Research And Implement Of Public Key Cryptosystem Based On Multivariate Polynomial

Public key cryptograph as an important method to guarantee the security of communication has been used in everyone's daily life. The security of classical public key cryptograph is based on numbertheoretic problem, like factoring and discrete logarithms. With the development of quantum computer, the classical public key cryptograph will become insecure. So, developing new schemes to resist quantum computer's attack is needed. Multivariate public key cryptograph is one of the main approaches to achieve this goal. Besides lattice-, code, hash-based cryptosystems, multivariate cryptography is more effective than others.However, there are some problems with multivariate cryptography. The key size of multivariate cryptography usually is large. Wolf proposed that key of UOV scheme contains lots of redundancy. So, this paper present a new scheme to reduce the size of public key by choosing some coefficients of the private maps from a small field GF?2?. Meanwhile, lots of multiplication and addition be reduced during verification process. The data of experiment tells that the public key size of 0/1 Rainbow scheme is half or less of the size of Rainbow scheme. And the time expended of verification of 0/1 Rainbow is half or less of the time of Rainbow scheme.There are lots of practical multivariate signature schemes. And, only few multivariate encryption schemes showed up. The Simple Matrix encryption scheme proposed by Tao is an efficient and secure multivariate encryption scheme in PQCrypto2013. However, the ratio of length of cipher text to plain text is always 2. Cubic AB encryption scheme is a way to fix it. It used a very wide matrix to replace square matrixes. It's easy to adjust the ratio of length of cipher text to plain text by change the size of the wide matrix. In addition, the elements of matrix A are random quadratic polynomials. So, the security of Cubic AB scheme is based on multivariate cubic problem which is harder than multivariate quadratic problem. With this method, the ratio of length of cipher text to plain text could be changed easily. Besides, rank attack can not be used to attack this scheme. At the same time, the length of cipher text and plain text will be shorter. That could make the process of decryption faster.