A cloud computing-oriented secure absolute value evaluation method

Abstract

This invention discloses a secure absolute value evaluation method for cloud computing, belonging to the field of cloud computing data security. Based on a variant of the Paillier partially homomorphic encryption algorithm with fast encryption and decryption capabilities and a dual-server architecture, this invention designs a secure absolute value evaluation protocol, SABS. The SABS protocol involves one server, S0, inputting a Paillier ciphertext and performing calculations via interactive communication, while another server, S1, outputs the absolute value x. * The present invention addresses the problems of low efficiency and high communication overhead in existing secure absolute value evaluation protocols based on the Paillier partially homomorphic encryption algorithm.

Description

Technical Field

[0001] This invention relates to the technical field of cloud computing data security, and in particular to a method for calculating the absolute value of security for cloud computing. Background Technology

[0002] In the era of cloud computing, people tend to outsource data and computation to cloud servers, which possess enormous storage and computing power. However, outsourcing data and computation to cloud servers can lead to privacy leaks. Therefore, before outsourcing data, fully homomorphic encryption can be used to encrypt the data, allowing the cloud server to perform computations on the encrypted data.

[0003] Currently, the Paillier partially homomorphic encryption algorithm is commonly used in the industry. While it boasts low overhead, it also suffers from limited computational types. To address this, various computational methods have been designed to perform calculations on data encrypted with Paillier partially homomorphic encryption; secure absolute value evaluation is one such method. However, existing secure absolute value evaluation protocols suffer from drawbacks such as high computational time and significant communication overhead. Summary of the Invention

[0004] The purpose of this invention is to overcome the problems of computation time and high communication costs in existing secure absolute value evaluation protocols, and to propose a secure absolute value evaluation method for cloud computing.

[0005] To achieve the above objectives, the technical solution provided by this invention is as follows: a secure absolute value evaluation method for cloud computing, based on a variant of the Paillier partially homomorphic encryption algorithm with fast encryption and decryption capabilities and a dual-server architecture, designing a secure absolute value evaluation protocol SABS; the secure absolute value evaluation protocol SABS takes a Paillier ciphertext as input from a server S0. The absolute value of x is calculated through interactive communication and output by another server S1. * Paillier cipher

[0006] The specific implementation of this secure absolute value evaluation protocol includes the following steps:

[0007] Step 1, SABS initialization: A data owner DO initializes a variant of the Paillier partially homomorphic encryption algorithm and recruits two non-colluding servers S0 and S1; DO generates an auxiliary tuple for each server S0 and server S1, denoted as Assisted0 and Assisted1;

[0008] Step 2, SABS Data Outsourcing: DO uses a variant of the Paillier partially homomorphic encryption algorithm to encrypt the outsourced data x to obtain ciphertext. and ciphertext The DO sends the Assisted0 and Assisted1 tuples to server S0 and server S1 respectively.

[0009] Step 3, SABS Calculation: Server S0 inputs the ciphertext specified by DO. The Secure Absolute Value (SABS) protocol is calculated via interactive communication with server S1, and finally server S1 obtains the ciphertext result. Where x * Represents the absolute value of data x;

[0010] Step 4: Decrypting the SABS calculation results: Server S1 will decrypt the calculation results. The message was sent back to the DO; subsequently, the DO used a decryption algorithm based on a variant of the Paillier partially homomorphic encryption algorithm to... After decryption, the absolute value x of the data x is obtained. * .

[0011] Further, in step 1, DO performs the following operations: DO uses a subtraction secret share to split 2α into two shares, <2α>0 and <2ɑ>1, satisfying <2ɑ>1 - <2ɑ>0 = 2ɑ, where ɑ is the private key of a variant of the Paillier partially homomorphic encryption algorithm; subsequently, DO uses the encryption algorithm of the Paillier partially homomorphic encryption algorithm variant to encrypt the number 1 to obtain the ciphertext. Finally, DO will combine the share <2ɑ>0 with the ciphertext. Store the data in the auxiliary tuple Assisted0, and store <2ɑ>1 in the auxiliary tuple Assisted1.

[0012] Furthermore, in step 3, the Secure Absolute Value Evaluation Protocol (SABS) includes the following steps:

[0013] (1) The ciphertext of the input data x on server S0 Server S0 selects two random numbers r1 and r2, which must satisfy the following requirements: the bit length of r1 is σ and r1 cannot be the digit 0. as well as Where σ is a security parameter related to the security level κ, σ needs to be much larger than the bit length l of the input data x of the SABS protocol and satisfy σ-l-2≥κ; subsequently, server S0 extracts the share <2α>0 and ciphertext from the auxiliary tuple Assisted0. Next, server S0 selects a random bit π ← {0, 1} and calculates the ciphertext C. The calculation process is as follows: Server S0 calculates the ciphertext D. If π = 0, the calculation process for ciphertext D is as follows: If π = 1, the calculation process for ciphertext D is as follows: Server S0 calculates the share z0, specifically by first calculating... Next, calculate z0←z0-r2; finally, server S0 sends (C, D, z0) to server S1.

[0014] The above DDLog N The calculation process of (*) includes: Let h = * mod N, h and h′ are the intermediate results required for the calculation; the output share z = h′·h -1 mod N;

[0015] (2) Server S1 extracts a share <2α>1 from the assisted tuple Assisted1; then Server S1 performs calculations. And d←z1-z0mod N, where z1 and d are intermediate calculation results; if Server S1 records μ0 = 0, if... Server S1 records μ0 = 1; finally, server S1 calculates... Obtain the absolute value of data x in encrypted form.

[0016] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0017] 1. Higher execution efficiency. Existing secure absolute value evaluation protocols based on Paillier partially homomorphic encryption algorithms suffer from low efficiency. The secure absolute value evaluation protocol designed in this invention can reduce the execution time of the protocol.

[0018] 2. Reduced communication overhead. Existing secure absolute value evaluation protocols based on Paillier partially homomorphic encryption algorithms consume significant communication overhead. The secure absolute value evaluation protocol designed in this invention can reduce the communication overhead required for protocol execution. Attached Figure Description

[0019] Figure 1 This is a framework diagram of the method of the present invention.

[0020] Figure 2 This is a flowchart of the method of the present invention. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0022] like Figure 1 and Figure 2 As shown, this embodiment provides a secure absolute value evaluation method for cloud computing, involving entities such as data owner DO and two servers S0 and S1. Its specific implementation includes the following steps:

[0023] Step 1, SABS Initialization: The data owner (DO) initializes a variant of the Paillier partially homomorphic encryption algorithm, first generating the relevant parameters (N, P, Q, p, q) through the following process:

[0024] a. Choice The odd prime numbers p and q of bits, choose The odd numbers of bits, p′ and q′;

[0025] b. Let P = 2pp' + 1;

[0026] c. Let Q = 2qq' + 1;

[0027] d. Test whether p, q, p′, q′ are coprime. If not, return to step a.

[0028] e. Discuss the cases separately; if P is not a prime number and Q is a prime number, then regenerate p′ until P is a prime number and p, q, p′, q′ are coprime; if P is a prime number and Q is not a prime number, then regenerate q′ until Q is a prime number and p, q, p′, q′ are coprime; if neither P nor Q is a prime number, return to step a.

[0029] f. Output (N = P·Q, P, Q, p, q);

[0030] Where κ is a safety parameter. and It is a function related to the security parameter κ; subsequently, the public-private key pair {pk, sk} of the Paillier partially homomorphic encryption algorithm variant is initialized; the public key pk = (N, h), where N = P·Q, P and Q are large prime numbers, and h = -y 2β mod N, y is in the integer group A random number, β = (P-1)(Q-1) / (4pq), where p and q are odd prime numbers smaller than P and Q; the private key sk = α, where α = p·q; next, DO uses subtraction secret sharing to split 2α into two shares <2α>0 and <2α>1, satisfying <2α>1-<2α>0 = 2α; the splitting process is as follows: from the interval (-2 5κ+1 +1, 2 5 κ+1-1) Select a random number as <2α>1, then let <2α>0 = <2α>1-2α; Next, DO uses a variant of the Paillier partially homomorphic encryption algorithm to encrypt the number 1 to obtain the ciphertext. The encryption algorithm is formally expressed as follows:

[0031]

[0032] Where r is a random number with a bit length less than or equal to the private key sk bit length; when executing the encryption algorithm, when a data m is less than 0, it is converted to m = N - |m|; specifically, the plaintext space [0, N / 2] and [N / 2+1, N-1] are used for non-negative and negative numbers respectively; finally, DO sets the share <2ɑ>0 and the ciphertext Store the data in the auxiliary tuple Assisted0, and store <2ɑ>1 in the auxiliary tuple Assisted1.

[0033] Step 2, SABS Data Outsourcing: DO uses a variant of the Paillier partially homomorphic encryption algorithm to encrypt the outsourced data x to obtain ciphertext. and ciphertext The DO sends the Assisted0 and Assisted1 tuples to server S0 and server S1 respectively.

[0034] Step 3, SABS Calculation: Servers S0 and S1 together complete the SABS calculation, and the steps are as follows:

[0035] (1) The ciphertext of the input data x on server S0 Server S0 selects two random numbers r1 and r2, which must satisfy the following requirements: the bit length of r1 is σ and r1 cannot be the digit 0. as well as Here, σ is a security parameter related to the security level κ. σ needs to be much larger than the bit length of the input data x of the SABS protocol, and satisfy σ - l - 2 ≥ κ. Subsequently, server S0 extracts the share <2ɑ>0 and the ciphertext from the auxiliary tuple Assisted0. Next, server S0 selects a random bit π ← {0, 1} and calculates the ciphertext C. The calculation process is as follows: Server S0 calculates the ciphertext D. If π = 0, the calculation process for ciphertext D is as follows: If π = 1, the calculation process for ciphertext D is as follows: Server S0 calculates the share z0, specifically by first calculating... Next, calculate z0←z0-r2; finally, server S0 sends (C, D, z0) to server S1.

[0036] The above DDLog N The calculation process of (*) includes: Let h = * mod N, h and h′ are the intermediate results required for the calculation; the output share z = h′·h -1 mod N;

[0037] (2) Server S1 extracts a share <2α>1 from the assisted tuple Assisted1; then Server S1 performs calculations. And d←z1-z0mod N, where z1 and d are intermediate calculation results; if Server S1 records μ0 = 0, if... Server S1 records μ0 = 1; finally, server S1 calculates... Obtain the absolute value of data x in encrypted form.

[0038] Step 4: Decrypting the SABS calculation results: Server S1 will decrypt the calculation results. The message was sent back to the DO; subsequently, the DO used a decryption algorithm based on a variant of the Paillier partially homomorphic encryption algorithm to... After decryption, the absolute value x′ of the data x is obtained; the decryption algorithm is formally expressed as:

[0039]

[0040] DO can also be incorrect Decrypt directly Send it to server S0 for the next calculation.

[0041] In actual deployment, the security parameter κ and related functions have the following values: when κ = 112, l(κ) = 448 and n(κ) = 2048; when κ = 128, l(κ) = 512 and n(κ) = 3072; when κ = 192, l(κ) = 768 and n(κ) = 7680; the range of data x is (-2... l ,2 l For the security level parameter σ, when the bit length of N is greater than or equal to 1024, σ can generally be taken as 162.

[0042] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A cloud computing-oriented secure absolute value evaluation method, characterized by, Based on the Paillier partial homomorphic encryption algorithm variant with fast encryption and decryption capabilities and the double-server architecture, a secure absolute value evaluation protocol SABS is designed; the secure absolute value evaluation protocol SABS is inputted with a Paillier ciphertext by a server S0 Through interactive communication calculation, the absolute value x of x is outputted by another server S1 * The Paillier ciphertext of x The secure absolute value evaluation protocol implementation includes the following steps: Step 1, SABS initialization: a data owner DO initializes a Paillier partial homomorphic encryption algorithm variant, recruits two non-colluding servers S0 and S1; the DO generates an auxiliary tuple for the server S0 and the server S1 respectively, denoted as Assisted0 and Assisted1; specifically, the DO performs the following operations: the DO splits 2α into two shares <2α>0 and <2α>1 using subtraction secret sharing, satisfying <2α>1-<2α>0=2α, where α is a private key of the Paillier partial homomorphic encryption algorithm variant; then, the DO encrypts the number 1 using an encryption algorithm of the Paillier partial homomorphic encryption algorithm variant to obtain a ciphertext Finally, the DO stores the share <2α>0 and the ciphertext into the auxiliary tuple Assisted0, and stores <2α>1 into the auxiliary tuple Assisted1; Step 2, SABS data outsourcing: DO uses the encryption algorithm of Paillier partial homomorphic encryption algorithm variant to encrypt the data x to be outsourced to obtain ciphertext and sends the ciphertext to the server S0; then, the DO sends the auxiliary tuples Assisted0 and Assisted1 to the server S0 and the server S1, respectively; Step 3, SABS computation: Server S0 inputs the ciphertext specified by DO and completes the secure absolute value evaluation protocol SABS computation with server S1 through interactive communication, and finally server S1 obtains the ciphertext result where x * represents the absolute value of data x; specifically, the relevant steps are as follows: (1) The ciphertext of the input data x of the server S0 The server S0 selects two random numbers r1 and r2, which need to satisfy the following requirements: the bit length of r1 is σ and r1 cannot take the number 0, and where σ is a security parameter related to the security level κ, σ needs to be much larger than the bit length l of the input data x of the SABS protocol and satisfy σ-l-2≥κ; then, the server S0 takes out the share <2α>0 and the ciphertext Next, the server S0 selects a random bit π←{0,1} and calculates the ciphertext C, and the calculation process is The server S0 calculates the ciphertext D, if π=0, the calculation process of the ciphertext D is If π=1, the calculation process of the ciphertext D is The server S0 calculates the share z0, and the specific process is to first calculate Then calculate z0←z0-r2; finally, the server S0 sends (C, D, z0) to the server S1; The DDLog N The calculation process of (*) includes: let h = * mod N, h and h' are intermediate results required for the calculation; the output share z = h' · h -1 mod N; (2) The server S1 takes the share <2a>1 from the auxiliary tuple Assisted1; then the server S1 performs the calculation and d <- z1 - z0 mod N, where z1 and d are some intermediate calculation results; if The server S1 records μ0 = 0, if The server S1 records μ0 = 1; finally the server S1 gets the absolute value of the data x in the form of ciphertext by calculating ​ Step 4, SABS computation result decryption: Server S1 sends the computation result back to DO; then, DO decrypts the result using the decryption algorithm of the Paillier partial homomorphic encryption variant and obtains the absolute value x of the data x * .

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