Research On Modulus Polynomials In Public Key Encryption Based On Ideal Lattices

From classical cryptography to modern cryptography, from symmetriccryptosystem to public key cryptosystem, applied cryptography is no longer confined tomilitary, politics and diplomacy as it was in the past, and it gradually comes into our life.With the rapid development of information technology, cryptography shows its charm.Since the emergence of quantum computing, the tradional public key systems based oninteger factorization and discrete logarithm are severely threatened. This leads that thestudy of lattice-based public-key cryptosystem gradually becomes a hot research. In thelattice-based public-key cryptosystem, the public key cryptosystem based on the ideallattices attracts the most attention. Because the ideal lattice has many outstandingproperties, such as simple representation, small space and so on. It has been widely usedto construct public key cryptosystem.This paper focuses on the ring whose ideals forms the ideal lattice. I maily researchon the effects of different modulus polynomials to the prototypes of cryptography. Themain results as described below:1. I verify that the distribution of the public key and the ciphertest of an encryptionsystem based on learning with errors over rings in the ringZ [x]/f x withf x that is irreducible are more uniform.2. I verify that the distribution of the public key of the NTRU encryption systemand its improved system in the ringZ [x]/f x are all uniform, when the value off x is different.3. I verify that generalized compact knapsack function is collision-resistant in theringZ [x]/f x with f x that is irreducible.