A Public Key Cryptosystem Algorithm Based On Hyperbolic Bundle

After the first one of the ideas of the one-way trap function,the people then put forward the idea of public key cryptosystem.The RSA cryptography realizes the idea of unidirectional trap function by means of number theory,which promotes the development of public key cryptosystem,such as elliptic curve cryptography System,EIGamal password system,the combination of passwords and so on.The cryptographer began to study the cryptographic system from another direction,making some cryptographic algorithms overcome and some cryptographic algorithms improved.At the same time with the continuous development of computer science,with the computer has been the original key length that is impossible to be broken into the key length may be broken.This makes the improvement of the algorithm and the algorithm of the breakthrough is imminent,otherwise,will cause immeasurable serious consequences.Usually establish a reliable and secure cryptography system is the design of mathematical difficulties,discrete logarithm problems or large integer decomposition.Based on the above-mentioned problem,we find a hyperbolic algorithm and a hyperbolic cluster cipher algorithm,which is a hyperbolic cluster cipher algorithm.It is a Pell equation in the modular sense,using the unit group of hyperbolic clusters and a group of elements Do coset operations.The algorithm of curve plexer cryptography takes into account the advantages of RSA cryptography and elliptic curve cryptography,which is based on two difficult problems:discrete logarithm problem and large integer decomposition.The diversity of hyperbolic clusters is different.Compared with the hyperbolic curve,the hyperbolic cluster has a larger code space and a larger key space.Compared with the traditional RSA,the RSA key is too long,the module is too large,the operation speed is slow,and the key of the hyperbolic cluster is much smaller than the RSA key under the same security.Compared with the elliptic curve,the solution of the elliptic curve is only in the general case and the additive group is not perfect.The hyperbolic cluster replaces the cubic equation of the elliptic curve with the quadratic equation so that the operation is more concise,and the multiplication group is used to replace the additive group simpler.Of course,the program for the first time there are incomplete places to be further research and discussion.