Design Of Multivariate Public Key Cryptosystems Based On QC-MDPC Code And Simple Matrix

Multivariate public key cryptosystems?MPKC?can resist quantum computers attacks and can be computed fastly.But its key length increases with the order of O?n^???n number of veriable,n?64,??{3,4}?,which influences its widely application in actual.Compared with other MPKC,the Simple Matrix Encryption scheme?ABC?based on matrix multiplication has fast efficiency of encryption and decryption,but the key length is longer?for example:when the number of columns of matrix A is no less than 8,i.e.,t?8,key length of ABC-13 scheme is about n³+10n²+4n?296kB?n=t²=64??,there exists decryption failure and other problems.In order to solve these problems,an affine map in the public key of ABC scheme is improved the generation matrix G of code,which reduces the key length.In order to reduce the failure probability of decryption,the central map F is improved under certain parameter.We consider public key ? and center map F of the ABC encryption scheme?ABC-13?in 2013.We also consider public key ? and center map F of the ABC encryption scheme?ABC-14?in 2014.The public key ?=L₂?F?L₁,The private key F are constructed based on the MQ difficult problem which affects the security and performance of the scheme.Affine map L₁,L₂ are constructed based on IP isomorphic problem which is used to hide F.We design two MPKC that combine QC-MDPC code with ABC scheme in this thesis.1.An affine map L₂ of the ABC-13^'s public key ? is improved to the generation matrix G of the QC-MDPC code,and a disturbance variable e is added to the public key which is ?=?F?L₁?G+e.We design the C-2-ABC scheme which combines QC-MDPC code with secondary ABC.Becase the generation matrix G only needs to store the first non-zero row of the check matrix H,so the key length of the scheme is about 11%less than ABC-13.2.Firstly,we generalize the three squares matrix of the ABC-14 scheme which is the non-square matrix.Therefore,the center map F is generated and 3-ABC scheme was designed.The scheme of the failure rate of decryption is decreased?q-1??q²?q order for finite field?and length ratio of plaintext and cipher is d:e?1:2.Secondly,the 3-ABC scheme combines with the generation matrix G of the QC-MDPC code and adds a disturbance variable E so it generates the new center map F?=F?G+E.Therefore,we design a C-3-ABC scheme which combines the QC-MDPC code with the three ABC schemes.The key length of the C-3-ABC scheme is reduced about 35%less than that of ABC-14.3.Using Magma to verify the scheme and analyse efficiency,the experiment shows that the the scheme is feasible and the decryption efficiency was high when the input information is less than 128bit.