On p-vectors, p-arrays and cryptographic protocols
|Keywords:||向量;陣列;密碼協定;array;vector;arithmetic function;algebra;ring;field;cryptography;public key;private key;lattice;encryption;decryption||Issue Date:||2016||Abstract:||
This thesis introduces the concept of p-vectors and p-arrays, which are algebraic constructions based on multiplicative arithmetic functions and prime numbers. With these concepts we construct several algebraic structures which allows us also to make a proposal for a public key encryption protocol. This public key encryption protocol, which we call p-array public key encryption protocol is a public-private key encryption system that allows the users to encrypt and decrypt messages of vectorial structure whose components are non negative integers upperly bounded. Along this work we present several of the theorems and lemmas that allow us to make the proof of correctness of the aforedmentioned protocol, and also to discuss some of the attacks that could potentially provide information of the private key to anyone performing them on the proposed algorithm.
|Appears in Collections:||數學系|
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