Cloud computing-oriented secure absolute value evaluation method

Abstract

The invention discloses a secure absolute value evaluation method for cloud computing, which belongs to the field of cloud computing data security, and designs a secure absolute value evaluation protocol SABS based on a Paillier partial homomorphic encryption algorithm variant with rapid encryption and decryption capabilities and a double-server architecture. According to the safe absolute value evaluation protocol SABS, a server S0 inputs a Paillier ciphertext # imgabs0 # for interactive communication calculation, and another server S1 outputs a Paillier ciphertext # imgabs1 # of an absolute value x * of x. The safe absolute value evaluation protocol based on the Paillier partial homomorphic encryption algorithm solves the problems that in an existing safe absolute value evaluation protocol based on the Paillier partial homomorphic encryption algorithm, efficiency is low, and communication overhead is large.

Description

Technical Field

[0001] The present invention relates to the technical field of cloud computing data security, and in particular to a secure absolute value evaluation method for cloud computing. Background Art

[0002] In the era of cloud computing, people tend to outsource data and computing to cloud servers with extremely large storage and computing capabilities. However, outsourcing data and computing to cloud servers may cause privacy leakage. To this end, before outsourcing data, fully homomorphic encryption technology can be used to encrypt the data, allowing the cloud server to perform calculations on the encrypted data.

[0003] At present, the industry often uses the Paillier partially homomorphic encryption algorithm, which has the advantage of low overhead, but also has the disadvantage of few calculation types. To this end, the industry has designed a variety of calculation methods so that people can perform calculations on data encrypted by the Paillier partially homomorphic encryption algorithm, and secure absolute value evaluation is one of them. However, the existing secure absolute value evaluation protocol has the disadvantages of time-consuming calculation and high communication cost. Summary of the invention

[0004] The purpose of the present invention is to overcome the problems of time-consuming calculation and high communication cost in the existing secure absolute value evaluation protocol, and propose a secure absolute value evaluation method for cloud computing.

[0005] To achieve the above purpose, the technical solution provided by the present invention is: a secure absolute value evaluation method for cloud computing, based on a Paillier partially homomorphic encryption algorithm variant with fast encryption and decryption capabilities and a dual-server architecture, a secure absolute value evaluation protocol SABS is designed; the secure absolute value evaluation protocol SABS is composed of a server S0 inputting a Paillier ciphertext Through interactive communication calculation, another server S1 outputs the absolute value x of x * Paillier ciphertext

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

[0007] Step 1, SABS initialization: A data owner DO initializes a Paillier partially homomorphic encryption algorithm variant and recruits two non-colluding servers S0 and S1; DO generates an auxiliary tuple for server S0 and server S1 respectively, 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 data x to be outsourced to obtain the ciphertext And the ciphertext Sent to server S0; then, DO sends auxiliary tuples Assisted0 and Assisted1 to server S0 and server S1 respectively;

[0009] Step 3, SABS calculation: Server S0 inputs the ciphertext specified by DO The server S1 completes the calculation of the secure absolute value evaluation protocol SABS through interactive communication, and finally the server S1 obtains the ciphertext result where x * Represents the absolute value of data x;

[0010] Step 4: Decryption of SABS calculation results: Server S1 will calculate the results Send back to DO; then, DO uses the decryption algorithm of the Paillier partially homomorphic encryption algorithm variant to After decryption, the absolute value x of data x is obtained * .

[0011] Further, in step 1, DO performs related operations: DO uses subtractive secret sharing to split 2α into two shares <2α>0 and <2ɑ>1, satisfying <2ɑ>1-<2ɑ>0=2ɑ, where ɑ is the private key of the Paillier partially homomorphic encryption algorithm variant; then, 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 share <2ɑ>0 and the ciphertext Store it into the auxiliary tuple Assisted0 and store <2ɑ>1 into the auxiliary tuple Assisted1.

[0012] Further, in step 3, the secure absolute value evaluation protocol SABS comprises the following steps:

[0013] (1) Server S0 inputs the ciphertext of data x Server S0 selects two random numbers r1 and r2. r1 and r2 need to meet the following requirements: the bit length of r1 is σ and r1 cannot be 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; then, server S0 takes the share <2α>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: Server S0 calculates the ciphertext D. If π=0, the calculation process of ciphertext D is: If π=1, the calculation process of ciphertext D is Server S0 calculates the share z0. The specific process is to first calculate Then 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 calculation; output share z = h′·h -1 mod N;

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

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

[0017] 1. Higher execution efficiency. The existing secure absolute value evaluation protocol based on the Paillier partially homomorphic encryption algorithm has the problem of low efficiency. The secure absolute value evaluation protocol designed by the present invention can reduce the execution time of the protocol.

[0018] 2. Less communication cost. The existing secure absolute value evaluation protocol based on the Paillier partially homomorphic encryption algorithm consumes a lot of communication cost. The secure absolute value evaluation protocol designed by the present invention can reduce the communication cost required for the protocol execution process. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0020] Figure 2 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0021] The present invention is further described in detail below in conjunction with embodiments and 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 a data owner DO, two servers S0 and S1, and its specific implementation includes the following steps:

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

[0024] a.Select Odd prime numbers p and q of bits, choose 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 each case; if P is not prime and Q is prime, regenerate p′ until P is prime and p, q, p′, q′ are relatively prime; if P is prime and Q is not prime, regenerate q′ until Q is prime and p, q, p′, q′ are relatively prime; if both P and Q are not prime, return to step a;

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

[0030] Among them, κ is the safety parameter, and is a function related to the security parameter κ; then, 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 in , β=(P-1)(Q-1) / (4pq), p and q are odd prime numbers smaller than P and Q; the private key sk=α, where α=p·q; Next, DO uses subtractive 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) selects a random number as <2α>1, and then sets <2α>0=<2α>1-2α; next, DO uses the Paillier partially homomorphic encryption algorithm variant 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 whose bit length is less than or equal to the bit length of the private key sk; when executing the encryption algorithm, when a data m is less than 0, it is converted to m = N-|m|; in particular, the plaintext space [0, N / 2] and [N / 2+1, N-1] are used for non-negative numbers and negative numbers respectively; finally, DO converts the share <2ɑ>0 and the ciphertext Store it into the auxiliary tuple Assisted0 and store <2ɑ>1 into the auxiliary tuple Assisted1.

[0033] Step 2: SABS data outsourcing: DO uses a variant of the Paillier partially homomorphic encryption algorithm to encrypt the data x to be outsourced to obtain the ciphertext And the ciphertext Send to server S0; then, DO sends the auxiliary tuples Assisted0 and Assisted1 to server S0 and server S1 respectively.

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

[0035] (1) Server S0 inputs the ciphertext of data x Server S0 selects two random numbers r1 and r2. r1 and r2 need to meet the following requirements: the bit length of r1 is σ and r1 cannot be 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 of the input data x of the SABS protocol and satisfy σ-l-2≥κ. Subsequently, server S0 takes 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: Server S0 calculates the ciphertext D. If π=0, the calculation process of ciphertext D is: If π=1, the calculation process of ciphertext D is Server S0 calculates the share z0. The specific process is to first calculate Then 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 calculation; output share z = h′·h -1 mod N;

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

[0038] Step 4: Decryption of SABS calculation results: Server S1 will calculate the results Send back to DO; then, DO uses the decryption algorithm of the Paillier partially homomorphic encryption algorithm variant 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 wrong Decrypt directly Sent 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 ), generally l=32; for the parameter σ related to the security level, when the bit length of N is greater than or equal to 1024, σ=162 can generally be taken;

[0042] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A secure absolute value evaluation method for cloud computing, characterized in that: Based on the Paillier partially homomorphic encryption algorithm variant with fast encryption and decryption capabilities and a dual-server architecture, a secure absolute value evaluation protocol SABS is designed; the secure absolute value evaluation protocol SABS consists of a server S0 inputting a Paillier ciphertext Through interactive communication calculation, another server S1 outputs the absolute value x of x * Paillier ciphertext The specific implementation of the safe absolute value evaluation protocol includes the following steps: Step 1, SABS initialization: A data owner DO initializes a Paillier partially homomorphic encryption algorithm variant and recruits two non-colluding servers S0 and S1; DO generates an auxiliary tuple for server S0 and server S1 respectively, denoted as Assisted0 and Assisted1; Step 2: SABS data outsourcing: DO uses a variant of the Paillier partially homomorphic encryption algorithm to encrypt the data x to be outsourced to obtain the ciphertext And the ciphertext Sent to server S0; then, DO sends auxiliary tuples Assisted0 and Assisted1 to server S0 and server S1 respectively; Step 3, SABS calculation: Server S0 inputs the ciphertext specified by DO The server S1 completes the calculation of the secure absolute value evaluation protocol SABS through interactive communication, and finally the server S1 obtains the ciphertext result where x * Represents the absolute value of data x; Step 4: Decryption of SABS calculation results: Server S1 will calculate the results Send back to DO; then, DO uses the decryption algorithm of the Paillier partially homomorphic encryption algorithm variant to After decryption, the absolute value x of data x is obtained * .

2. A secure absolute value evaluation method for cloud computing according to claim 1, characterized in that: In step 1, DO performs the following operations: DO uses subtractive secret sharing to split 2α into two shares <2α>0 and <2α>1, satisfying <2ɑ>1-<2ɑ>0=2ɑ, where ɑ is the private key of the Paillier partially homomorphic encryption algorithm variant; then, 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 share <2ɑ>0 and the ciphertext Store it into the auxiliary tuple Assisted0 and store <2ɑ>1 into the auxiliary tuple Assisted1.

3. A secure absolute value evaluation method for cloud computing according to claim 2, characterized in that: In step 3, the secure absolute value evaluation protocol SABS comprises the following steps: (1) Server S0 inputs the ciphertext of data x Server S0 selects two random numbers r1 and r2. r1 and r2 need to meet the following requirements: the bit length of r1 is σ and r1 cannot be 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. Then, server S0 takes 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: Server S0 calculates the ciphertext D. If π=0, the calculation process of ciphertext D is: If π=1, the calculation process of the ciphertext D is Server S0 calculates the share z0. The specific process is to first calculate Then calculate z0←z0-r2; finally, server S0 sends (C, D, z0) to server S1; The above DDLog N The calculation process of (*) includes: let h = * mod N, h and h′ are the intermediate results required for calculation; output share z = h′·h -1 mod N; (2) Server S1 extracts the share <2α>1 from the auxiliary tuple Assisted1; then server S1 calculates and d←z1-z0mod N, where z1 and d are some intermediate calculation results; if Server S1 records μ0=0, if Server S1 records μ0=1; finally, server S1 calculates Get the absolute value of data x in ciphertext form

Images