Realization And Research Of CA Based On HFEM

PKI is short for Public Key Infrastructure. It is a set of important system for network and information security. PKI system is able to support secure transmission of information, secure storage of information, identity authentication, non-repudiation operation. Certificate Authority CA is the core of PKI. The most crucial technology of PKI is encryption and signature by public key cryptography. This paper proposes Hidden Field Ergodic Matrices′public key cryptography (HFEM) based on the difficulty of BMQ problem over finite field and characteristic of ergodic matrices. The trap door of HFEM is different from all current MQ public key cryptography. It involves basic operation of base field and extended field. And it also involves basic operation of matrices over base field. Therefore, HFEM is a new public key cryptography. Afterwards, this paper optimizes HFEM and proposes improved scheme I-HFEM. I-HFEM can encrypt message and sign message. According to the vicelike theories, this paper executes specific analogue experiment for the correlative process of CA based on I-HFEM. It proves the feasibility of the above scheme.i. The new public key cryptography1. The conception of HFEM(1) Imagine that Matrices′collections A and B are satisfied with the following four conditions: is linearly independent ( A is perceived as a vector group of n 2 dimension over F_q ).(2) is linearly independent. And is invertible .(3) ;(4) Rank ( AB ) = 2n。The construction of HFEM can use the intractability of E ( A, B ,T ) and Recognition after getting ( A , B ,T ) to construct trap door. It will realize Hidden Field Matrices′public key cryptography (HFM-PKC). The specific conception is as follows:Part of key generation(1) The matrices′collections are chosen randomly and satisfied with the above four constraint conditions.(2) We randomly choose a group of base over F_q and solve coordinate matrix related to R AB that .(3) R AB can generate 2n BMQ polynomials over(4) is the public key and ( A , B ,λ)is the private key. Part of encryption(1) The plaintext or session key is , andα,β∈F_qⁿ\{0}.(2) The sender gets the public key of receiver .(3) The sender use the public key of receiver to encrypt plaintexts:(4) The sender sends ciphertext C to the receiver.Part of decryption(1) Computing T =λC, the receiver can get matrix T∈(V S ( A ) VS ( B))\{0}.(2) The receiver solves a group of untrivial solutions of equations(3) According to y′and B , the receiver computes .(4) The receiver solves inverse matrix of w by Gauss elimination.(5) The receiver solves coordinate related to(6) According to ( x ,y ), the receiver gets plaintext: .2. The improved scheme of HFEMThe improved HFEM (I-HFEM) optimizes HFEM in order to reducing the cost of decryption algorithm of HFEM. It realizes by refining the four constraint conditions.Imagine that ( A, B ) are satisfied with the following conditions:(1) is linearly independent.(2) is linearly independent. And(3)(4) Rank ( AB ) = 2n. Therefore, we can use ( A, B ) to realize I-HFEM:Part of key generation(1) The matrices′collections are chosen randomly and satisfied with the above conditions.(2) We randomly choose a group of base over F_q and solve coordinate matrix of related to R AB that .(3) R AB can generate 2n BMQ polynomials over(4) is the public key and ( A , B ,λ)is the private key.Part of encryption(1) The plaintext or session key is .(2) The sender gets the public key of receiver .(3) The sender use the public key of receiver to encrypt plaintexts:(4) The sender sends ciphertext C to the receiver.Part of decryption(1) Computing T =λC, the receiver can get matrix .(2) The receiver solves a group of untrivial solutions of equations .(3) According to y′and B , the receiver computes .(4) The receiver solves inverse matrix of w by Gauss elimination.(5) The receiver solves coordinate related to .(6) According to ( x ,y ), the receiver gets plaintext: .3. The digital signature scheme based on I-HFEMThe digital signature scheme based on I-HFEM consists of three parts: key generation of digital signature, digital signature and signature verification. The specific operation processes are as follows.Part of key generation of digital signature Part of key generation of digital signature is able to provide every signer with a pair of publickey and private key that is used by CA or authority. If the public key and private key of signer are only used in signature, the specific implement method is as follows:(1) We chooses ergodic matrices Q₁ , Q₂∈F_q^n×n randomly ( qⁿ must be big enough.).(2) We chooses M∈F_q^n×n randomly. M is satisfied with Exp (Q₁ , M , Q₂ ) = 1 and .(3) We randomly choose the bases and and over F_q .(4) We randomly choose i , j∈{ 1, ,n}, and compute(5) If Rank ( ?? AB ?? ) <2n, we turn to (4).(6) We randomly choose a group of base over F_q and solve coordinate matrix of related to R_AB that(7) R AB can generate 2n BMQ polynomials over(8) is the public key and ( A , B ,λ)is the private key. t is the length of padding vector. If q = 2, we get t = 2 or t = 3, else t = 3.Part of digital signaturePart of digital signature is able to provide signers with digital signature of the message. First, signers need to get the public key and the private key of signature. If signers get the public key and the private key ( A , B ,λ), the processes of digital signature are as follows.(1) Signers use certain one-way hash function H to compute summary of message m :(2) Signers randomly choose pad∈Fqt, and suppose that(3) If , it will turn to (2). (4) Signers compute by private key and (5) ( H , s_m) is the signature of message m .Suppose that value domain of hash function H is . If the length of H ( m ) is not enough( 2n - t), it will be padded up to( 2n ? t). The padding method is not limited. For example, it can pad by the partial contents of .Part of signature verificationPart of signature verification is able to verify digital signature of message. This part is used by verifiers, in order to verify whether or not message issue by the alleged signer. First, verifiers need to get the public key of signer, message m and signature ( H , s m)of m .The verifiable processes are as follows.(1) The verifiers compute summary of message(2) The verifiers use public key of signer to compute : .(3) If d_m′= d_m′′, the signature is passed, else the signature is not passed.ii. The practical application1. X.509 v3i public key certificatesX.509 v3i public key certificates consist of basic domain and extended domain. First, they increase an optional field of Union Authentication Center in basic domain. After the digital certificates are signed by CA, Union Authentication Center will sign the certificates in an orderly way. In the end, the signature is the final signature. In this way, the flexibility and security of digital certificates are improved drastically. Then the certificates increase a customizable extended field in extended domain. The special requirements of users become clear by being bounded to multiple attributes. In this way, the flexibility and convenience of certificates are improved drastically.2. The certificates issue and certificates verificationIt finishes certificates issue of CA and certificates verification by HFEM and I-HFEM. First, CA sets initialization parameter and values of each field of X.509 v3i certificates. Afterwards CA uses MD5 algorithm to compute summary. Then CA uses I-HFEM signature scheme to sign the summary of certificates. It shows the complete content of certificates. If certificates need to be verified, it will use MD5 algorithm to compute hash value of the message. If the computational hash value is equal to the existing hash value, it will show related prompt of valid certificates. Else, it will show related prompt of invalid certificates. 3. The security management of certificatesThe security management of certificates is a complex and a huge management system. And every part needs to be analysed and studied in depth. We introduce the processes and principles of application, issue, storage, update and abolishment of certificates. The above processes and principles are also applicable to the new public key cryptography system.The results from theoretical and practical exploration prove that HFEM and I-HFEM have strong security and practicality. They are playing gigantic pushing role to the fields of public key cryptography and PKI.