping the security of ECC over finite fields. We give a method to select generators of the cryptographic groups, and give a way to represent the elements of the quotient groups with finitely bounded storage by establishing a bijection between these elements and their approximate coordinates. The addition formula under this representation is also presented.
