CN113888163A - Intelligent contract bill recording and processing method based on completely homomorphic encryption - Google Patents
Intelligent contract bill recording and processing method based on completely homomorphic encryption Download PDFInfo
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Abstract
The intelligent block chain contract technology features that all block chain nodes share all data and participate in all calculation of intelligent contract related business operation. The result of this operation mode is that each node can grasp all input and output parameters of the intelligent contract and all details and intermediate results in the execution process, and if these data relate to sensitive information, privacy protection cannot be realized. After the fully homomorphic encryption-based intelligent contract bill recording and processing method provided by the invention is used, sensitive information is protected by fully homomorphic encryption and appears in an intelligent contract in a ciphertext form, each block link point still can perform appointed business logic operation processing, the operation of the sensitive information is related, and the privacy problem of the original method can be solved by using a ciphertext operation technology corresponding to the fully homomorphic encryption method.
Description
Technical Field
The invention relates to a block chain intelligent contract bill recording and processing method for carrying out encryption protection on sensitive data by using a completely homomorphic encryption technology.
Background
A Smart contract (Smart contract) is a computer protocol intended to propagate, verify or execute contracts in an informational manner. Smart contracts allow for trusted transactions and reliable script program execution without third parties, these transactions and execution processes are transparent, traceable, irreversible, and the results of their execution cannot be tampered with.
The fully homomorphic encryption technology is an advanced cryptography technology, can completely protect data privacy while not influencing data operation, and has iteration of three generations of algorithms since the first fully homomorphic encryption technology is proposed in 2009.
The invention patent application with the application number of CN 201710965216.5 and the name of 'a method and a medium for protecting privacy of block chain intelligent contracts' discloses a method for protecting privacy of block chain intelligent contracts, which can mask transaction details and verify the correctness of transactions, and can protect user privacy and verify the validity and validity of operations. The technical scheme is as follows: privacy data in the block chain is encrypted homomorphically using the addition, and a non-interactive zero-knowledge proof is generated during the transaction to prove the validity of the transaction.
The aforementioned patent application of the invention uses an additive homomorphic, i.e., semi-homomorphic, encryption method in combination with non-interactive zero-knowledge proof to achieve data protection.
The invention patent application with the application number of CN 201910359650.8 and the name of 'a privacy protection method and system based on homomorphic encryption block chain' discloses a privacy protection method and system based on homomorphic encryption block chain, which comprises the following steps: each home intelligent gateway is a node, and a plurality of home intelligent gateways form a block chain; distributing a pair of secret keys for each home intelligent gateway in the block chain, and setting a whole network secret key simultaneously; dividing the whole network nodes in the block chain into special nodes and common nodes, wherein the special nodes store the public key of each home intelligent gateway; each home intelligent gateway receives and stores monitoring terminal acquired information acquired by the sensor, divides the information into visible information and invisible information, homomorphically encrypts the invisible information through a whole network public key, packages the visible information and the invisible information into a data packet, signs the data packet through a private key, and sends the signed data packet to a network through the home intelligent gateway; carrying out whole network verification on the data packet; and the accounting node writes all verified data into a new block in a period of time and is connected to the tail part of the main block chain.
The aforementioned patent application focuses mainly on the network structure and the usage of public and private keys, and does not create a completely homomorphic encryption algorithm.
Disclosure of Invention
The purpose of the invention is: the method solves the data protection problem of the block chain intelligent contract, supports the recording of the encrypted data in the intelligent contract, and simultaneously uses a homomorphic cryptograph operation technology to directly process the encrypted data to obtain an operation result, so that the method can be applied to the application scenes of block chain bill recording and processing of various mechanisms in various industries.
In order to achieve the above object, the technical solution of the present invention is to provide an intelligent contract bill recording and processing method based on fully homomorphic encryption, which is characterized by comprising the following steps:
step 1, selecting different homomorphic encryption same family KEYs from KEY family KEYs (f (x)) related to a function KEY f (x) to distribute to different client users, wherein the KEY family KEYs (f (x)) are expressed as: KEY (f (x) ═ { KEYiI belongs to I, and the same KEY family KEY (f (x)) shares the same operationDictionary, KeyiEncrypting a family KEY for homomorphism belonging to a current KEY family KEY (f (x)), I being a polynomial KEY dimension subscript set;
each homomorphic encryption family KeyiFrom a polynomial key yiAnd a function key f (x), wherein x is a positive integer, the function key f (x) is a positive integer in a value range, and the function key f (x) is a discrete function which is discontinuous everywhere; all homomorphic encryption family KEY KEYs in the same KEY family KEY (f (x))iIs the same, only the polynomial key yiDifferently, a ciphertext obtained by encrypting the homomorphic encryption homomorphic key is called a homomorphic ciphertext;
step 2, processing the order data field needing to be encrypted in the order information into an integer, and recording the integer as an integer plaintext m; user locally uses pre-distributed homomorphic encryption family KeyiEncrypting the whole plaintext m by adopting a simplified ciphertext expression as follows:
Pi＝a·f(x)·yi-b
in the formula, PiThe family ciphertext is further represented by a vector { a, x, b }; x, a and b are positive integers, x is generated randomly, a is a coefficient generated randomly, and b is an offset;
step 3, carrying out hexadecimal coding on the congeneric ciphertext obtained in the step 2 to obtain a final ciphertext;
step 4, after the encryption of all order data fields in the order information is completed in the step 2 and the step 3, transmitting the encrypted order information into a bill processing intelligent contract through a user application program interface in a parameter transmission mode;
step 5, the bill processing intelligent contract receives the encrypted order information and stores the corresponding ciphertext in a contract variable to realize bill recording;
step 6, when bill processing is needed, acquiring related cryptographs saved in contract variables according to a bill processing contract of specific data content needing to be processed; then, calling a ciphertext operation contract to perform addition and/or multiplication ciphertext operation on the ciphertext based on the operation support function G to obtain a result ciphertext;
wherein, the operation support function G is defined as: g ═ G1,g2,g3And (4) the following steps:
in the formula, h1() And h2() Is a bias function; x is the number of1And x2Is any integer in the definition domain D of the function f (x), then h1() And h2() The value range of (a) is also D;
step 7, obtaining the result ciphertext by the bill processing contract;
step 8, the user calls the intelligent contract to obtain the result ciphertext obtained in the step 7, and the bill amount information is checked after local decryption;
and if other users except the current user need to check the result ciphertext obtained in the step 7, converting the result ciphertext of the current user obtained in the step 7 into the ciphertext of the key space of other users by using a ciphertext conversion method, and then decrypting and checking by using the homomorphic encryption homomorphic key distributed to other users.
Preferably, in step 1, the function key f (x) is any hash function with strict one-way property.
Preferably, in step 1, the function key f (x) is constructed by using a hash function, and for an unknown integer k, the function key f (x) constructed by using the hash function is written into a hash (x + k), and the unknown integer k is referred to as a function key.
Preferably, in step 1, a secondary hash function is used to construct the function key f (x), which is specifically defined as follows:
assuming that there are a function key k1 and a function key k2, and q1 is a smaller integer and q2 is a larger integer, f (x) -hash 1(hash2(x + k1) modq1+ k2) modq2 is defined, where hash1() is a first-level hash function and hash2() is a second-level hash function;
when the family cipher text is formed by encryption, the server responsible for cipher text operation is informed of the key k 1.
Preferably, the first-level hash function is the same as or different from the second-level hash function.
Preferably, if the function Key f (x) is constructed by using a secondary hash function, the encryption Key is homomorphiciThe generation steps are as follows:
101, randomly selecting a hash algorithm hash1 adopted by a first-level hash function and a hash algorithm hash2 adopted by a second-level hash function;
step 102, randomly generating two integers as a function key k1 and a function key k 2;
step 103, randomly generating an integer as a polynomial key yi；
Step 104, generating a homomorphic encryption family KeyiExpressed in the following form: key (R)i＝{hash1，k1，hash2，k2，yi}。
Preferably, in step 6, any two ciphertexts P obtained from the order information uploaded by the same user are obtained1、P2If the polynomial key in the homomorphic encryption family key is defined as y, then: p1＝a1·f(x1)·y-b1，P2＝a2·f(x2)·y-b2The following steps are adopted to realize the ciphertext P1And ciphertext P2The addition ciphertext operation of (2):
P1+P2＝a1·f(x1)·y-b1+a2·f(x2)·y-b2
＝[a1·f(x1)+a2·f(x2)]·y-(b1+b2)
＝[a1·g1(x1，x2)·f(h1(x1，x2))+a2·g2(x1，x2)·f(h1(x1，x2))]·y-b3
＝[a1·g1(x1，x2)+a2·g2(x1，x2)]·f(h1(x1，x2))·y-b3
＝a3·f(x3)·y-b3
wherein, a3＝a1·g1(x1，x2)+a2·g2(x1，x2)，x3＝h1(x1，x2)，b3＝b1+b2。
Preferably, in step 6, any two ciphertexts P obtained from the order information uploaded by the same user are obtained1、P2If the polynomial key in the homomorphic encryption family key is defined as y, then: p1＝a1·f(x1)·y-b1，P2＝a2·f(x2)·y-b2The following steps are adopted to realize the ciphertext P1And ciphertext P2The multiplication ciphertext operation of (1):
P1·P2＝[a1·f(x1)·y-b1]·[a2·f(x2)·y-b2]
＝a1·f(x1)·a2·f(x2)·y2-[b1·a2·f(x2)+b2·a1·f(x1)]·y+b1·b2
＝a1·a2·g3(x1，x2)·f(h2(x1，x2))·y2-[b1·a2·g2(x1，x2)·f(h1(x1，x2))+b2·a1·g1(x1，x2)·f(h1(x1，x2))]·y+b1·b2
＝a4·f(x4)·y2-a5·f(x5)·y+b4
in the formula, a4＝a1·a2·g3(x1，x2)，a5＝b1·a2·g2(x1，x2)+b2·a1·g1(x1，x2)，x4＝h2(x1，x2)，x5＝h1(x1，x2)，b4＝b1·b2；
The quadratic form is reduced to the primary form by using a reduction technology, and the specific method is to calculate the square term y of the polynomial secret key y in advance2And discloses its ciphertext:
substituting the square term ciphertext into the multiplication result can obtain:
preferably, in step 8, the ciphertext C for any two different users1、C2The specific ciphertext transformation operation is as follows:
step 901, generating a ciphertext C1Homomorphic encryption family Key1And for generating ciphertext C2Homomorphic encryption family Key2When the current is over;
family Key for homomorphic encryption1Polynomial key y in (1)1Two vectors are obtained: (a)y1，xy1)、(ay1′，xy1') satisfies the following two formulas:
y1＝ay1·f(xy1)
y1＝ay1′/f(xy1′)
family Key for homomorphic encryption2Polynomial key y in (1)2Two vectors are obtained: (a)y2，xy2)、(ay2′，xy2') satisfies the following two formulas:
y2＝ay2·f(xy2)
y2＝ay2′/f(xy2′)
in the formula, ay1、xy1、ay1′、xy1′、ay2、xy2、ay2′、xy2' are positive integers;
vector (a) calculated in steps 902 and 901y1，xy1)、(ay1′，xy1′)、(ay2，xy2)、(ay2′，xy2') upload to the server end, as the operation key of the cryptograph conversion;
step 903, for the ciphertext C1Based on the operation key obtained in step 902, there are:
step 904, according to the definition of the operation support function G, can obtain:
after further simplification, the following results are obtained: c1＝a2·f(x２)·y２-b, wherein,
g3(x1，xy1)·g3(h2(x1，xy1)，xy2′)，x2＝h2(h2(x1，xy1)，xy2') to finish the conversion operation of the family cipher text.
The complete homomorphic encryption method described in the invention patent with the patent number ZL 201510192143.1 and the name of polynomial complete homomorphic encryption method and system based on coefficient mapping transformation is an encryption, decryption and operation processing method aiming at real data and aims at realizing the encryption protection of the data in the real operation process. The patent adopts a polynomial completely homomorphic encryption technology based on coefficient mapping transformation, improves a polynomial encryption algorithm, performs function mapping transformation on the coefficient of each item in a ciphertext polynomial once, and provides an operation support function according to the function for homomorphic operation of a ciphertext. The method has the advantages of being capable of guaranteeing high safety by means of solving difficulty of a non-specific state function equation, simple to implement, high in operation speed, small in ciphertext expansibility and the like. The core technology of the patent forms the basis of the completely homomorphic encryption technology of the invention. The application scenario aimed at by the invention is the recording and processing of order information by a benefit block chain intelligent contract technology, and the invention makes the following improvements on a polynomial complete homomorphic encryption method and system based on coefficient mapping transformation according to the specific application scenario:
1) in the prior patent, all parameters are floating point numbers, and the cipher text occupies a large number of bytes to be stored. The encrypted fields required in the order information, such as the charge amount and the order amount, are floating point numbers, but have a fixed decimal number, and can be regarded as an integer process. Therefore, the invention is specially designed according to the characteristics of order information to save the ciphertext storage overhead on the block chain.
2) In the prior patent, the number of terms of the ciphertext expression needs at least two terms. The invention adopts special design, introduces the discrete function which can be nested to construct the key function, ensures the encryption strength and simultaneously reduces the number of terms of the ciphertext expression to one term, thereby saving the ciphertext storage overhead on a block chain by more than 50 percent.
3) Homomorphic encryption is characterized in that ciphertext can be directly operated, but only keys generated by the same key can be directly operated, and ciphertext generated by different keys cannot be directly operated. Therefore, a unique dictionary of operations is required for each key to support ciphertext operations. Because the storage space required by the operation dictionary is large, if a plurality of different keys exist in the system, a large amount of storage space is required for storing the operation dictionaries corresponding to the keys, and the use cost is increased. The invention provides the concept of the same family key, namely, a plurality of keys can share the same operational dictionary, so that the storage expense of the operational dictionary can be greatly reduced;
4) because the ciphertexts generated by different keys cannot be directly operated, the cipher text conversion operation needs to be firstly carried out, and the two ciphertexts are in the same cipher text space. Compared with the ciphertext conversion operation under the family key, the ciphertext conversion operation corresponding to the structure of the prior patent has larger operation overhead and storage overhead.
The block chain intelligent contract technology is characterized in that all block chain nodes share all data and participate in all calculation work of intelligent contract related business operation processing, on one hand, the credible execution of intelligent contract business logic is realized through a consensus process, and on the other hand, single-point faults can be eliminated and the reliable execution is realized. However, as a result of this operation mode, each node can grasp all input and output parameters of the intelligent contract and all details and intermediate results in the execution process, and if these data relate to sensitive information, privacy protection cannot be achieved. After the method provided by the invention is used, sensitive information is protected by complete homomorphic encryption and appears in an intelligent contract in a ciphertext form, each block link point can still perform appointed service logic operation processing, the operation of the sensitive information is related, and the privacy problem of the original method can be solved by using a ciphertext operation technology corresponding to the complete homomorphic encryption method.
Compared with the prior art, the invention has the following advantages:
the invention encrypts the order amount information submitted by the application program through a completely homomorphic encryption technology, performs hexadecimal coding, and transmits the obtained ciphertext as a parameter to an intelligent contract for recording. Because the invention adopts the polynomial completely homomorphic encryption method based on coefficient mapping transformation, the cryptograph operation processing complexity is low, and the method can be realized by adopting an intelligent contract, so when the bill is generated in a gathering way, the invention can realize the sum operation of order encryption data by utilizing the intelligent contract, thereby obtaining the cryptograph of the bill amount, and simultaneously the whole operation process keeps the state of the cryptograph.
The invention adopts a mode of completely homomorphic encryption and intelligent contracts, so that on one hand, the complicated account checking problem in the traditional centralized bill system can be solved by utilizing the characteristics of openness, auditability and traceability of the block chain intelligent contracts, and on the other hand, the problem of possible privacy disclosure caused by the fact that a plurality of mechanisms with competitive relationships participate in deploying block chain nodes and synchronizing data in the bill system in the practical application scene can be perfectly solved.
According to the characteristics of the intelligent contract of the block chain, the invention improves and optimizes the coding length of the ciphertext, the complexity of ciphertext operation and the volume of an operation dictionary on the basis of the existing completely homomorphic encryption technology. The invention improves the ciphertext processing performance and reduces the operation overhead, simultaneously, based on the special trust assumption of the union block chain platform and the basic trust of the platform operator, reduces the encryption strength of the ciphertext to a certain extent in the process of ciphertext operation, thereby obtaining higher performance.
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FIG. 1 is an overall process flow diagram of the present invention.
Detailed Description
The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
The invention provides an intelligent contract bill recording and processing method based on complete homomorphic encryption, which is based on the improvement and upgrade of the application scene of an intelligent contract on the basis of an invention patent (hereinafter referred to as 'the prior patent') with the patent number of ZL 201510192143.1 and the name of a polynomial complete homomorphic encryption method and system based on coefficient mapping transformation, and as shown in figure 1, the method specifically comprises the following steps:
step 1, selecting different homomorphic encryption same family KEYs from KEY family KEY (f (x)) related to function KEY f (x) to distribute to different client users. Key family KEY (f (x)) is represented by: KEY (f (x) ═ { KEYi|i∈I}，KeyiFor homomorphic encryption family KEYs belonging to the current KEY family KEY (f (x)), I is a polynomial KEY dimension index set. Each homomorphic encryption family KeyiFrom a polynomial key yiAnd a function key f (x). All homomorphic encryption family KEY KEYs in the same KEY family KEY (f (x))iIs the same, only the polynomial key yiDifferent. In the present invention, a ciphertext encrypted by a homomorphic encryption homomorphic key is referred to as a homomorphic ciphertext.
For the function key f (x), x is a positive integer, and the function key f (x) is a positive integer in the value range, in the present invention, the function key f (x) is a discrete function discontinuous everywhere. The eligible function key f (x) may be any hash function that can greatly increase the security of the family cipher if the hash function has strict unidirectionality. Specifically, the function key f (x) may be constructed by using a hash function, where the hash function may be a hash function such as md4, md5, sha1, sha256, sm3, and for the unknown integer k, the function key f (x) constructed by using the hash function may be written as sha1(x + k), and the unknown integer k is referred to as a function key.
The value range of x is more than or equal to 214If the calculation dictionary is calculated directly for each possible value, the calculation dictionary contains 228An integer, which results in a very large memory overhead and is not practical. The invention introduces a secondary hash function to construct a function key f (x), which is specifically defined as follows:
assume that there is a function key k1 and a function key k2, and q1 is a smaller integer, e.g., q1 is 28Q2 is a larger integer, e.g. q 2-21665535, f (x) sha1(sha1(x + k1) modq1+ k2) modq2 can be defined. When a family cipher text is formed by encryption, if the key k1 is notified to a server responsible for cipher text calculation, the calculation dictionary only has q2 equal to 216The number of integers is only needed, so that the storage overhead of the operation dictionary can be greatly reduced.
In the example given above, the same hashing algorithm, sha1, is used for both the first-level hash function and the second-level hash function. The two-level hash function of the function key f (x) may also be a different hash algorithm, for example:
f(x)＝sm3(sha256(x+k1)modq1+k2)modq2
or
f(x)＝sha1(md5(x+k1)modq1+k2)modq2
If a second-level hash function is adopted to construct the function Key f (x), the Key Key is encrypted in a homomorphic wayiThe generation steps are as follows:
101, randomly selecting a hash algorithm hash1 adopted by a first-level hash function and a hash algorithm hash2 adopted by a second-level hash function;
step 102, randomly generating two integers as a function key k1 and a function key k 2;
step 103, randomly generating an integer as a polynomial key yi；
Step 104, generating a homomorphic encryption family KeyiIt can be expressed as follows: key (R)i＝{hash1，k1，hash2，k2，yi}。
According to the definition of the operation dictionary in the prior patent, the operation dictionaries corresponding to the homomorphic encryption homomorphic KEYs are the same, that is, the same KEY family KEY (f (x)) shares the same operation dictionary, so that the storage cost of the operation dictionary can be greatly reduced after the homomorphic encryption homomorphic KEYs are used for encrypting the plaintext. All the family ciphertexts obtained by encrypting the family KEY by using any homomorphic encryption KEY in the same KEY family KEY (f (x)), the function KEYs f (x) in the cipher text expression are the same, and therefore the cipher texts are called as the family cipher texts.
Assuming that a secondary hash function is used to construct the function key f (x), the function key k2 used by the secondary hash function must be the same for two different homomorphic encryption homomorphic keys, but the function key k1 used by the primary hash function may be different, so that the two different homomorphic encryption homomorphic keys have sufficient difference and are difficult to break.
Step 2, order data needing to be encrypted in order informationThe field (e.g., the order amount field) is processed as an integer, denoted as integer plaintext m. Client user locally uses pre-distributed homomorphic encryption family KeyiThe whole plaintext m is encrypted. The invention does not need to recalculate the operation dictionary for each client key because of adopting the same family key. In order to improve the efficiency of ciphertext homomorphic operation and save ciphertext storage overhead, the invention provides a simplified ciphertext expression aiming at a positive integer type plaintext, which has the following formula:
Pi＝a·f(x)·yi-b
in the formula, PiThe family ciphertext is further represented by a vector { a, x, b }; x, a and b are positive integers, x is generated randomly, a is a coefficient generated randomly, and b is an offset.
The short ciphertext expression shown in the formula can effectively reduce the volume of the ciphertext, reduce the cost of ciphertext storage and be beneficial to the application scene of the block chain intelligent contract. Meanwhile, because the number of the ciphertext items is only one, the operation steps are reduced by times when the ciphertext operation is carried out, the ciphertext operation efficiency can be effectively improved, the operation overhead is reduced, and the method is more suitable for executing and realizing the ciphertext operation in a mode with highly limited performance, namely an intelligent contract.
Based on the simplified ciphertext expression, the invention adopts the following steps to realize the encryption of the integer plaintext m:
step 201, randomly generating a positive integer x, and calculating f (x);
step 202, randomly generating a coefficient a, and calculating a multiplied by f (x);
step 203, calculating an offset b ═ m-a × f (x);
step 204, obtaining the family cipher text PiIs shown as Pi＝{a，x，b}。
And 3, carrying out hexadecimal coding on the family ciphertext obtained in the step 2 to obtain a final ciphertext.
And 4, after the encryption of all order data fields in the order information is completed in the steps 2 and 3, transmitting the encrypted order information into a bill processing intelligent contract through a client user application program interface in a parameter transmission mode.
And 5, receiving the encrypted order information by the bill processing intelligent contract, and storing the corresponding ciphertext in a contract variable to realize bill recording.
And 6, when bill processing is required, acquiring the related ciphertext saved in the contract variable according to the specific data content bill processing contract required to be processed. For example, if the order amount in the order information needs to be processed, the ciphertext of the saved order amount is obtained. And then calling a ciphertext operation contract to perform addition and/or multiplication ciphertext operation on the ciphertext based on the operation support function G to obtain a result ciphertext.
The operation support function G is defined as: g ═ G1，g2，g3And (4) the following steps:
in the formula, h1() And h2() Is a bias function; x is the number of1And x2Is any integer in the definition domain D of the function f (x), then h1() And h2() The value range of (D) is also D.
Obtaining any two cryptographs P for order information uploaded by the same client user1、P2If the polynomial key in the homomorphic encryption family key is defined as y, then: p1＝a1·f(x1)·y-b1，P2＝a2·f(x2)·y-b2The invention adopts the following steps to realize the ciphertext P1And ciphertext P2The addition ciphertext operation of (2):
P1+P2＝a1·f(x1)·y-b1+a2·f(x2)·y-b2
＝[a1·f(x1)+a2·f(x2)]·y-(b1+b2)
＝[a1·g1(x1，x2)·f(h1(x1，x2))+a2·g2(x1，x2)·f(h1(x1，x2))]·y-b3
＝[a1·g1(x1，x2)+a2·g2(x1，x2)]·f(h1(x1，x2))·y-b3
＝a3·f(x3)·y-b3
wherein, a3＝a1·g1(x1，x2)+a2·g2(x1，x2)，x3＝h1(x1，x2)，b3＝b1+b2。
For any two ciphertexts P mentioned before1、P2The invention adopts the following steps to realize the ciphertext P1And ciphertext P2The multiplication ciphertext operation of (2):
P1·P2＝[a1·f(x1)·y-b1]·[a2·f(x2)·y-b2]
＝a1·f(x1)·a2·f(x2)·y2-[b1·a2·f(x2)+b2·a1·f(x1)]·y+b1·b2
＝a1·a2·g3(x1，x2)·f(h2(x1，x2))·y2-[b1·a2·g2(x1，x2)·f(h1(x1，x2))+b2·a1·g1(x1，x2)·f(h1(x1，x2))]·y+b1·b2
＝a4·f(x4)·y2-a5·f(x5)·y+b4
in the formula, a4＝a1·a2·g3(x1，x2)，a5＝b1·a2·g2(x1，x2)+b2·a1·g1(x1，x2)，x4＝h2(x1，x2)，x5＝h1(x1，x2)，b4＝b1·b2。
After the ciphertext multiplication operation, the obtained result is a quadratic form, and in order to keep the unification of the ciphertext expressions, the quadratic form is reduced into a primary form by using a descending technology. The specific method is that the square term y of the polynomial key y is calculated in advance2And discloses its ciphertext:
substituting the square term ciphertext into the multiplication result can obtain:
step 7, obtaining the result ciphertext by the bill processing contract;
and 8, calling the intelligent contract by the client user to acquire the result ciphertext obtained in the step 7, and viewing the bill amount information after local decryption.
The invention realizes the decryption of the ciphertext C ═ { a, x, b } by adopting the following steps:
step 801, substituting a positive integer x into a function key f (x) constructed by a secondary hash function, and calculating f (x) ═ sha1(sha1(x + k1) modq1+ k2) modq 2;
step 802, an integer plaintext m is obtained by calculation, where m is a × f (x) -b.
And 9, if the platform side user needs to check the result ciphertext obtained in the step 7, a ciphertext conversion method needs to be used for converting the result ciphertext obtained in the step 7 into a ciphertext of a platform side user key space, and then the homomorphic encryption homomorphic key distributed to the platform side user is used for decryption and checking.
In the present invention, the result ciphertextAnd the ciphertext of the platform side user key space is the same family ciphertext, and the same family ciphertext is very close to the same family ciphertext because only the polynomial key is different. Although the invention can not directly carry out mutual operation, the ciphertext space mutual conversion method between the same-family ciphertexts can be greatly simplified compared with the common ciphertexts. Ciphertext C for any two different users1、C2The specific ciphertext transformation operation is as follows:
step 901, generating a ciphertext C1Homomorphic encryption family Key1And for generating ciphertext C2Homomorphic encryption family Key2Then (c) is performed.
Family Key for homomorphic encryption1Polynomial key y in (1)1Two vectors are obtained: (a)y1，xy1)、(ay1′，xy1') satisfies the following two formulas:
y1＝ay1·f(xy1)
y1＝ay1′/f(xy1′)
family Key for homomorphic encryption2Polynomial key y in (1)2Two vectors are obtained: (a)y2，xy2)、(ay2′，xy2') satisfies the following two formulas:
y2＝ay2·f(xy2)
y2＝ay2′/f(xy2′)
in the formula, ay1、xy1、ay1′、xy1′、ay2、xy2、ay2′、xy2' are all positive integers.
Vector (a) calculated in steps 902 and 901y1，xy1)、(ay1′，xy1′)、(ay2，xy2)、(ay2′，xy2') to the server side as the operation key for ciphertext transformation.
Step 903, for the ciphertext C1Based on the operation obtained in step 902As a key, there are:
step 904, according to the definition of the operation support function G, can obtain:
after further simplification, the following results are obtained: c1＝a2·f(x2)·y2-b, wherein,
g3(x1，xy1)·g3(h2(x1，xy1)，xy2′)，x2＝h2(h2(x1，xy1)，xy2') finishing the conversion operation of the family cipher text.
The invention is further illustrated below by a specific example:
1) the Key in this embodiment is { sm3, 123, sm3, 456, 89 }. It represents a two-layer function key, with the expression P ═ a · f2(f1(x，k1)，k2) Y-b (1), wherein the first layer function f1Is sm3 hash function, and its corresponding function key k1Is 123; second layer function f2Is sm3 hash function, and its corresponding function key k2Is 456; the polynomial key y is 89.
2) Assuming that the plaintext amount data of the first order input is m1 ═ 100, and the formula (1) is substituted, the ciphertext is obtained as a triplet c1 ═ {57, 8228, 21519566}, where a ═ 57, x ═ 8228, and b ═ 21519566.
3) Then, the compact 16-ary representation is used to represent the triplet ciphertext as c 1-392024 feb7a 332.
4) The amount value of the order is recorded in the intelligent contract as 392024feb7a 332.
5) Assuming that the plaintext amount data of the second order input is m2 ═ 156, and formula (1) is also substituted, the ciphertext is c2 ═ {46, 10982, 204654810}, where a ═ 46, x ═ 10982, and b ═ 204654810.
6) The compact 16-ary representation is used to represent the ciphertext as c2 ═ 2e2ae6f3cd 3726.
7) The amount value of the order is recorded as 2e2ae6f3cd3726 in the intelligent contract.
8) Assuming that a bill needs to be generated according to the two orders in a gathering manner and the bill amount data is calculated, the following steps are provided:
A) firstly, acquiring an amount ciphertext 392024feb7a332 of a first order, decoding the amount ciphertext into a triple {57, 8228, 21519566}, acquiring an amount ciphertext 2e2ae6f3cd3726 of a second order, and decoding the amount ciphertext into a triple {46, 10982, 204654810 };
B) after ciphertext addition, a resultant ciphertext c3 ═ {55, 37097, 127543864}, where a ═ 55, x ═ 37097, and b ═ 127543864 is obtained;
C) carrying out 16-system coding on c3 to obtain 3790e9f865d5c8, and recording the result into an intelligent contract;
D) the user with the Key can obtain the bill amount ciphertext 3790e9f865d5c8, and substitute the ciphertext and the Key into the formula (1), and after decryption operation, the final result is 256.
The blockchain platform widely adopts an intelligent contract technology to realize the application bearing capacity of the blockchain platform, wherein a typical example is Ethereum (Ethereum), and the Ethereum virtual machine EVM is used for realizing the operation of the intelligent contract, so that the application field of the blockchain technology is greatly expanded, and the application landing of the blockchain technology is promoted. However, the block chain technology is transparent and traceable, so that all nodes can view and verify all historical input and output and current state data of the intelligent contract, adverse factors are brought to privacy protection of business data in actual application, and particularly in billing application, once a certain participant can know actual enterprise information corresponding to a certain block chain address from other channels, all orders and detailed billing data in the enterprise history can be listed, and serious business confidentiality leakage risk is brought.
The invention uses the completely homomorphic encryption technology to carry out encryption protection on the data in the intelligent contract, and because the technology can realize direct operation and processing aiming at the ciphertext, the processing of the encrypted data in the intelligent contract can be completed on the premise of not needing decryption. Data are firstly encrypted and then recorded into a block chain intelligent contract, various operations in the intelligent contract keep a ciphertext state, the data are enabled to be computationally invisible on a block chain platform, and finally, data protection of the whole flow on the chain is achieved.
It should be noted that: the basic algorithmic principles and system implementations of the fully homomorphic encryption methods involved in the present invention have been described in detail in prior patents. The invention is purposefully modified aiming at the method disclosed by the prior patent, and comprises the following steps: the ciphertext expression is simplified, the function key may be a discontinuous function, ciphertext hexadecimal coding, and conversion operation between family ciphertexts, the above specific implementation process is only described in detail with respect to the above improvement point, and other technical contents may refer to the existing patent by those skilled in the art, and are not described herein again.
Claims (9)
1. An intelligent contract bill recording and processing method based on fully homomorphic encryption is characterized by comprising the following steps:
step 1, selecting different homomorphic encryption same family KEYs from KEY family KEYs (f (x)) related to a function KEY f (x) to distribute to different client users, wherein the KEY family KEYs (f (x)) are expressed as: KEY (f (x) ═ { KEYiI belongs to I, and the same KEY family KEY (f (x)) shares the same operation dictionary, KeyiEncrypting a family KEY for homomorphism belonging to a current KEY family KEY (f (x)), I being a polynomial KEY dimension subscript set;
each homomorphic encryption family KeyiFrom a polynomial key yiAnd a function key f (x), wherein x is a positive integer, the function key f (x) is a positive integer in a value range, and the function key f (x) is a discrete function which is discontinuous everywhere; all homomorphic encryption family KEYs Ke in the same KEY family KEY (f (x))yiIs the same, only the polynomial key yiDifferently, a ciphertext obtained by encrypting the homomorphic encryption homomorphic key is called a homomorphic ciphertext;
step 2, processing the order data field needing to be encrypted in the order information into an integer, and recording the integer as an integer plaintext m; user locally uses pre-distributed homomorphic encryption family KeyiEncrypting the whole plaintext m by adopting a simplified ciphertext expression as follows:
Pi＝a·f(x)·yi-b
in the formula, PiThe family ciphertext is further represented by a vector { a, x, b }; x, a and b are positive integers, x is generated randomly, a is a coefficient generated randomly, and b is an offset;
step 3, carrying out hexadecimal coding on the congeneric ciphertext obtained in the step 2 to obtain a final ciphertext;
step 4, after the encryption of all order data fields in the order information is completed in the step 2 and the step 3, transmitting the encrypted order information into a bill processing intelligent contract through a user application program interface in a parameter transmission mode;
step 5, the bill processing intelligent contract receives the encrypted order information and stores the corresponding ciphertext in a contract variable to realize bill recording;
step 6, when bill processing is needed, acquiring related cryptographs saved in contract variables according to a bill processing contract of specific data content needing to be processed; then, calling a ciphertext operation contract to perform addition and/or multiplication ciphertext operation on the ciphertext based on the operation support function G to obtain a result ciphertext;
wherein, the operation support function G is defined as: g ═ G1，g2，g3And (4) the following steps:
in the formula, h1() And h2() Is a bias function; x is the number of1And x2Is the function f (x) is fixedAny integer in sense domain D, then h1() And h2() The value range of (a) is also D;
step 7, obtaining the result ciphertext by the bill processing contract;
step 8, the user calls the intelligent contract to obtain the result ciphertext obtained in the step 7, and the bill amount information is checked after local decryption;
and if other users except the current user need to check the result ciphertext obtained in the step 7, converting the result ciphertext of the current user obtained in the step 7 into the ciphertext of the key space of other users by using a ciphertext conversion method, and then decrypting and checking by using the homomorphic encryption homomorphic key distributed to other users.
2. The method as claimed in claim 1, wherein in step 1, the function key f (x) is any hash function with strict one-way property.
3. The method as claimed in claim 2, wherein in step 1, the function key f (x) is constructed by using a hash function, and for the unknown integer k, the function key f (x) constructed by using the hash function is written into a hash (x + k), and the unknown integer k is referred to as the function key.
4. The method as claimed in claim 3, wherein in step 1, a secondary hash function is used to construct the function key f (x), which is specifically defined as follows:
assuming that there are a function key k1 and a function key k2, and q1 is a smaller integer and q2 is a larger integer, f (x) -hash 1(hash2(x + k1) modq1+ k2) modq2 is defined, where hash1() is a first-level hash function and hash2() is a second-level hash function;
when the family cipher text is formed by encryption, the server responsible for cipher text operation is informed of the key k 1.
5. The intelligent contract billing method based on fully homomorphic encryption of claim 4 wherein the first level hash function is the same as or different from the second level hash function.
6. The method for recording and processing the bills of smart contracts based on fully homomorphic encryption as claimed in claim 4, wherein if the function Key f (x) is constructed by using a secondary hash function, the homomorphic encryption Key Key isiThe generation steps are as follows:
101, randomly selecting a hash algorithm hash1 adopted by a first-level hash function and a hash algorithm hash2 adopted by a second-level hash function;
step 102, randomly generating two integers as a function key k1 and a function key k 2;
step 103, randomly generating an integer as a polynomial key yi；
Step 104, generating a homomorphic encryption family KeyiExpressed in the following form: key (R)i＝{hash1，k1，hash2，k2，yi}。
7. The fully homomorphic encryption based intelligent contract bill recording and processing method according to claim 1, wherein in step 6, any two cryptographs P obtained from order information uploaded by the same user1、P2If the polynomial key in the homomorphic encryption family key is defined as y, then: p1＝a1·f(x1)·y-b1，P2＝a2·f(x2)·y-b2The following steps are adopted to realize the ciphertext P1And ciphertext P2The addition ciphertext operation of (2):
P1+P2＝a1·f(x1)·y-b1+a2·f(x2)·y-b2
＝[a1·f(x1)+a2·f(x2)]·y-(b1+b2)
＝[a1·g1(x1，x2)·f(h1(x1，x2))+a2·g2(x1，x2)·f(h1(x1，x2))]·y-b3
＝[a1·g1(x1，x2)+a2·g2(x1，x2)]·f(h1(x1，x2))·y-b3
＝a3·f(x3)·y-b3
wherein, a3＝a1·g1(x1，x2)+a2·g2(x1，x2)，x3＝h1(x1，x2)，b3＝b1+b2。
8. The fully homomorphic encryption based intelligent contract bill recording and processing method according to claim 1, wherein in step 6, any two cryptographs P obtained from order information uploaded by the same user1、P2If the polynomial key in the homomorphic encryption family key is defined as y, then: p1＝a1·f(x1)·y-b1，P2＝a2·f(x2)·y-b2The following steps are adopted to realize the ciphertext P1And ciphertext P2The multiplication ciphertext operation of (1):
P1·P2＝[a1·f(x1)·y-b1]·[a2·f(x2)·y-b2]
＝a1·f(x1)·a2·f(x2)·y2-[b1·a2·f(x2)+b2·a1·f(x1)]·y+b1·b2
＝a1·a2·g3(x1，x2)·f(h2(x1，x2))·y2-[b1·a2·g2(x1，x2)·f(h1(x1，x2))+b2·a1·g1(x1，x2)·f(h1(x1，x2))]·y+b1·b2
＝a4·f(x4)·y2-a5·f(x5)·y+b4
in the formula, a4＝a1·a2·g3(x1，x2)，a5＝b1·a2·g2(x1，x2)+b2·a1·g1(x1，x2)，x4＝h2(x1，x2)，x5＝h1(x1，x2)，b4＝b1·b2；
The quadratic form is reduced to the primary form by using a reduction technology, and the specific method is to calculate the square term y of the polynomial secret key y in advance2And discloses its ciphertext:
substituting the square term ciphertext into the multiplication result can obtain:
9. the fully homomorphic encryption based intelligent contract bill recording and processing method according to claim 1, wherein in step 8, the cryptographs C for any two different users1、C2The specific ciphertext transformation operation is as follows:
step 901, generating a ciphertext C1Homomorphic encryption family Key1And for generating ciphertext C2Homomorphic encryption family Key2When the current is over;
family Key for homomorphic encryption1Polynomial key y in (1)1Two vectors are obtained: (a)y1，xy1)、(ay1′，xy1') satisfies the following two formulas:
y1＝ay1·f(xy1)
y1＝ay1′/f(xy1′)
family Key for homomorphic encryption2Polynomial key y in (1)2Two vectors are obtained: (a)y2，xy2)、(ay2′，xy2') satisfies the following two formulas:
y2＝ay2·f(xy2)
y2＝ay2′/f(xy2′)
in the formula, ay1、xy1、ay1′、xy1′、ay2、xy2、ay2′、xy2' are positive integers;
vector (a) calculated in steps 902 and 901y1，xy1)、(ay1′，xy1′)、(ay2，xy2)、(ay2′，xy2') upload to the server end, as the operation key of the cryptograph conversion;
step 903, for the ciphertext C1Based on the operation key obtained in step 902, there are:
step 904, according to the definition of the operation support function G, can obtain:
after further simplification, the following results are obtained: c1＝a2·f(x2)·y2-b, wherein,
x2＝h2(h2(x1，xy1)，xy2') to finish the conversion operation of the family cipher text.
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