New Public Key Encryption Scheme And Application Research

It is arguably that constructing new secure encryption schemes and designing high-ly efficient secure computation protocols based on secure encryption schemes are popular research concerns in network security field.This dissertation addresses these concerns by studying the following research questions:(1)constructing encryption schemes with new properties and proving their security;(2)designing highly efficient secure protocols with new-type encryption schemes.The contributions of this dissertation are as follows.1.A new RSA-type encryption scheme that applying pairing function and coding ran-domization is proposed,which it can hide the statistic property of plaintext.Compared with some known RSA-type schemes,the new scheme possesses the following advantages:(1)A new way is developed to deal with plaintext before encrypting,which is able to hide the property of plaintext;(2)The security proof is based on a new RSA variant problem,called chosen XOR with randomness;(3)There is no need to negotiate the order between encrypt-ing modulus and signing modulus when it is applied in signcryption;(4)It is proved to be indistinguishably secure under adaptive chosen ciphertext attacks in the standard model.2.Two new RSA-type encryption schemes in the standard model are developed,where one is secure under chosen plaintext attack while keeping homomorphism,and the other is secure under adaptive chosen ciphertext attack.These two schemes can achieve ciphertext indistinguishability without introducing randomness to plaintext.Using the "code substi-tution" technique,not only can the first probabilistic RSA-type encryption scheme encrypt one single bit("0" or "1"),but also the multiplicative homomorphic encryption scheme can be transformed to "and","or:and "exclusive-or" homomorphic encryption schemes.Then,based on the first RSA-type encryption scheme and the semi-honest model,a two-party protocol for privately computing hamming distance is constructed.Additionally,a new RSA variant problem(called RSA decision problem)is proposed.3.Firstly,a homomorphically algebraic idea is proposed to prevent the non-participants in communication from using the Malleability of ciphertext.Then,combining this idea with key agreement,asymmetric and symmetric encryption techniques,a homomorphic encryp-tion scheme is proposed,which blocks the adversary using the Malleability of ciphertext to amount adaptive chosen ciphertext attack.4.Firstly,a homomorphic encryption scheme transformed from Paillier scheme and proved to be indistinguishability under chosen-plaintext attack is constructed,where the base is calculated by sender during encryption.Then,based on this homomorphic encryp-tion scheme,a protocol that can safely calculate a straight line by two private coordinate point(an open unsolved problem)in the semi-honest model is designed.Furthermore,this protocol can be applied to solve any secure multi-party computational geometry problem that can be reduced to computing coordinate difference quotient,which indicate that a non-negligible probability of private information leakage in the current coordinate difference quotient calculation protocols based on homomorphic encryption,has been solved.5.Firstly,a homomorphic-encryption-analogous-decryption system,whose encryp-tion algorithm CEnc is proved to be secure as Paillier's encryption algorithm,is constructed.Then using this constructed system,two efficient secure comparison protocols are developed where one protocol is applicable to securely compare two integers on Zn,while the other is applicable to securely compare two fractions(less than,n = pq,where p and q are two big primes with the same length).These two protocols based on homomorphic encryption,are cryptographically secure.Without using the expensive OT techniques but with the aid of cloud,the proposed protocols comparatively improve the computational efficiency,and can be applied to a variety of settings.The analysis shows that this method is more powerful and practical than previous methods.At last,we have a summarization of this paper and bring forward some future direc-tions.