WO2020258373A1 - 一种基于同态加密的百万富翁问题解决方法 - Google Patents
一种基于同态加密的百万富翁问题解决方法 Download PDFInfo
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- WO2020258373A1 WO2020258373A1 PCT/CN2019/095167 CN2019095167W WO2020258373A1 WO 2020258373 A1 WO2020258373 A1 WO 2020258373A1 CN 2019095167 W CN2019095167 W CN 2019095167W WO 2020258373 A1 WO2020258373 A1 WO 2020258373A1
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/008—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols involving homomorphic encryption
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/085—Secret sharing or secret splitting, e.g. threshold schemes
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
- H04L9/0863—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving passwords or one-time passwords
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
- H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
- H04L2209/46—Secure multiparty computation, e.g. millionaire problem
Definitions
- the invention relates to the research field of information computing, in particular to a method for solving the millionaire problem based on homomorphic encryption.
- the problem for millionaires is not to divulge the digital information owned by the two parties and determine which number is greater. This problem can be applied in e-commerce.
- the bidding comparison needs to ensure security and not leak any information. Supporting such auctions requires a secure comparison protocol. Solving the problem of millionaires has become a research hotspot in cryptography. At present, many scholars have researched and given different solutions. Some of these schemes have some shortcomings, such as a large amount of calculation, large communication overhead, and difficult implementation.
- Hsiao-Ying Lin and others in the document "An Efficient Solution to The Millionaires’ Problem Based on Homomorphic Encryption” mainly proposed an effective solution to the millionaire problem.
- This scheme mainly uses 0 coding and 1 coding to transform the millionaire problem into the intersection problem of sets. This scheme is relatively efficient, but there are security problems.
- the main purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art and provide a solution to the millionaire problem based on homomorphic encryption. Solving the millionaire problem is similar to the problem of judging which number the two parties hold is larger. Because in many application scenarios, users need to use their own data to compare with any party, and during the comparison process, privacy protection is required, and no information about the other party will be learned. Aiming at the shortcomings of the existing solutions to the millionaire problem, the present invention improves on the original solution to improve the security of the solution.
- T[i][j], where i ⁇ 0,1 ⁇ , 1 ⁇ j ⁇ n, and perform ciphertext according to the binary value of the first data party’s private input x and the position of the corresponding T table Fill, T[x i′ ][j′] E(z), where z ⁇ 0,1 ⁇ , E(z) is the ciphertext for homomorphic encryption of z; r i′ is a randomly selected number, E(ri ′ ) is the ciphertext of homomorphic encryption of r i′ ; 1 ⁇ i′ ⁇ n, 1 ⁇ j′ ⁇ n, Is the opposite value of x i′ to get the filled table:
- the homomorphic encryption algorithm is one of Paillier encryption algorithm and ElGamal encryption algorithm.
- the generating of the private key and the public key is specifically:
- G q is a cyclic group with a valence of prime q
- g is a generator of G q
- Z q is composed of the set ⁇ 1,2,...,q-1 ⁇ .
- h g -a
- r′ ⁇ ′ is a random number, 1 ⁇ ′ ⁇ n, 1 ⁇ i′ ⁇ n, 1 ⁇ j′ ⁇ n, r′ ⁇ ′ ⁇ Z q , Z q is determined by the set ⁇ 1,2,...,q-1 ⁇ constitute;
- step S4 is specifically:
- decryption is specifically as follows:
- table T[i][j] is a 2*n table.
- the second data party calculates ⁇ c 1 ,c 2 ,...,c d ⁇ and ⁇ z 1 ,z 2 ,...,z nd ⁇ , and converts ⁇ c 1 ,c 2 ,...,c d ⁇ And ⁇ z 1 ,z 2 ,...,z nd ⁇ two ciphertext sets are combined into a ciphertext set ⁇ c 1 ,c 2 ,...,c d ,z 1 ,z 2 ,...
- the present invention has the following advantages and beneficial effects:
- the present invention uses random numbers for calculation to solve the millionaire problem, which is similar to the problem of judging which number the two parties hold is larger. At the same time, the data party will not obtain any information from the other data party based on the decrypted plaintext; In many application scenarios, users need to use their own data to compare with any party, and during the comparison process, privacy protection is required, and no information about the other party is learned at the same time, so that the privacy of both parties is protected; the present invention uses 0 coding and 1 Coding intersection and homomorphic encryption algorithm are combined, the data party calculates the ciphertext locally, and the homomorphic property can support ciphertext addition operation or ciphertext multiplication operation, reducing the calculation cost, and the two data parties only interact once, reducing communication overhead .
- Fig. 1 is a method flow chart of the method for solving the millionaire problem based on homomorphic encryption according to the present invention.
- a solution to the millionaire problem based on homomorphic encryption, as shown in Figure 1, includes the following steps:
- the first data party performs 1 encoding on the data it owns to get the encoding set
- the second data party performs 0 encoding on the data it owns to get the encoding set
- the first step is to set G as the key generation process of the homomorphic encryption algorithm, E as the encryption process of the homomorphic encryption algorithm, and D as the decryption process of the homomorphic encryption algorithm;
- the homomorphic encryption algorithm includes Paillier encryption algorithm and ElGamal Encryption Algorithm;
- the second step is to generate a private key sk and a public key pk through the key generation process G;
- G q is a cyclic group with a valence of prime q
- g is a generator of G q
- Z q is composed of the set ⁇ 1,2,...,q-1 ⁇ .
- the third step is to prepare a table T[i][j], the table T[i][j] is a 2*n table, where i ⁇ 0,1 ⁇ , 1 ⁇ j ⁇ n, according to the first
- T[x i′ ][j′] E(z), where z ⁇ 0,1 ⁇ , E(z) Is the ciphertext of homomorphic encryption of z;
- r i′ is a randomly selected number, E(ri ′ ) is the ciphertext of homomorphic encryption of r i′ ; 1 ⁇ i′ ⁇ n, 1 ⁇ j′ ⁇ n, Is the opposite value of x i′ to get the filled table:
- the first data party uses the Paillier encryption algorithm, the first data party performs ciphertext filling according to the binary value x n x n-1 L x 1 of the private input x and the position of the binary bit corresponding to the T table.
- the first data party uses the ElGamal encryption algorithm
- the first data party performs ciphertext filling according to the binary value x n x n-1 L x 1 of the private input x and the position of the binary bit corresponding to the T table.
- h g -a
- r′ ⁇ ′ is a random number, 1 ⁇ ′ ⁇ n, 1 ⁇ i′ ⁇ n, 1 ⁇ j′ ⁇ n, r′ ⁇ ′ ⁇ Z q , Z q is determined by the set ⁇ 1,2,...,q-1 ⁇ constitute;
- r i′ and r′′ ⁇ ′ are random numbers, 1 ⁇ ′ ⁇ n, 1 ⁇ i′ ⁇ n, 1 ⁇ j′ ⁇ n, r i′ ⁇ G q , G q is a prime number q Cyclic group
- the fourth step is specifically:
- the random ciphertext preparation process is specifically as follows:
- the second data party calculates ⁇ c 1 ,c 2 ,...,c d ⁇ and ⁇ z 1 ,z 2 ,...,z nd ⁇ , and converts ⁇ c 1 ,c 2 ,...,c d ⁇ And ⁇ z 1 ,z 2 ,...,z nd ⁇ two ciphertext sets are combined into a ciphertext set ⁇ c 1 ,c 2 ,...,c d ,z 1 ,z 2 ,...
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Abstract
Description
Claims (9)
- 一种基于同态加密的百万富翁问题解决方法,其特征在于,包括以下步骤:S1、设定G为同态加密算法的生成密钥过程,E为同态加密算法的加密过程,D为同态加密算法的解密过程;第一数据方有一个私有输入x,将私有输入x转为二进制数,即二进制值,则有x=x nx n-1L x 1,对第一数据方私有输入x的二进制数进行1编码,得到编码集S2、通过生成密钥过程G产生私钥sk和公钥pk;S3、准备表T[i][j],其中,i∈{0,1},1≤j≤n,根据第一数据方私有输入x的二进制值和位数对应T表的位置进行密文填充,T[x i′][j′]=E(z),其中z∈{0,1},E(z)是对z进行同态加密的密文; r i′为随机选取的一个数,E(r i)是对r i′进行同态加密的密文; 1≤i′≤n,1≤j′≤n, 是x i′的相反值,得到填充表格:{T[x 1][1]=E(z),L,T[x n][n]=E(z),再将填充表格发送第二数据方;S4、第二数据方根据自己的私有输入y,转为二进制数,则有,y=y ny n-1L y 1,对第二数据方私有输入的二进制数进行0编码,得到编码集 即编码集 中有d个元素,集合 中一个元素H k,k∈{1,2,...,d},其中 根据 中每一位 有对应的 i″≤l≤n,1≤k≤d,随机选取一个数t l,进行计算:得到:把{c 1,c 2,...,c d}和{z 1,z 2,...,z n-d}两个密文集合组合成一个密文集合,再将组合后密文集合中每个元素进行随机置换位置,得到密文集合{C 1,C 2,...,C n},再把密文集合{C 1,C 2,...,C n}发送给第一数据方;S6、第一数据方将接收到的集合{C 1,C 2,...,C n}进行同态加密中的解密过程,得到D(C l′)=m l′,1≤l′≤n,当且仅当存在m l′=z(z∈{0,1}),则有x>y,否则x<y。
- 根据权利要求1所述的一种基于同态加密的百万富翁问题解决方法,其特征在于,所述同态加密算法为Paillier加密算法和ElGamal加密算法其中一种。
- 根据权利要求2所述的一种基于同态加密的百万富翁问题解决方法,其特征在于,所述产生私钥和公钥,具体为:gcd(L(g λ(N)mod N 2),N)=1,定义L(x′)=(x′-1)/N,则有:公钥为pk=(g,N),私钥为sk=λ(N)=lcm((p-1),(q-1));则有:公钥为:pk=h=g -α,私钥为:sk=α∈Z q,Z q由集合{1,2,...,q-1}构成。
- 根据权利要求2所述的一种基于同态加密的百万富翁问题解决方法,其特征在于,所述填表具体为:当第一数据方使用Paillier加密算法,第一数据方根据私有输入x的二进制值x nx n-1L x 1和二进制的位数对应T表的位置进行密文填充,计算:T[x i′][j′]=E(0)=g 0r β′ Nmod N 2,计算:得到填充后的表格:{T[x 1][1]=E(0),...,T[x n][n]=E(0)再将填充表格发送给第二数据方;当第一数据方使用ElGamal加密算法,第一数据方根据私有输入x的二进制值x nx n-1L x 1和二进制的位数对应T表的位置进行密文填充,计算:其中,h=g -a,r′ β′是随机数,1≤β′≤n,1≤i′≤n,1≤j′≤n,r′ β′∈Z q,Z q由集合{1,2,...,q-1}构成;计算:其中,r i′和r″ β′是随机数,r i′∈G q,G q是价为素数q的循环群,r″ β′∈Z q,Z q由集合{1,2,...,q-1}构成;得到填充后的表格:{T[x 1][1]=E(1),...,T[x n][n]=E(1)再将填充表格发送给第二数据方。
- 根据权利要求4所述的一种基于同态加密的百万富翁问题解决方法,其特征在于,所述表T[i][j]为2*n的表。
- 根据权利要求2所述的一种基于同态加密的百万富翁问题解决方法,其特征在于,所述步骤S4具体为:第二数据方接收到T表后,根据自己的私有输入y转为二进制数,则有y=y ny n-1L y 1,对第二数据方私有输入的二进制数进行0编码,得到编码集 其中 即编码集 有d个元素,编码集中一个元素H k,k∈{1,2,...,d},其中 根据 中每一位 有对应的 i″≤l≤n,1≤k≤d,进行计算,根据加密方法不同,则有以下情况:得到:得到:其中,i″≤l≤n,1≤k≤d。
- 根据权利要求2所述的一种基于同态加密的百万富翁问题解决方法,其特征在于,所述随机密文准备过程具体如下:其中,i″≤l≤n,1≤k≤d;当T表中的密文是Paillier加密算法加密的,准备n-d个随机密文z j″,其中 u j″为随机选取的一个数,u j″∈Z N,Z N={0,...,N-1}是一个关于模N加法运算的群;r″′ j″为一个随机数, 由集合{1,2,...,N-1}中与N互素的整数构成;
- 根据权利要求1所述的一种基于同态加密的百万富翁问题解决方法,其特征在于,所述把{c 1,c 2,...,c d}和{z 1,z 2,...,z n-d}组合的具体过程为:第二数据方计算得到{c 1,c 2,...,c d}和{z 1,z 2,...,z n-d},将{c 1,c 2,...,c d}和{z 1,z 2,...,z n-d}两个密文集合组合成一个密文集合{c 1,c 2,...,c d,z 1,z 2,...,z n-d},再将密文集合{c 1,c 2,...,c d,z 1,z 2,...,z n-d}中每个元素随机置换位置得密文集合{C 1,C 2,...,C n},例{C 1,C 2,...,C n}={c 2,z n-d,...c, n},再把集合{C 1,C 2,...,C n}发送给第一数据方。
- 根据权利要求2所述的一种基于同态加密的百万富翁问题解决方法,其特征在于,所述解密具体如下:第一数据方将接收到的集合{C 1,C 2,...,C n}中C l′进行同态加密中的解密过程,分两种情况:当集合{C 1,C 2,...,C n}中的密文是Paillier加密算法加密的,对集合{C 1,C 2,...,C n}中每个元素C l′进行解密,其计算过程:其中λ(N)=lcm((p-1),(q-1)),L(x′)=(x′-1)/N,1≤l′≤n,当且仅当存在m l′=0,则有x> y,说明第一数据方的私有输入x大于第二数据方的私有输入y,否则x< y,说明第一数据方的私有输入x小于第二数据方的私有输入y;当集合{C 1,C 2,...,C n}中的密文是ElGamal加密算法加密的,对集合{C 1,C 2,...,C n}中每个元素C l′进行解密,其计算过程:D(C l′)=(C l′,1,C l′,2)=C l′,2·C l′,1 α=m l′,其中,私钥sk=α,当且仅当存在m l′=1,则有x>y,说明第一数据方的私有输入x大于第二数据方的私有输入y,否则x<y,说明第一数据方的私有输入x小于第二数据方的私有输入y。
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