An information encryption method and related components

Abstract

The present invention discloses an information encryption method and related components, and relates to the field of information security technology. A multiplication homomorphic encryption algorithm is pre-designed, and a public key and a corresponding private key used for information encryption and decryption processing are determined according to a specific key determination rule of the multiplication homomorphic encryption algorithm. After obtaining the public key and the corresponding encryption rule, the encryption terminal can directly encrypt the plaintext to be encrypted according to the public key and the encryption rule to obtain the ciphertext. Compared with the hash encryption algorithm in the prior art, a large number of hash value calculations are reduced, and the calculation cost is reduced; when the decryption terminal obtains the ciphertext sent by the encryption terminal, the ciphertext is directly decrypted according to the public key, the private key and the decryption rule to obtain the plaintext, without a large number of tedious verifications, saving the verification cost, the private key is private data and will not be disclosed, and only the decryption terminal with the private key can crack the ciphertext encrypted by the corresponding public key and encryption rule, thereby ensuring the security of information transmission.

Description

Technical Field

[0001] The present invention relates to the field of information security technology, and in particular to an information encryption method and related components. Background Art

[0002] With the development of network technology, people are paying more and more attention to network privacy and security protection. Data encryption can effectively resist active and passive attacks on transmitted data. Common encryption algorithms include hash encryption algorithms that rely on hash algorithms. However, this method is limited by its own algorithm setting mechanism. The encryption process requires a large number of hash calculations, and the decryption process contains a large number of redundant verifications. Specifically, in the encryption process, a large number of hash values ​​need to be calculated based on the information to be encrypted to generate encrypted summary information, and then the original data and the encrypted summary information are sent to the decryption party together. The decryption party performs a large number of redundant checks on the original data to verify whether the original data has been tampered with for subsequent use. It can be seen that this method consumes too high computing and verification costs.

[0003] Therefore, how to find an encryption method that effectively ensures information security has become a problem that needs to be solved urgently. Summary of the invention

[0004] The purpose of the present invention is to provide an information encryption method and related components, and a multiplication homomorphic encryption algorithm is pre-designed. Compared with the hash encryption algorithm in the prior art, it reduces the calculation of a large number of hash values, reduces the calculation cost, and does not require a large amount of tedious verification, saves verification costs, and ensures the security of information transmission.

[0005] In order to solve the above technical problems, the present invention provides an information encryption method, which is applied to an encryption terminal. The information encryption method comprises:

[0006] Obtaining a public key published by a decryption terminal and a pre-designed encryption rule of a multiplication homomorphic algorithm, wherein the public key is determined by the decryption terminal according to a key determination rule of the multiplication homomorphic algorithm;

[0007] The key determination rule is: the decryption terminal determines a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, and the first selected data is the first data n obtained by multiplying the p and the q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1, and A2=q-1; the least common multiple is determined to be a private key λ corresponding to the public key, and the public key is determined based on the first data n and the private key λ;

[0008] Determine the plaintext to be encrypted;

[0009] The plaintext is encrypted according to the public key and the encryption rule to obtain a ciphertext.

[0010] Preferably, determining the public key based on the first data n and the private key λ includes:

[0011] Select a second data g from a positive integer, wherein the selected second data g satisfies: the greatest common divisor between the third data B and the first data n is 1, and the third data B is determined based on the second data g, the private key λ, the first data n and a first preset relationship;

[0012] The first preset relationship is:

[0013]

[0014] And among them g λ mod n 2 Indicates g λ For 2 Take the mold;

[0015] Determine a first set based on the first data n Among them, the first set The set elements in are {0,1,...,(n-1)};

[0016] Determine the first set The first set element that is relatively prime to n among all the set elements in ;

[0017] Select a fourth data Y from the first set elements;

[0018] The first data n, the second data g, and the fourth data Y are determined to be the public key.

[0019] Preferably, encrypting the plaintext according to the public key and the encryption rule to obtain the ciphertext includes:

[0020] Based on the first data n, select an integer from integers between 0 and n / 2 as fifth data k1;

[0021] Select one from the first set of elements as the sixth data r1;

[0022] Based on the first data n, the second data g, the fourth data Y, the fifth data k1, the sixth data r1, the second preset relationship and the third preset relationship, the plaintext M is encrypted to obtain a ciphertext, wherein 0≤M<n 2, the ciphertext includes seventh data C1 determined based on the second preset relationship and eighth data C2 determined based on the third preset relationship;

[0023] The second preset relationship is:

[0024]

[0025] And among them, express For 2 Take the mold;

[0026] The third preset relationship is:

[0027]

[0028] And among them, express For 2 Take the model.

[0029] Preferably, determining the public key based on the first data n and the private key λ includes:

[0030] Select a ninth data h from a positive integer, wherein the selected ninth data h satisfies: the greatest common divisor between the tenth data D and the first data n is 1, and the tenth data D is determined based on the ninth data h, the private key λ, the first data n and a fourth preset relationship;

[0031] The fourth preset relationship is:

[0032]

[0033] And among them h λ mod n 2 Indicates h λ For 2 Take the mold;

[0034] Based on the first data n, select an integer from integers between 1 and n-1 as the eleventh data a;

[0035] Determine twelfth data X based on the eleventh data a, the first data n and a fifth preset relationship;

[0036] Wherein, the fifth preset relationship is:

[0037] X=a*n+1

[0038] The first data n, the ninth data h, and the twelfth data X are determined to be the public key.

[0039] Preferably, encrypting the plaintext according to the public key and the encryption rule to obtain the ciphertext includes:

[0040] Based on the first data n, selecting an integer from integers between 0 and n as the thirteenth data k2;

[0041] Determine a second set based on the first data n Among them, the second set The set elements in are {0,1,...,(n-1)};

[0042] Determine the second set The second set element that is relatively prime to n among the set elements in ;

[0043] Select one from the second set elements as the fourteenth data r2;

[0044] Based on the first data n, the ninth data h, the twelfth data X, the thirteenth data k2, the fourteenth data r2, the sixth preset relationship and the seventh preset relationship, the plaintext M is encrypted to obtain a ciphertext, wherein 0≤M<n 2 , the ciphertext includes fifteenth data C3 determined based on the sixth preset relationship and sixteenth data C4 determined based on the seventh preset relationship;

[0045] The sixth preset relationship is:

[0046]

[0047] And among them, express For 2 Take the mold;

[0048] The seventh preset relationship is:

[0049]

[0050] And among them, express For 2 Take the model.

[0051] In order to solve the above technical problems, the present invention further provides an information decryption method, which is applied to a decryption terminal. The information decryption method comprises:

[0052] Determine a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, the first selected data is the first data n obtained by multiplying the p and the q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1; A2=q-1; determine the least common multiple as a private key λ, and determine a public key corresponding to the private key λ based on the first data n and the private key λ;

[0053] Obtaining the ciphertext sent by the encryption terminal after encrypting the plaintext to be transmitted according to the public key and the encryption rules of the pre-designed multiplication homomorphic encryption algorithm;

[0054] The ciphertext is decrypted according to the public key, the private key λ corresponding to the public key and the pre-designed decryption rule of the multiplication homomorphic encryption algorithm to obtain the plaintext to be transmitted.

[0055] Preferably, the public key includes first data n, second data g and third data Y; the ciphertext includes fourth data C5 and fifth data C6;

[0056] Decrypting the ciphertext according to the public key, the private key λ corresponding to the public key and the pre-designed decryption rule of the multiplication homomorphic encryption algorithm to obtain the plaintext to be transmitted, including:

[0057] Processing the fourth data C5 based on the private key λ, the first data n, the second data g and a first preset relationship to obtain sixth data k3;

[0058] The first preset relationship is:

[0059]

[0060] Among them, (C5) λ mod n 2 Indicates (C5) λ For 2 Modulus, g λ mod n 2 Indicates g λ For 2 Take the model, express modulo n;

[0061] Processing the fifth data C6 based on the third data Y, the sixth data k3, the first data n and the second preset relationship to obtain the plaintext E to be transmitted;

[0062] The second preset relationship is:

[0063]

[0064] in, express For 2 Modulus; Y -1 It means taking the inverse of Y.

[0065] In order to solve the above technical problems, the present invention further provides an information encryption system, which is applied to an encryption terminal. The information encryption system comprises:

[0066] A first acquisition unit is used to acquire a public key published by a decryption terminal and a pre-designed encryption rule of a multiplication homomorphic algorithm, wherein the public key is determined by the decryption terminal according to a key determination rule of the multiplication homomorphic algorithm;

[0067] The key determination rule is: the decryption terminal determines a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, and the first selected data is the first data n obtained by multiplying the p and the q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1, and A2=q-1; the least common multiple is determined to be a private key λ corresponding to the public key, and the public key is determined based on the first data n and the private key λ;

[0068] A determination unit, used for determining the plaintext to be encrypted;

[0069] The encryption unit is used to encrypt the plaintext according to the public key and the encryption rule to obtain the ciphertext.

[0070] In order to solve the above technical problems, the present invention further provides an information decryption system, which is applied to a decryption terminal. The information decryption system comprises:

[0071] A key determination unit, used to determine a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, the first selected data is the first data n obtained by multiplying the p and the q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1; A2=q-1; the least common multiple is determined to be a private key λ, and a public key corresponding to the private key λ is determined based on the first data n and the private key λ;

[0072] A second acquisition unit is used to obtain the ciphertext sent by the encryption terminal after encrypting the plaintext to be transmitted according to the public key and the encryption rules of the pre-designed multiplication homomorphic encryption algorithm;

[0073] A decryption unit is used to decrypt the ciphertext according to the public key, the private key λ corresponding to the public key and the pre-designed decryption rule of the multiplication homomorphic encryption algorithm to obtain the plaintext to be transmitted.

[0074] In order to solve the above technical problems, the present invention further provides an information processing device, comprising:

[0075] Memory for storing computer programs;

[0076] A processor is used to execute the steps of the information encryption method as described above.

[0077] The present invention provides an information encryption method and related components. A multiplication homomorphic encryption algorithm is pre-designed. A public key and a corresponding private key used for information encryption and decryption processing are determined according to a specific key determination rule of the multiplication homomorphic encryption algorithm. The plaintext to be encrypted is determined according to the encryption rule set in the multiplication homomorphic encryption algorithm. The encryption terminal can directly encrypt the plaintext according to the obtained public key and the encryption rule to obtain the ciphertext. Compared with the hash encryption algorithm in the prior art, the calculation of a large number of hash values ​​is reduced, and the calculation cost is reduced; similarly, when the decryption terminal obtains the ciphertext sent by the encryption terminal, it indicates that there is a decryption demand at this time. Therefore, according to the public key, the corresponding private key and the decryption rule of the multiplication homomorphic encryption algorithm, the ciphertext can be directly decrypted to obtain the plaintext to be transmitted. Compared with the hash encryption algorithm in the prior art, a large amount of tedious verification is not required, which saves the verification cost. The private key is private data and will not be disclosed, which means that only the decryption terminal with the private key can crack the ciphertext encrypted by the corresponding public key and the encryption rule, thereby ensuring the security of information transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the prior art and the drawings required for use in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0079] Figure 1 A flowchart of an information encryption method provided by the present invention;

[0080] Figure 2 A flowchart of an information decryption method provided by the present invention;

[0081] Figure 3 A schematic diagram of the structure of an information encryption system provided by the present invention;

[0082] Figure 4 A schematic diagram of the structure of an information decryption system provided by the present invention;

[0083] Figure 5 A schematic structural diagram of an information processing device provided by the present invention. DETAILED DESCRIPTION

[0084] The core of the present invention is to provide an information encryption method and related components, and pre-design a multiplication homomorphic encryption algorithm. Compared with the hash encryption algorithm in the prior art, it reduces the calculation of a large number of hash values, reduces the calculation cost, and does not require a large amount of tedious verification, saving verification costs and ensuring the security of information transmission.

[0085] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0086] Please refer to Figure 1 , Figure 1 The present invention provides a flowchart of an information encryption method.

[0087] The information encryption method is applied to an encryption terminal, and the information encryption method includes:

[0088] S11: Obtaining a public key published by the decryption terminal and a pre-designed encryption rule of a multiplication homomorphic algorithm, wherein the public key is determined by the decryption terminal according to a key determination rule of the multiplication homomorphic algorithm;

[0089] The key determination rule is: the decryption terminal determines a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, and the first selected data is the first data n obtained by multiplying p and q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1, A2=q-1; the least common multiple is determined to be a private key λ corresponding to the public key, and the public key is determined based on the first data n and the private key λ;

[0090] S12: Determine the plaintext to be encrypted;

[0091] S13: Encrypt the plaintext according to the public key and encryption rules to obtain the ciphertext.

[0092] In this embodiment, considering that common encryption algorithms in the prior art, such as hash encryption algorithms, consume excessively high computing costs and verification costs, in order to solve the above technical problems, the present application provides an information encryption method. According to a pre-designed multiplication homomorphic encryption algorithm, encryption of the plaintext to be encrypted can be achieved, thereby ensuring the secure transmission of information.

[0093] The information encryption method is applied to an encryption terminal, and is specifically applicable to various devices with information encryption requirements, including but not limited to servers, clients, etc., which are not particularly limited here.

[0094] When the encryption terminal wants to securely transmit plaintext to the decryption terminal, it needs to encrypt the plaintext in accordance with the encryption specification of the decryption terminal. Therefore, the encryption terminal needs to obtain the public key and encryption rules used for information encryption when sending information to the decryption terminal, which are pre-announced by the decryption terminal, so that the encryption terminal can transmit the encrypted ciphertext to the decryption terminal. Specifically, the decryption terminal here will determine a pair of keys, that is, a public key and a corresponding private key, according to the pre-designed multiplication homomorphic encryption algorithm: First, determine the first prime number p and the second prime number q that are different from each other, wherein the conditions that need to be satisfied for the selection of the first prime number p and the second prime number q are as described above, and will not be repeated here. It should be noted that in actual applications, the first prime number p and the second prime number q here can be selected as large as possible. The larger the values ​​of the first prime number p and the second prime number q, the higher the security of the encryption. Therefore, the lowest common multiple is determined as the private key λ, and the public key is determined based on the first data n and the private key λ, thereby obtaining a pair of keys. It can be understood that based on the Paillier algorithm, the above-mentioned key determination rules satisfy semantic security, that is, the ciphertext obtained using the multiplicative homomorphic encryption algorithm provided in this application will not leak other information of the plaintext.

[0095] It should be noted that the private key here will be saved as private information by the decryption terminal that generates the pair of keys. The decryption terminal has the public key, the corresponding private key, the corresponding encryption rules and decryption rules, while the encryption terminal can only have the public key and encryption rules published by the decryption terminal. It is very difficult to decrypt the corresponding private key by having the public key, which ensures the security of the scheme.

[0096] Then, the plaintext to be encrypted is determined, and the plaintext is encrypted according to the public key and the encryption rules of the pre-designed multiplication homomorphic encryption algorithm to obtain the ciphertext. It should also be noted that the obtained ciphertext is sent to the decryption terminal, so the decryption terminal that has the public key, private key and corresponding decryption rules can directly decrypt it to obtain the plaintext.

[0097] In summary, the present application provides an information encryption method, which pre-designs a multiplication homomorphic encryption algorithm, and determines the public key and the corresponding private key used for information encryption and decryption according to the specific key determination rule of the multiplication homomorphic encryption algorithm. After obtaining the public key and the corresponding encryption rule, the encryption terminal can directly encrypt the plaintext to be encrypted according to the public key and the encryption rule to obtain the ciphertext. Compared with the hash encryption algorithm in the prior art, the calculation of a large number of hash values ​​is reduced, the calculation cost is reduced, and the private key will not be disclosed as private data, which means that only the decryption terminal with the private key can crack the ciphertext encrypted by the corresponding public key and the encryption rule, thereby ensuring the security of information transmission.

[0098] Based on the above embodiments:

[0099] As a preferred embodiment, determining the public key based on the first data n and the private key λ includes:

[0100] Select a second data g from a positive integer, wherein the selected second data g satisfies: the greatest common divisor between the third data B and the first data n is 1, and the third data B is determined based on the second data g, the private key λ, the first data n and the first preset relationship;

[0101] The first preset relationship is:

[0102]

[0103] And among them g λ mod n 2 Indicates g λ For 2 Take the mold;

[0104] Determine a first set based on the first data n Among them, the first set The set elements in are {0,1,...,(n-1)};

[0105] Determine the first set The first set element that is relatively prime to n among all the set elements in ;

[0106] Select a fourth data Y from the first set of elements;

[0107] The first data n, the second data g, and the fourth data Y are determined to be public keys.

[0108] In this embodiment, the first specific determination process of the public key by the decryption terminal is given. The public key here includes three data, namely the first data n, the second data g and the fourth data Y. First, the second data g is determined. The rules that need to be satisfied are as described above and will not be repeated here. Then the fourth data Y is determined. The determination process has also been described above. Finally, the first data n, the determined second data g and the fourth data Y are used as the public key for subsequent processing. The above process of determining the public key is simple, reliable and easy to implement.

[0109] In addition, it should be noted that the fourth data Y and the second data g can also be set to the same value, that is, both are n+1, which can speed up the processing speed of the encryption rules and decryption rules of the multiplicative homomorphic encryption algorithm in this application.

[0110] As a preferred embodiment, encrypting the plaintext according to the public key and the encryption rule to obtain the ciphertext includes:

[0111] Based on the first data n, select an integer from integers between 0 and n / 2 as the fifth data k1;

[0112] Select one from the first set of elements as the sixth data r1;

[0113] Based on the first data n, the second data g, the fourth data Y, the fifth data k1, the sixth data r1, the second preset relationship and the third preset relationship, the plaintext M is encrypted to obtain the ciphertext, wherein 0≤M<n 2 , the ciphertext includes seventh data C1 determined based on the second preset relationship and eighth data C2 determined based on the third preset relationship;

[0114] The second preset relationship is:

[0115]

[0116] And among them, express For 2 Take the mold;

[0117] The third preset relationship is:

[0118]

[0119] And among them, express For 2 Take the model.

[0120] In this embodiment, the first encryption rule corresponding to the encryption terminal based on the above-determined public key and the multiplication homomorphic encryption algorithm is given, that is, how to implement the encryption of the plaintext to be encrypted. The specific encryption process is as described above and will not be repeated here. It should be noted that, in fact, according to the above encryption process, if the fifth data k1 is regarded as another plaintext to be encrypted, the setting of the above encryption rules essentially realizes the encryption of two plaintexts to be encrypted at the same time, and it is further easy to prove based on the Paillier algorithm and the ElGamal algorithm that the seventh data C1 satisfies the additive homomorphism, and the eighth data C2 satisfies the multiplication homomorphism.

[0121] It should also be noted that there are restrictions on the specific value of the plaintext, 0≤M<n 2 , and when the plaintext to be encrypted is non-decimal information, it can be converted into decimal information first.

[0122] It can be seen that the encryption process of the decrypted plaintext based on the public key and the encryption rules of the multiplicative homomorphic encryption algorithm is simple and reliable, easy to implement, and ensures the security of information transmission.

[0123] As a preferred embodiment, determining the public key based on the first data n and the private key λ includes:

[0124] Select a ninth data h from the positive integers, wherein the selected ninth data h satisfies: the greatest common divisor between the tenth data D and the first data n is 1, and the tenth data D is determined based on the ninth data h, the private key λ, the first data n and the fourth preset relationship;

[0125] The fourth preset relationship is:

[0126]

[0127] And among them h λ mod n 2 Indicates h λ For 2 Take the mold;

[0128] Based on the first data n, select an integer from integers between 1 and n-1 as the eleventh data a;

[0129] Determine twelfth data X based on the eleventh data a, the first data n and the fifth preset relationship;

[0130] Among them, the fifth preset relationship is:

[0131] X=a*n+1

[0132] The first data n, the ninth data h, and the twelfth data X are determined to be public keys.

[0133] In this embodiment, a second specific determination process of the public key by the decryption terminal is provided, and this method is also simple, reliable and easy to implement, and is helpful for the expansion of data selection in the corresponding encryption rules, thereby enhancing the practicality of the method. Specifically, the public key here includes three data, namely the first data n, the ninth data h and the twelfth data X. First, the ninth data h is determined, and the rules that need to be satisfied are as described above, which will not be repeated here; then the twelfth data X is determined, and the determination process has also been described above. Finally, the first data n, the determined ninth data h and the twelfth data X are used as the public key for subsequent disclosure.

[0134] As a preferred embodiment, encrypting the plaintext according to the public key and the encryption rule to obtain the ciphertext includes:

[0135] Based on the first data n, select an integer from integers between 0 and n as the thirteenth data k2;

[0136] Determine the second set based on the first data n Among them, the second set The set elements in are {0,1,...,(n-1)};

[0137] Determine the second set The second set element that is relatively prime to n among the set elements in ;

[0138] Select one from the second set of elements as the fourteenth data r2;

[0139] Based on the first data n, the ninth data h, the twelfth data x, the thirteenth data k2, the fourteenth data r2, the sixth preset relationship and the seventh preset relationship, the plaintext M is encrypted to obtain a ciphertext, wherein 0≤M<n 2 , the ciphertext includes fifteenth data C3 determined based on the sixth preset relationship formula and sixteenth data C4 determined based on the seventh preset relationship formula;

[0140] The sixth preset relationship is:

[0141]

[0142] And among them, express For 2 Take the mold;

[0143] The seventh preset relationship is:

[0144]

[0145] And among them, express For2 Take the model.

[0146] In this embodiment, the corresponding second encryption rule of the encryption terminal based on the above-determined public key and the multiplication homomorphic encryption algorithm is given, that is, how to implement the encryption of the plaintext to be encrypted. Different from the value-taking step of the fifth data k1 in the above encryption rule, here corresponds to the change of the public key determination mechanism, the thirteenth data k2 can expand a certain value range, that is, an integer can be selected from integers between 0 and n. Compared with the above method, the first corresponding encryption rule can only realize the multiplication homomorphism between the two ciphertexts obtained after encryption, but according to the setting of the second encryption rule in this embodiment, it can be extended to the multiplication homomorphism between multiple encrypted ciphertexts, that is, as shown in the following formula:

[0147] J d (J e (m1)*...*J e (m l )=m1*...*m l mod n 2

[0148] Among them, J d () represents the decryption of the content in brackets, J e () indicates encryption of the content in brackets. m1 here indicates the first plaintext. l Here, represents the lth plaintext. It can be seen that the above formula reflects that multiplication homomorphism in the sense of modulus can be achieved without cracking the corresponding plaintext.

[0149] It can be seen that the encryption rules based on the public key and the multiplicative homomorphic encryption algorithm are simple and reliable for the encryption process of the decrypted plaintext, easy to implement, and can be extended to the multiplicative homomorphism between multiple encrypted ciphertexts. It is more practical and ensures the security of information transmission.

[0150] Please refer to Figure 2 , Figure 2 The present invention provides a flowchart of an information decryption method.

[0151] The information decryption method is applied to a decryption terminal, and the information decryption method comprises:

[0152] S21: Determine a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, the first selected data is the first data n obtained by multiplying p and q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1; A2=q-1; determine the least common multiple as a private key λ, and determine a public key based on the first data n and the private key λ;

[0153] S22: Obtain the ciphertext sent by the encryption terminal after encrypting the plaintext to be transmitted according to the public key and the encryption rules of the pre-designed multiplication homomorphic encryption algorithm;

[0154] S23: Decrypt the ciphertext according to the public key, the private key λ corresponding to the public key and the pre-designed decryption rule of the multiplication homomorphic encryption algorithm to obtain the plaintext to be transmitted.

[0155] The multiplication homomorphic encryption algorithm pre-designed by the decryption terminal includes three parts: key determination rules, encryption rules and decryption rules. It can be seen that the multiplication homomorphic encryption algorithm can not only realize the encryption of plaintext to be transmitted, but also realize the decryption of the ciphertext sent after the encryption terminal encrypts the plaintext to be transmitted according to the public key and the encryption rules of the pre-designed multiplication homomorphic encryption algorithm according to the decryption rules of the multiplication homomorphic encryption algorithm. The decryption terminal here includes but is not limited to the server and the client, etc., and is not particularly limited here.

[0156] It should be noted that, for step S21, in practical applications, the first prime number p and the second prime number q can be selected to be larger, and the larger the values ​​of the first prime number p and the second prime number q are, the higher the encryption security is. The encryption rules here are the encryption rules described in the above embodiments, so they are not repeated here.

[0157] It should also be noted that, as a special case, for some decryption terminals that want to process plain text but do not want the information processor to obtain the ciphertext that is encrypted after the plain text to decrypt the data, according to the multiplicative homomorphic encryption algorithm provided in this application, the decryption terminal may not disclose the public key and the corresponding encryption rule to the information processor, but only send the encrypted ciphertext to the information processor for data processing. At this time, since the multiplicative homomorphic encryption algorithm satisfies the multiplicative homomorphic principle, data processing can be performed directly without decryption. The processed data is then sent to the decryption terminal that has the private key, public key, encryption rule and decryption rule. In this way, for the decryption terminal, the plain text will not be leaked and data processing is achieved.

[0158] In summary, this application can reliably implement information encryption and decryption through a pre-designed multiplication homomorphic encryption algorithm. According to the public key, the corresponding private key and the decryption rules of the multiplication homomorphic encryption algorithm, the ciphertext can be directly decrypted to obtain the plaintext to be transmitted. Compared with the hash encryption algorithm in the prior art, there is no need for a lot of tedious verification, which saves the verification cost, and the private key is private data and will not be made public, which means that only the decryption terminal with the private key can crack the ciphertext encrypted by the corresponding public key and the encryption rules, ensuring the security of information transmission.

[0159] As a preferred embodiment, the public key includes the first data n, the second data g and the third data Y; the ciphertext includes the fourth data C5 and the fifth data C6;

[0160] According to the public key, the private key λ corresponding to the public key and the pre-designed decryption rules of the multiplication homomorphic encryption algorithm, the ciphertext is decrypted to obtain the plaintext to be transmitted, including:

[0161] Processing the fourth data C5 based on the private key λ, the first data n, the second data g and the first preset relationship to obtain sixth data k3;

[0162] The first preset relationship is:

[0163]

[0164] Among them, (C5) λ mod n 2 Indicates (C5) λ For 2 Modulus, g λ mod n 2 Indicates g λ For 2 Take the model, express modulo n;

[0165] Processing the fifth data C6 based on the third data Y, the sixth data k3, the first data n and the second preset relationship to obtain the plaintext E to be transmitted;

[0166] The second preset relationship is:

[0167]

[0168] in, express For 2 Modulus; Y -1 It means to invert Y.

[0169] In this embodiment, a specific process of decrypting the ciphertext by the decryption terminal is given. It should be noted that, corresponding to the setting of the encryption rule in this application, the ciphertext includes two parts, the fourth data C5 and the fifth data C6. In practical applications, it can be pre-specified that, according to the order of time transmission, the first data transmitted is the fourth data C5, and the second data transmitted is the fifth data C6; of course, it is also possible to adopt a marking method to distinguish the two parts of the fourth data C5 and the fifth data C6, which is not particularly limited here.

[0170] Therefore, the fourth data C5 is processed based on the private key λ, the first data n, the second data g and the first preset relationship to obtain the sixth data k3 used to process the fifth data C6. The fifth data C6 is processed based on the third data Y, the sixth data k3, the first data n and the second preset relationship to finally obtain the plaintext E to be transmitted. The decryption method is simple, reliable and easy to implement.

[0171] It should be noted that, based on the Paillier algorithm and the ElGamal algorithm, the key to setting the encryption rules in the present application lies in solving the sixth data k3 in the above embodiment. If the sixth data k3 is known, the plaintext E can be solved in polynomial time. However, it can be understood that based on the Paillier algorithm and the above steps for solving the sixth data k3, the sixth data k3 is unsolvable for the attacker. The inherent security of the solution provided by the present application depends on the security of the Paillier algorithm, that is, the algorithm security is changed from a discrete logarithm problem to a factor decomposition problem. Therefore, the multiplication homomorphic encryption algorithm provided by the present application meets semantic security and multiplication homomorphism.

[0172] As a verification explanation for all the above embodiments, the multiplication homomorphic verification proof of the multiplication homomorphic encryption algorithm provided in this scheme is given below.

[0173] Assume that there are two plaintexts S1 and S2, both of which satisfy: 0<S1<n 2 , 0<S2<n 2 ;

[0174] First, when the public key in the above embodiment is the first data n, the second data g, and the fourth data Y, the homomorphism proof is performed in combination with the above decryption rules and the corresponding encryption rules:

[0175] The determined data corresponding to the plaintext S1 is k1 1 and r1 1 , the determined data corresponding to plaintext S2 is k1 2 and r1 2 , so, assuming that the encryption result of plaintext S1 is (C 11 , C 12 ), the encryption result of plaintext S2 is (C 21 , C 22 ), so we have the following formula:

[0176]

[0177]

[0178] Furthermore, the above C 11 C 21 Decryption yields the following formula:

[0179] k 12 =(k1 1 +k1 2 )modn

[0180] Since 0<k1 1 <n / 2 and 0 <k1 2 <n / 2, we know 0<k1 1 +k1 2 <n / 2, so k 12 =k1 1 +k1 2 Therefore, for the above C 12 C 22 After decryption, we can get

[0181] S 12 =S1S2modn 2

[0182] That is, decryption first and then multiplication is equivalent to multiplication first and then decryption in the sense of modulus. It can be seen that the multiplication homomorphic encryption algorithm provided in this application satisfies multiplication homomorphism.

[0183] Furthermore, when the public key in the above embodiment is the first data n, the ninth data h and the twelfth data X, combined with the above decryption rules, there is still:

[0184] The determined data corresponding to the plaintext S1 is k1 1 and r1 1 , the determined data corresponding to plaintext S2 is k1 2 and r1 2 , so, assuming that the encryption result of plaintext S1 is (C 11 , C 12 ), the encryption result of plaintext S2 is (C 21 , C 22 ), so we have the following formula:

[0185]

[0186]

[0187] For the twelfth data X=an+1, the following formula is obtained:

[0188] X bn =1mod n 2

[0189] Here, b is an integer, so any 0 < k1 1 <n / 2 and 0 <k1 2 <n / 2, the following formula holds true:

[0190]

[0191] Therefore, the decryption result is as follows:

[0192]

[0193] That is, the multiplicative homomorphic encryption algorithm provided by this application satisfies multiplicative homomorphism.

[0194] As a simulation example for all the above embodiments, firstly, for the above embodiments, when the public key is the first data n, the second data g and the fourth data Y, a simulation example is described in combination with the above decryption rules and the corresponding encryption rules:

[0195] Among them, for the first prime number p, the second prime number q, the first data n, the square of the first data n n 2 The determination results of , private key λ, second data g and fourth data Y are shown in Table 1:

[0196] Table 1 Data determination results

[0197] The first prime number p 855851 The second prime number q 792983 First data n 678675293533 <![CDATA[The square of the first data n, n 2 > 460600154052103711622089 Private Key λ 339336822350 The second data g 394933033873654051394520 Fourth data Y 75003797457

[0198] Applying the encryption rule and the public key to encrypt the first plaintext M1=2294456045 and the second plaintext M2=2101345860 to be encrypted, the encryption result of the first plaintext M1 can be (129977620333377804252437, 451645887883734363280541), and the encryption result of the first plaintext M2 is (154549051015919661688505, 116733819850376740400238). After decrypting the above encryption results, the first plaintext M1 and the second plaintext M2 are still obtained, which verifies the correctness of the present application scheme; further, the product of the data before encryption is M 12 =M1M2=4821445711112723700, the encrypted data product is n 2 The modulus is (126769322407780410649588, 264452249411852880672138), which is still equal to 4821445711112723700 after decryption, verifying that the multiplication homomorphic encryption algorithm provided in this application satisfies the multiplication homomorphism.

[0199] Then, for the above embodiment, when the public key is the first data n, the ninth data h and the twelfth data X, a simulation example is described in combination with the above decryption rules and the corresponding encryption rules:

[0200] Among them, for the first prime number p, the second prime number q, the first data n, the square of the first data n n 2 The determination results of , private key λ, ninth data h and twelfth data X are shown in Table 2:

[0201] Table 2 Data determination results

[0202] The first prime number p 564667 The second prime number q 786959 First data n 444369777653 <![CDATA[The square of the first data n, n 2 > 197464499291376658188409 Private Key λ 222184213014 Ninth Data h 114233549500403192274048 12th Data X 444369777654

[0203] Applying the encryption rule and the public key to encrypt the first plaintext M1=1762281960 and the second plaintext M2=1323915952, the encryption result of the first plaintext M1 can be obtained as (19198652150315657740946, 124545380395580196320509, and the encryption result of the first plaintext M2 is (189292518629998566063510, 104360002336348274180848). After decrypting the above encryption results, the first plaintext M1 and the second plaintext M2 are still obtained, which verifies the correctness of the present application scheme. Furthermore, the product of the data before encryption is M 12 =M1M2=2333113198765825920, the encrypted data product is n 2 The modulus is (105040897001554975887307, 34421633312151982265523), which is still equal to 2333113198765825920 after decryption, verifying that the multiplication homomorphic encryption algorithm provided in this application satisfies the multiplication homomorphism.

[0204] Please refer to Figure 3 , Figure 3 A schematic diagram of the structure of an information encryption system provided by the present invention.

[0205] The information encryption system, applied to an encryption terminal, includes:

[0206] The first acquisition unit 31 is used to acquire the public key published by the decryption terminal and the pre-designed encryption rule of the multiplication homomorphic algorithm, wherein the public key is determined by the decryption terminal according to the key determination rule of the multiplication homomorphic algorithm;

[0207] The key determination rule is: the decryption terminal determines a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, the first selected data is the first data n obtained by multiplying p and q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1; A2=q-1; the least common multiple is determined to be a private key λ, and a public key is determined based on the first data n and the private key λ;

[0208] A determination unit 32, used to determine the plaintext to be encrypted;

[0209] The encryption unit 33 is used to encrypt the plaintext according to the public key and the encryption rules of the pre-designed multiplication homomorphic encryption algorithm to obtain the ciphertext.

[0210] For an introduction to the information encryption system provided in the present invention, please refer to the above-mentioned embodiment of the information encryption method, which will not be repeated here.

[0211] Please refer to Figure 4 , Figure 4 A schematic diagram of the structure of an information decryption system provided by the present invention.

[0212] The information decryption system is applied to a decryption terminal and includes:

[0213] The key determination unit 41 is used to determine a first prime number p and a second prime number q that are different from each other, wherein the first prime number p and the second prime number q are selected to satisfy: the greatest common divisor between the first selected data and the second selected data is 1, the first selected data is the first data n obtained by multiplying p and q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1; A2=q-1; the least common multiple is determined as a private key λ, and a public key is determined based on the first data n and the private key λ;

[0214] The second acquisition unit 42 is used to obtain the ciphertext sent by the encryption terminal after encrypting the plaintext to be transmitted according to the public key and the encryption rules of the pre-designed multiplication homomorphic encryption algorithm;

[0215] The decryption unit 43 is used to decrypt the ciphertext according to the public key, the private key λ corresponding to the public key and the pre-designed decryption rule of the multiplication homomorphic encryption algorithm to obtain the plaintext to be transmitted.

[0216] For an introduction to the information decryption system provided in the present invention, please refer to the above-mentioned embodiment of the information decryption method, which will not be described in detail here.

[0217] Please refer to Figure 5 , Figure 5 A schematic structural diagram of an information processing device provided by the present invention.

[0218] The information processing device comprises:

[0219] A memory 51, used for storing computer programs;

[0220] The processor 52 is used to execute the steps of the information encryption method as described above.

[0221] For an introduction to the information processing device provided in the present invention, please refer to the embodiments of the above-mentioned information encryption method and information decryption method, which will not be described in detail here.

[0222] It should be noted that when the information processing device executes the steps of the information encryption method, it essentially encrypts the plaintext to be encrypted; when the information processing device executes the steps of the information decryption method, it essentially decrypts the ciphertext to be decrypted.

[0223] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0224] It should also be noted that, in this specification, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the statement "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element.

[0225] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in the above description according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0226] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An information encryption method, characterized in that: Applied to an encryption terminal, the information encryption method includes: Obtaining a public key published by a decryption terminal and a pre-designed encryption rule of a multiplication homomorphic algorithm, wherein the public key is determined by the decryption terminal according to a key determination rule of the multiplication homomorphic algorithm; The key determination rule is: the decryption terminal determines a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, and the first selected data is the first data n obtained by multiplying the p and the q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1, and A2=q-1; the least common multiple is determined to be a private key λ corresponding to the public key, and the public key is determined based on the first data n and the private key λ; Determine the plaintext to be encrypted; Encrypting the plaintext according to the public key and the encryption rule to obtain a ciphertext; The determining of the public key based on the first data n and the private key λ includes: Select a ninth data h from a positive integer, wherein the selected ninth data h satisfies: the greatest common divisor between the tenth data D and the first data n is 1, and the tenth data D is determined based on the ninth data h, the private key λ, the first data n and a fourth preset relationship; Based on the first data n, select an integer from integers between 1 and n-1 as the eleventh data a; Determine twelfth data X based on the eleventh data a, the first data n and a fifth preset relationship; The first data n, the ninth data h, and the twelfth data X are determined to be the public key.

2. The information encryption method according to claim 1, characterized in that: Determining the public key based on the first data n and the private key λ further includes: Select a second data g from a positive integer, wherein the selected second data g satisfies: the greatest common divisor between the third data B and the first data n is 1, and the third data B is determined based on the second data g, the private key λ, the first data n and a first preset relationship; The first preset relationship is: And among them g λ mod n 2 Indicates g λ For 2 Take the mold; Determine a first set based on the first data n Among them, the first set The set elements in are {0,1,...,(n-1)}; Determine the first set The first set element that is relatively prime to n among all the set elements in ; Select a fourth data Y from the first set elements; The first data n, the second data g, and the fourth data Y are determined to be the public key.

3. The information encryption method according to claim 2, characterized in that: Encrypting the plaintext according to the public key and the encryption rule to obtain ciphertext includes: Based on the first data n, select an integer from integers between 0 and n / 2 as fifth data k1; Select one from the first set of elements as the sixth data r1; Based on the first data n, the second data g, the fourth data Y, the fifth data k1, the sixth data r1, the second preset relationship and the third preset relationship, the plaintext M is encrypted to obtain a ciphertext, wherein 0≤M<n 2 , the ciphertext includes seventh data C1 determined based on the second preset relationship and eighth data C2 determined based on the third preset relationship; The second preset relationship is: And among them, express For 2 Take the mold; The third preset relationship is: And among them, express For 2 Take the model.

4. The information encryption method according to claim 1, characterized in that: The fourth preset relationship is: And among them h λ mod n 2 Indicates h λ For 2 Take the mold; The fifth preset relationship is: X=a*n+1.

5. The information encryption method according to claim 4, characterized in that: Encrypting the plaintext according to the public key and the encryption rule to obtain ciphertext includes: Based on the first data n, selecting an integer from integers between 0 and n as the thirteenth data k2; Determine a second set based on the first data n Among them, the second set The set elements in are {0,1,...,(n-1)}; Determine the second set The second set element that is relatively prime to n among the set elements in ; Select one from the second set elements as the fourteenth data r2; Based on the first data n, the ninth data h, the twelfth data X, the thirteenth data k2, the fourteenth data r2, the sixth preset relationship and the seventh preset relationship, the plaintext M is encrypted to obtain a ciphertext, wherein 0≤M<n 2 , the ciphertext includes fifteenth data C3 determined based on the sixth preset relationship and sixteenth data C4 determined based on the seventh preset relationship; The sixth preset relationship is: And among them, express For 2 Take the mold; The seventh preset relationship is: And among them, express For 2 Take the model.

6. A method for decrypting information, characterized in that: Applied to a decryption terminal, the information decryption method comprises: Determine a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, the first selected data is the first data n obtained by multiplying the p and the q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1; A2=q-1; determine the least common multiple as a private key λ, and determine a public key corresponding to the private key λ based on the first data n and the private key λ; Obtaining the ciphertext sent by the encryption terminal after encrypting the plaintext to be transmitted according to the public key and the encryption rules of the pre-designed multiplication homomorphic encryption algorithm; Decrypting the ciphertext according to the public key, the private key λ corresponding to the public key and the pre-designed decryption rule of the multiplication homomorphic encryption algorithm to obtain the plaintext to be transmitted; Wherein, determining a public key corresponding to the private key λ based on the first data n and the private key λ further includes: Select a ninth data h from a positive integer, wherein the selected ninth data h satisfies: the greatest common divisor between the tenth data D and the first data n is 1, and the tenth data D is determined based on the ninth data h, the private key λ, the first data n and a fourth preset relationship; Based on the first data n, select an integer from integers between 1 and n-1 as the eleventh data a; Determine twelfth data X based on the eleventh data a, the first data n and a fifth preset relationship; The first data n, the ninth data h, and the twelfth data X are determined to be the public key.

7. The information decryption method according to claim 6, characterized in that: The public key includes first data n, second data g and third data Y; the ciphertext includes fourth data C5 and fifth data C6; Decrypting the ciphertext according to the public key, the private key λ corresponding to the public key and the pre-designed decryption rule of the multiplication homomorphic encryption algorithm to obtain the plaintext to be transmitted, including: Processing the fourth data C5 based on the private key λ, the first data n, the second data g and a first preset relationship to obtain sixth data k3; The first preset relationship is: Among them, (C5) λ mod n 2 Indicates (C5) λ For 2 Modulus, g λ mod n 2 Indicates g λ For 2 Take the model, express modulo n; Processing the fifth data C6 based on the third data Y, the sixth data k3, the first data n and the second preset relationship to obtain the plaintext E to be transmitted; The second preset relationship is: in, express For 2 Modulus; Y -1 It means taking the inverse of Y.

8. An information encryption system, characterized in that: Applied to an encryption terminal, the information encryption system comprises: A first acquisition unit is used to acquire a public key published by a decryption terminal and a pre-designed encryption rule of a multiplication homomorphic algorithm, wherein the public key is determined by the decryption terminal according to a key determination rule of the multiplication homomorphic algorithm; The key determination rule is: the decryption terminal determines a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, and the first selected data is the first data n obtained by multiplying the p and the q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1, and A2=q-1; the least common multiple is determined to be a private key λ corresponding to the public key, and the public key is determined based on the first data n and the private key λ; A determination unit, used for determining the plaintext to be encrypted; An encryption unit, used to encrypt the plaintext according to the public key and the encryption rule to obtain a ciphertext; Wherein, determining the public key based on the first data n and the private key λ further includes: Select a ninth data h from a positive integer, wherein the selected ninth data h satisfies: the greatest common divisor between the tenth data D and the first data n is 1, and the tenth data D is determined based on the ninth data h, the private key λ, the first data n and a fourth preset relationship; Based on the first data n, select an integer from integers between 1 and n-1 as the eleventh data a; Determine twelfth data X based on the eleventh data a, the first data n and a fifth preset relationship; The first data n, the ninth data h, and the twelfth data X are determined to be the public key.

9. An information decryption system, characterized in that: Applied to a decryption terminal, the information decryption system comprises: A key determination unit, used to determine a first prime number p and a second prime number q that are different from each other, wherein the selection of the first prime number p and the second prime number q satisfies: the greatest common divisor between the first selected data and the second selected data is 1, the first selected data is the first data n obtained by multiplying the p and the q; the second selected data is the least common multiple between A1 and A2, wherein A1=p-1; A2=q-1; the least common multiple is determined to be a private key λ, and a public key corresponding to the private key λ is determined based on the first data n and the private key λ; A second acquisition unit is used to obtain the ciphertext sent by the encryption terminal after encrypting the plaintext to be transmitted according to the public key and the encryption rules of the pre-designed multiplication homomorphic encryption algorithm; A decryption unit, configured to decrypt the ciphertext according to the public key, a private key λ corresponding to the public key and a pre-designed decryption rule of the multiplication homomorphic encryption algorithm to obtain the plaintext to be transmitted; Wherein, determining a public key corresponding to the private key λ based on the first data n and the private key λ further includes: Select a ninth data h from a positive integer, wherein the selected ninth data h satisfies: the greatest common divisor between the tenth data D and the first data n is 1, and the tenth data D is determined based on the ninth data h, the private key λ, the first data n and a fourth preset relationship; Based on the first data n, select an integer from integers between 1 and n-1 as the eleventh data a; Determine twelfth data X based on the eleventh data a, the first data n and a fifth preset relationship; The first data n, the ninth data h, and the twelfth data X are determined to be the public key.

10. An information processing device, characterized in that: include: Memory for storing computer programs; A processor, configured to execute the steps of the information encryption method according to any one of claims 1 to 7.

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