CN103916248A - Fully homomorphic encryption public key space compression method - Google Patents

Abstract

The invention discloses a fully homomorphic encryption public key space compression method. The method comprises the following steps that (1) a private key is generated first, a prime number in the range of [2Eta-1,2Eta) is generated randomly as the private key p, a series of random numbers Nui in the range of (-2Rho , 2Rho ) and a series of random integers qi in the range of [0, q0) are then generated randomly, a public key generating factor xi=p*qi+Nui is obtained, and (a, x1, x2, x3,..., xN) are used as a public key generating sequence x, wherein the a is a public key module value, a = q0*p, the q0 is any integer whose square root cannot be extracted and is in the range of [0, 2Nu/p), and the Eta, the Nu and the Rho are safety parameters determined by a required safety factor Lambada; (2) the length of the obtained public key generating sequence x is N, and the value of the N is /2Alpha + 1. According to the fully homomorphic encryption public key space compression method, under the premise that algorithm safety is not influenced, the compression on the public space is achieved by adopting the method of compressing a two-dimensional public key space to a one-dimensional sequence.

Description

A kind of full homomorphic cryptography PKI space compression method

technical field

The present invention relates to a kind of public-key process method in full homomorphic cryptography technology, be specifically related to a kind of full homomorphic cryptography PKI space compression method.

background technology

Along with the appearance of the emerging technologies such as cloud computing, people improve greatly for the disposal ability of technical resource, and human being's production and life have obtained very big facility.But as a kind of emerging technology, the security performance of cloud computing system and secret protection will face darker challenge, address these problems the key that has just become development.

Relied on its retrieval mode and fail safe reliably flexibly by the full homomorphic cryptography method of the title titled with " cryptographic Holy grail ", have huge development prospect in cloud computing field.So-called full homomorphic cryptography algorithm refers to that the data to encrypting are processed and obtains an output, this output is decrypted, its result be the same with the Output rusults that Same Way processing unencrypted initial data obtains.Its meaning is to protect cleartext information, simultaneously also can be in the enterprising line function computing of ciphertext.These two features of full homomorphic cryptography, it can be used in cloud computing environment, entrust computation schema---input that user will calculate obtains ciphertext after by full homomorphic cryptography algorithm for encryption, and the function that will calculate and ciphertext send to cloud center, carry out after functional operation ciphertext at cloud center, return to again result of calculation, deciphered the final result obtaining by user.

Full homomorphic cryptography is an important topic of field of cryptography always.2009, the Craig Gentry of IBM published thesis and has proposed the feasible method of full homomorphic cryptography from mathematics, made this technology obtain in realization breakthrough.But in this scheme, the memory space of PKI is excessive, this has had a strong impact on the practical application of full homomorphic cryptography method.Therefore, find suitable feasible PKI compression scheme and just become the task of top priority.

summary of the invention

technical problem:the present invention proposes a kind of full homomorphic cryptography PKI space compression method, do not affecting under the prerequisite of algorithm security, by two-dimentional PKI space compression is realized to the compression to PKI space to the method for one-dimensional sequence.

summary of the invention:for solving the problems of the technologies described above, the invention provides a kind of full homomorphic cryptography PKI space compression method, the method comprises the steps,

Step 1: first generate private key; Exist by one of random generation prime number in scope is as private key ; Again random generate a series of random number in scope , and a series of in interval interior random integers , obtain PKI and generate the factor , will as PKI formation sequence ; Wherein for PKI mould value, , be one in scope arbitrarily can not evolution integer, and , with by the coefficient of safety requiring definite security parameter;

Step 2: for the PKI formation sequence obtaining , its length is value is ;

Step 3: for PKI formation sequence in element, obtain the required PKI of actual encrypted by multiplying each other between two ; ? , wherein, with , corresponding relation be , size be , wherein , and i<N, j<N.

Preferably, the using method of public and private key in encryption and decryption process is:

Ciphering process: for given plaintext , first generate size and be random vector , one of regeneration exists random number in scope , by calculating , obtain corresponding ciphertext , wherein right modulo operation;

Decrypting process: for ciphertext , by calculating , obtain corresponding plaintext .

beneficial effect:

The PKI space compression method that the present invention proposes can be by the PKI space of using in full homomorphic cryptography method from being be reduced to for level (wherein for the dimension value of matrix); And this corresponds in actual full homomorphic cryptography application process, actual key space is reduced to the level of hundred MBits from the level of GBits.This has greatly promoted the practicality of full homomorphic cryptography.

accompanying drawing explanation

Fig. 1 is that PKI of the present invention generates schematic diagram.

Fig. 2 is full homomorphic cryptography schematic flow sheet of the present invention.

embodiment

Below in conjunction with drawings and the embodiments, patent of the present invention is described in further detail.

The full homomorphic cryptography PKI of one provided by the invention space compression method, the method comprises the steps,

Step 1: first generate private key; Exist by one of random generation prime number in scope is as private key ; Again random generate a series of random number in scope , and a series of in interval interior random integers , obtain PKI and generate the factor , will as PKI formation sequence ; Wherein for PKI mould value, , be one in scope arbitrarily can not evolution integer, and , with by the coefficient of safety requiring definite security parameter;

Step 2: for the PKI formation sequence obtaining , its length is value is ;

Step 3: for PKI formation sequence in element, obtain the required PKI of actual encrypted by multiplying each other between two ; ? , wherein, with , corresponding relation be , size be , wherein , and i<N, j<N.

The using method of public and private key in encryption and decryption process is:

Ciphering process: for given plaintext , first generate size and be random vector , one of regeneration exists random number in scope , by calculating , obtain corresponding ciphertext , wherein right modulo operation;

Decrypting process: for ciphertext , by calculating , obtain corresponding plaintext .

Full homomorphic cryptography PKI space compression method as shown in Figure 1, PKI formation sequence by composition, and for PKI formation sequence in element, obtain the required PKI of actual encrypted by multiplying each other between two ; ? , wherein, with , corresponding relation be , size be , wherein .

The concrete steps that realize are as follows:

Step 1: first generate private key, exist by one of random generation prime number in scope is as private key ; Again random generate a series of random number in scope , and a series of in interval interior random integers , obtain PKI and generate the factor , will as PKI formation sequence ; Wherein for PKI mould value, , be one in scope arbitrarily can not evolution integer, and , with by the coefficient of safety requiring definite security parameter;

Step 2: for the PKI formation sequence obtaining , its length is value is ;

Step 3: for PKI formation sequence in element, obtain the required PKI of actual encrypted by multiplying each other between two ; ? , wherein, with , corresponding relation be , size be , wherein .

As shown in Figure 2 be full homomorphic cryptography schematic flow sheet of the present invention, the full homomorphic cryptography PKI of described one spatial manipulation method, is characterized in that the using method of public and private key in encryption and decryption process is

Ciphering process: for given plaintext , first generate size and be random vector , one of regeneration exists random number in scope , by calculating , obtain corresponding ciphertext , wherein right modulo operation;

Decrypting process: for ciphertext , by calculating , obtain corresponding plaintext .

Should understand above-described embodiment only for the embodiment of technical solution of the present invention is described, limit the scope of the invention and be not used in.After having read the present invention, modification and the replacement of those skilled in the art to various equivalents of the present invention all falls within the protection range that the application's claim limits.

Claims (2)

1. a full homomorphic cryptography PKI space compression method, is characterized in that, the method comprises the steps,

Step 1: first generate private key; Exist by one of random generation prime number in scope is as private key ; Again random generate a series of random number in scope , and a series of in interval interior random integers , obtain PKI and generate the factor , will as PKI formation sequence ; Wherein for PKI mould value, , be one in scope arbitrarily can not evolution integer, and , with by the coefficient of safety requiring definite security parameter;

Step 2: for the PKI formation sequence obtaining , its length is value is ;

Step 3: for PKI formation sequence in element, obtain the required PKI of actual encrypted by multiplying each other between two ; ? , wherein, with , corresponding relation be , size be , wherein , and i<N, j<N.

2. full homomorphic cryptography PKI space compression method according to claim 1, is characterized in that, the using method of public and private key in encryption and decryption process is:

Ciphering process: for given plaintext , first generate size and be random vector , one of regeneration exists random number in scope , by calculating , obtain corresponding ciphertext , wherein right modulo operation;

Decrypting process: for ciphertext , by calculating , obtain corresponding plaintext .