Realization And Research Of PKI Based On HFEM

i. 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. This article is based on open source EJBCA PKI system, and we make a study on PKI. We explained EJBCAD architecture, certificate issuance process, the certificate and key management and how to transplant the HFEM algorithm to the system of so EJBCA . We also use this system which we make to do an experiment, and successfully get a certificate which we need.It proves the feasibility of the above scheme. This article is introduced in accordance with the following two aspects, one is The new public key cryptography and the other is The practical application.ii. The new public key cryptographyThe 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 chosen randomly and satisfied with the above four constraint conditions.(2) We randomly choose a group of baseover Fq and solve coordinate matrix AB 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 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 ( )w ?1∈VS B\{0} of w by Gauss elimination.(5) The receiver solves coordinate y∈Fqn\{0} of w? 1 related (6) According to ( x ,y ), the receiver gets plaintext: P = x?y=α?β.Part of key generation of digital signature Part of key generation of digital signature is able to provide every signer with a pair of public key 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:We chooses ergodic matrices Q1 , Q2∈Fq n×n randomly ( q n must be big enough.).We chooses M∈Fq n×nrandomly. M is satisfied with Exp (Q 1 , M , Q2 ) = 1andWe randomly choose the bases over Fq .We randomly choose i , j∈{ 1, ,n}, and computeIf Rank ( AB ) <2n, we turn to (4).We randomly choose a group of base [ ] and solve coordinate matrixλ∈Fq2 n×2nof ?? AB?? related to R AB thatR AB can generate 2n BMQ polynomials overis 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.Signers use certain one-way hash function H to compute summary of message m :Signers randomly choose pad∈Fqt, and suppose that sm =α,β∈Fqn\{0} by private key and( H , s m) is the signature of message m .Suppose that value domain of hash function H is Fq 2n-t. 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 H ( m H ( m )).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 m : ( )(2) The verifiers use public key of signer to(3) If d m′= dm′′, the signature is passed, else the signature is not passed. iii. The practical application1. X.509 v3i public key certificatesX.509 v3i public key certificates consist of basic domain and extended domain. First, theyincrease 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. About EJBCAEJBCA is an advanced enterprise class open source PKI-implementation (it's a CA!) written in a Java/J2EE environment. The focus for the EJBCA project is to create a flexible, platform independent and scalable CA/RA solution, fulfilling various requirements a large enterprise could have, concerning not only security aspects but also connectivity, administrative delegation and event logging. Its features include:Flexible, component based architecture.Using standard, high performance RDBMS for storage.Support for X.509 certificates and Card Verifiable certificates.CRL creation and URL-based CRLDistribution Points according to RFC5280.Standalone or integrated in any J2EE application.Key recovery module to store private keys for recovery for selected users and certificates3. 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. We introduced the source files and the structures in this 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.