Research On Functional Encryption And Digital Signature Theory

Confidentiality and authentication are two basic properties of the information security.Generally,encryption can guarantee the confidentiality of information,and digital signature can guarantee the authentication of information.However,the common encryption cannot compute on ciphertext.Functional encryption extends the common encryption,enables the third party to calculate and output a function value of plaintext without decryption.This paper studies the functional encryption and digital signature respectively.Firstly,this paper designs a functional encryption scheme by the idea of key encapsulation,which combines public key encryption and symmetric encryption.When encrypting,one key is used to encrypt the message(plaintext)to one part of the ciphertext through the symmetric encryption,and then this key is encrypted to another part of the ciphertext through the public key encryption.When decrypting,the key of symmetric encryption is obtained by decryption algorithm of the public key encryption,and then a function value of the message is obtained by decryption algorithm of the symmetric encryption.In the design of functional encryption scheme,this paper uses the public key encryption,the symmetric encryption,the non-interactive proof system,the indistinguishable obfuscator and the commitment scheme.In addition,this paper proves that the functional encryption scheme has indistinguishable security.Secondly,this paper designs an elliptic curve digital signature scheme with forward security.The commonly used digital signatures include RSA digital signature,El Gamal digital signature and elliptic curve digital signature.When the key length is equal,elliptic curve digital signature has the highest security.This paper analyzes the traditional elliptic curve digital signature scheme(ECDSA scheme).It is found that this scheme not only has complex operation process,but also has no forward security.Once the attacker gets the private key,he can forge the signature of all messages,which will destroy the whole cryptosystem.In view of the shortcomings of ECDSA scheme,this paper designs an elliptic curve digital signature scheme(improved scheme)with forward security,and proves the security of the improved scheme under the random oracle model.Compared with ECDSA scheme,the computational complexity of the improved scheme is much less than ECDSA scheme in the process of signature generation and signature verification.