CN114422219B - Data encryption transmission method based on dimension-reducing polynomial - Google Patents
Data encryption transmission method based on dimension-reducing polynomial Download PDFInfo
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Classifications
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
- H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
- H04L63/0442—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload wherein the sending and receiving network entities apply asymmetric encryption, i.e. different keys for encryption and decryption
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0891—Revocation or update of secret information, e.g. encryption key update or rekeying
Abstract
The invention relates to the technical field of information, in particular to a data encryption transmission method based on a dimension-reduction polynomial, which comprises the following steps: the sender and the receiver agree on an initial binary polynomial; replacing the coefficients of the initial binary polynomial with n plaintext values; the sender reduces the dimension of the initial binary polynomial, and the dimension reduction value is marked as A; generating variable values of n+m groups of dimension-reduced unitary polynomials and unitary polynomial value data pairs; the sender sends { A, (x_i, f_i) } |i E [1, n+m ] to the receiver; the receiver uses the A and n groups of data pairs (x_i, f_i) to calculate the coefficient of the dimension-reduced unitary polynomial, namely n plaintext values; the receiving side uses m groups of data to verify the obtained n plaintext values, if the verification is met, a successful signal of receiving is sent to the sending side, otherwise, a failed signal of receiving is sent to the sending side. The invention has the following substantial effects: the security of data transmission is improved, and the data encryption transmission is safer.
Description
Technical Field
The invention relates to the technical field of information, in particular to a data encryption transmission method based on a dimension-reduction polynomial.
Background
The information encryption technology is a technology for protecting electronic information in a transmission process and a storage body by using mathematical or physical means so as to prevent leakage. The data is converted into a message which cannot be read by anyone without a correct key through the cryptographic arithmetic. And these data in an unreadable form are generally referred to as ciphertext. However, in the current encryption algorithm, the plaintext and the ciphertext are in one-to-one correspondence, namely the same plaintext and the same secret key, and the obtained ciphertext is the same and is easy to crack. The asymmetric encryption Elgamal introduces a random number during encryption, so that the ciphertext obtained by the same key and plaintext is not unique. But asymmetric encryption algorithms have the problem of inefficiency. The encryption algorithm with non-unique ciphertext has higher security. Thus, continued research into cryptographic algorithms that are not ciphertext-unique is needed.
For example, chinese patent CN106357391a, publication date 2017, month 1 and 25, discloses a secure information decentralized encryption algorithm, and the encryption process includes the following steps: selecting a symmetric encryption algorithm (such as AES); reading data, and dividing the data into N sections of M bytes each; symmetrically encrypting the first segment of data by using Key 1; data extraction, namely extracting the ith byte of each piece of data, and combining the ith byte and the ith byte to form an N byte unit; matrix transformation, which uses an N-dimensional reversible matrix A to perform matrix transformation on N byte units; data recombination, restoring the result after matrix transformation to the corresponding position of each data segment; and the second layer is encrypted, and the first section of the data is symmetrically encrypted by using Key 2. The decryption process is substantially the same as the encryption process, which is the inverse of the encryption process. The whole encryption of the data is realized under the condition of encrypting part of the data through the data transformation process, and the encryption speed is higher. And only Key2 is replaced and the first piece of data is re-encrypted when the data is re-encrypted. Under the same Key, the plaintext and the ciphertext have strict corresponding relation, and the safety is low.
Disclosure of Invention
The invention aims to solve the technical problems that: at present, the technical problem of efficient cipher text non-unique encryption algorithm is lacking. The data encryption transmission method based on the dimension-reducing polynomial can improve the security of data encryption transmission.
In order to solve the technical problems, the invention adopts the following technical scheme: a data encryption transmission method based on a dimension-reducing polynomial comprises the following steps: the sender and the receiver agree on an initial binary polynomial; replacing the coefficients of the initial binary polynomial with n plaintext values; the sender reduces the dimension of the initial binary polynomial, the dimension-reduced variable is a contracted variable, the dimension-reduced value is marked as A, and the dimension-reduced unitary polynomial has n single expressions with coefficients other than 0; generating n+m groups of variable values of the dimension-reduced unitary polynomial and unitary polynomial value data pairs, and recording the variable values and the unitary polynomial value data pairs as data pairs (x_i, f_i), wherein i epsilon [1, n+m ], m is a confusion margin, and m is more than or equal to 0; the sender sends { A, (x_i, f_i) } |i E [1, n+m ] to the receiver; the receiver uses the A and n groups of data pairs (x_i, f_i) to calculate the coefficient of the dimension-reduced unitary polynomial, namely n plaintext values; the receiving party uses m groups of data to verify n plaintext values obtained, if the verification is met, a successful signal of receiving is sent to the sending party, otherwise, a failed signal of receiving is sent to the sending party; and if the sender receives the receiving success signal in the preset time period, the next n plaintext values are sent.
Preferably, the method for retransmitting the current n plaintext values includes: regenerating n+m groups of reduced-dimension unitary polynomial variable values and polynomial value data pairs (x '_i, f' _i); { A, (x '_i, f' _i) } |i ε [1, n+m ] is sent to the receiver.
Preferably, the method for the sender and the receiver to agree on the initial binary polynomial comprises the following steps: the sender generates an initial unitary polynomial, and the highest degree of the initial unitary polynomial does not exceed N; the sender generates more than N groups of variable value and initial unitary polynomial value data pairs, and sends the data pairs to the receiver, and the receiver calculates an initial unitary polynomial; the receiving party generates a plurality of groups of variable value and initial unitary polynomial value data pairs, and sends the variable value and initial unitary polynomial value data pairs to the sending party, and the sending party verifies that the data pairs are correct, and if the data pairs are not correct, the sending party sends a resolving success signal, otherwise, the sending party sends a resolving identification signal; if the solution fails, the sender regenerates the initial unitary polynomial; regenerating more than N groups of variable values and initial unitary polynomial value data pairs, and sending the data pairs to a receiver until the receiver successfully calculates; the sender uses another variable to generate a plurality of coefficient unitary polynomials, the highest degree of the coefficient unitary polynomials is not more than N, and the coefficient unitary polynomials are multiplied by the coefficients of the initial unitary polynomials to be used as the coefficients of the single polynomials of the initial unitary polynomials; and generating a plurality of groups of variable values and coefficient unitary polynomial value data pairs for each coefficient unitary polynomial respectively, and sending the variable values and the coefficient unitary polynomial value data pairs to a receiver until the receiver calculates all coefficient unitary polynomials.
Preferably, after selecting the dimension reduction value A, the sender substitutes into the initial binary polynomial to generate a variable value and a unitary polynomial value data pair, and the variable value and the unitary polynomial value data pair are marked as (x_0, f_0); the sender sends { (x_0, f_0), (x_i, f_i) } |i epsilon [1, n+m ], n+m+1 group data pairs to the receiver; after the receiver receives the data, the dimension reduction value A is calculated by using (x_0, f_0) and an initial binary polynomial; the receiver uses the A and n groups of data pairs (x_i, f_i) to calculate the coefficient of the dimension-reduced unitary polynomial, namely n plaintext values.
Preferably, the sender sends data pairs corresponding to k×n plaintext values to the receiver together; the receiver uses the first data pair to calculate the dimension-reduction value A, and uses the subsequent n data pairs to recover n plaintext values; subsequently verifying the subsequent data pairs one by one until data pairs which do not match the recovered n plaintext values appear; and repeatedly calculating a dimension reduction value A by using the unmatched data, and recovering n plaintext values by using the subsequent n data pairs until all the data pairs are used.
The invention has the following substantial effects: the encrypted data transmission with the non-unique ciphertext is provided, so that information leakage can be effectively avoided, and the safety of data transmission is improved; the binary polynomial is used for data transmission after dimension reduction, changing dimension reduction values is equivalent to changing secret keys, the difficulty of data cracking is improved, and data encryption transmission is safer.
Drawings
Fig. 1 is a schematic diagram of a data encryption transmission method according to an embodiment.
FIG. 2 is a schematic diagram of a method for specifying an initial binary polynomial according to an embodiment.
Fig. 3 is a schematic diagram of an embodiment of a data encryption transmission method.
Fig. 4 is a schematic diagram of a method for continuously sending multiple cipher texts according to the second embodiment.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings.
Embodiment one:
a data encryption transmission method based on dimension-reducing polynomial, the sender wants to send the following data {3,9,12,6,23,8}, the transmission step please refer to figure 1, comprising: step A01) the sender and the receiver agree on an initial bivariate polynomial: f (x, y) =5 x 4 x y 3+7 x 3 x y 2+11 x 2 x, the contracted initial binary polynomial has a total of 3 single-terms.
Step a 02) replaces the coefficients of the initial binary polynomial with n plaintext values. First the first 3 plaintext values are sent, 3,9,12, and after substitution with plaintext values, the initial binary polynomial is converted into:
f(x,y)=3*x^4*y^3+9*x^3*y^2+12*x^2*y。
and A03) the sender reduces the dimension of the initial binary polynomial, the dimension-reduced variable is a contracted variable, the dimension-reduced value is recorded as A, and the dimension-reduced unitary polynomial has n single expressions with coefficients other than 0. Y is selected as the dimension-reduced variable. The dimension reduction value a=3, i.e. y=3 is substituted into the binary polynomial. Obtaining a unitary polynomial: f (x) =3 x≡4 x≡3++9 x≡3 x≡3++12 x≡2 x 3) =81 x≡4+81 x≡3+36 x≡2.
Step A04) generating n+m groups of variable values of the dimension-reduced unitary polynomial and unitary polynomial value data pairs, and recording the variable values and the unitary polynomial value data pairs as data pairs (x_i, f_i), wherein i is [1, n+m ], and m is a confusion margin, and m is more than or equal to 0.
The unitary polynomial is f (x) =81 x≡4+81 x≡3+36 x≡2, m takes on the value 2, and the sender generates 5 sets of data pairs: { (3,9072), (5,61650), (16,5649408), (11,1298088), (9,593406) }.
Step a 05) the sender sends { a, (x_i, f_i) } |i e [1, n+m ] to the receiver. I.e., data {3, (3,9072), (5,61650), (16,5649408), (11,1298088), (9,593406) } is sent to the recipient.
Step A06) the receiver uses the data pairs (x_i, f_i) of the group A and n to calculate the coefficient of the unitary polynomial after the dimension reduction, namely n plaintext values. Substituting A into the initial binary polynomial by the receiver to obtain f (x) =27x4xx4a3xx3+3x2xx2, where a4, a3 and a2 represent coefficients of the single formulae of times 4, 3 and 2, respectively. The receiver calculates 3 of the 5 data pairs received by the receiver, and is used for calculating a4, a3 and a2 to obtain a4=3, a3=9 and a2=12, namely, plaintext value {3,9,12}.
Step A07) the receiving side uses m groups of data pairs to verify n plaintext values obtained, if the verification is met, a receiving success signal is sent to the sending side, otherwise, a receiving failure signal is sent to the sending side.
And then the receiving party uses the rest two groups of data to verify the obtained plaintext numerical value, and sends a successful receiving signal to the sending party when the verification is found to be in conformity. And finishing the transmission of the current numerical plaintext.
Step A08), if the sender does not receive a successful signal or a failed signal within a preset time period, resending the current n plaintext values; step A09), if the sender receives the successful signal in the preset time, the next n plaintext values are sent.
The method for retransmitting the current n plaintext values comprises the following steps: regenerating n+m groups of reduced-dimension unitary polynomial variable values and polynomial value data pairs (x '_i, f' _i); { A, (x '_i, f' _i) } |i ε [1, n+m ] is sent to the receiver. The value of the dimension reduction value A can not be changed during retransmission, or the value of the dimension reduction value A can be changed and then transmitted.
Referring to fig. 2, the method for the sender and the receiver to agree on the initial binary polynomial includes: step B01) the sender generates an initial univariate polynomial, the highest degree of which does not exceed N. In this embodiment n=4, i.e. the highest order index of the variable does not exceed 4. The value of N may be transmitted by encryption in the prior art or may be agreed on-line. The univariate polynomial can be expressed as: f (x) =a4×χ ζ4+a3×χ ζ3+a2×χ2+a1×x+a0, a0 to a4 total of five coefficients. Specifically, a4=5, a3=7, a2=11, a1=a0=0. Step B02) the sender generates more than N groups of variable values and initial univariate polynomial value data pairs, and sends the data pairs to the receiver, and the receiver calculates the initial univariate polynomial. More than N, i.e. at least n+1, data pairs, i.e. 5 data pairs. The 5 sets of data pairs can just solve for the five coefficients a0 to a4, and the receiver can obtain the univariate polynomial. Step B03), the receiving party generates a plurality of groups of variable value and initial unitary polynomial value data pairs and sends the variable value and initial unitary polynomial value data pairs to the sending party. After the receiving party calculates five coefficients a0 to a4, a plurality of data pairs are randomly generated and verified for the transmitting party. If the sender verifies that the sender is error-free, the plaintext transmits a resolving success signal, otherwise, the plaintext transmits a resolving identification signal; step B04), if the resolving fails, the sender regenerates an initial unitary polynomial; step B05) regenerating more than N groups of variable values and initial unitary polynomial value data pairs, and sending the data pairs to a receiver until the receiver successfully calculates.
When the polynomial function is solved back from the sample data, there are numerous sets of solutions if the highest degree N of the polynomial is not known. The sender and receiver agree on N and thus can deduce a specific univariate polynomial from limited sample data. Without the eavesdropper knowing the value of N, it is not possible to infer a specific univariate polynomial because there are countless univariate polynomials that satisfy the pairs of eavesdropped data. To further obfuscate, the sender may generate 6 or more sets of data pairs. The recipient is still able to solve for the univariate polynomial, but the eavesdropper would be more difficult to break.
Step B06) the sender uses another variable to generate a plurality of coefficient unitary polynomials, the highest degree of the coefficient unitary polynomials does not exceed N, and the coefficient unitary polynomials are multiplied by the coefficients of the initial unitary polynomials to be used as the coefficients of the single polynomials of the initial unitary polynomials.
Since a1=a0=0, the result is 0 regardless of the form of the coefficient univariate polynomial, the convention for univariate polynomials of the order and constant terms can be omitted for implementation.
The sender generates a univariate polynomial with 3 non-0 coefficients corresponding to the 4 th, 3 rd and 2 nd order terms, respectively. I.e. f (x, y) =
(b14*y^4+b13*y^3+b12*y^2+b11*y+b10)*5*x^4
+
(b24*y^4+b23*y^3+b22*y^2+b21*y+b20)*7*x^3
+
(b34*y^4+b33*y^3+b32*y^2+b31*y+b30)*11*x^2 。
The sender makes b13=5, b22=7, b31=11, the remaining coefficients b take on values of 0, an initial binary polynomial f (x, y) =5×4×y3+7×3×y2+11×2×3.
Step B07) respectively generating a plurality of groups of variable values and coefficient unitary polynomial value data pairs for each coefficient unitary polynomial, and sending the variable values and the coefficient unitary polynomial value data pairs to a receiver until the receiver calculates all coefficient unitary polynomials. In the same manner as the description of the contracted initial unitary polynomial of step B02) to step B05), 3 coefficient polynomials are contracted one by one. The final receiver will also derive the initial binary polynomial f (x, y) =5 x 4 x 3+7 x 3 x 2+11 x 2 x.
Since the value of n is defined as the unigram after dimension reduction in this embodiment, the unigram has n coefficients other than 0. Thus allowing the initial binary polynomial before dimension reduction to have more single terms than n when implemented. For example, f (x, y) =5×4×3+3×2+9×12) +7×3×2+11×2×2. When fully developed, there are 6 single expressions, but when y is used as a dimension-reducing variable, the dimension is reduced, and then the single-element polynomial with 3 single expressions is obtained. This embodiment provides a higher security for the initial binary polynomial.
The beneficial technical effects of this embodiment are: the encrypted data transmission with the non-unique ciphertext is provided, so that information leakage can be effectively avoided, and the safety of data transmission is improved; the binary polynomial is used for data transmission after dimension reduction, changing dimension reduction values is equivalent to changing secret keys, the difficulty of data cracking is improved, and data encryption transmission is safer.
Embodiment two:
compared with the first embodiment, the data encryption transmission method based on the dimension-reducing polynomial can hide the dimension-reducing value, and further improves the security of an encryption algorithm. Referring to fig. 3, the method includes: step C01), after selecting the dimension reduction value A, the sender substitutes into an initial binary polynomial to generate a variable value and a unitary polynomial value data pair, and the variable value and the unitary polynomial value data pair are marked as (x_0, f_0); step C02) the sender sends { (x_0, f_0), (x_i, f_i) } |i e [1, n+m ], n+m+1 total data pairs to the receiver; step C03), after the receiving party receives the data, calculating a dimension reduction value A by using the (x_0, f_0) and the initial binary polynomial; step C04) the receiver uses the A and n groups of data pairs (x_i, f_i) to calculate the coefficient of the dimension-reduced unitary polynomial, namely n plaintext values. In the first embodiment, when data { a=3, (3,9072), (5,61650), (16,5649408), (11,1298088), (9,593406) } is transmitted to the receiving party, the dimension-reduced value a is always directly exposed. The security of encrypted transmissions is reduced. In this embodiment, the value of the dimension reduction value a is not directly provided. Instead, a group of data pairs is provided, after the data pairs are substituted into the initial binary polynomial, an equation only containing y is obtained, and the y value is solved to obtain the dimension reduction value. Thereby increasing the security of encrypted transmissions.
In order to improve the transmission efficiency of the ciphertext, the embodiment provides the following technical scheme, please refer to fig. 4, including: step D01), the sender sends data pairs corresponding to k x n plaintext values to the receiver together; step D02) the receiver uses the first data pair to calculate the dimension-reduction value A, and uses the subsequent n data pairs to recover n plaintext values; step D03) then verifying the subsequent data pairs one by one until data pairs which do not match the recovered n plaintext values appear; step D04) using the unmatched data to recalculate the reduced dimension value A, and then using the subsequent n data pairs to recover the n plaintext values until all the data pairs are used.
I.e. n pairs of data are followed by at least 2 pairs of data for verification. And then follows a set of data pairs for solving the new dimension reduction value a. The receiver first uses the data pair for solving the new dimension reduction value a to verify the last group of plaintext values and finds out that the verification is not correct. But it has been verified that there are at least two pairs of data that are valid, no more reception error signals are emitted. Instead, the non-conforming data pairs are substituted into the initial binary polynomial to calculate the new value of the dimension reduction value A. And then using the new value of the dimension reduction value A, and combining the subsequent n data pairs to calculate the next n plaintext values.
Compared with the first embodiment, the technical scheme described in the first embodiment can hide the dimension reduction value A, so that an eavesdropper cannot recover the binary polynomial.
The above-described embodiment is only a preferred embodiment of the present invention, and is not limited in any way, and other variations and modifications may be made without departing from the technical aspects set forth in the claims.
Claims (5)
1. A data encryption transmission method based on a dimension-reducing polynomial is characterized in that,
comprising the following steps:
the sender and the receiver agree on an initial binary polynomial;
replacing the coefficients of the initial binary polynomial with n plaintext values;
the sender reduces the dimension of the initial binary polynomial, the dimension-reduced variable is a contracted variable, the dimension-reduced value is marked as A, and the dimension-reduced unitary polynomial has n single expressions with coefficients other than 0;
generating n+m groups of variable values of the dimension-reduced unitary polynomial and unitary polynomial value data pairs, and recording the variable values and the unitary polynomial value data pairs as data pairs (x_i, f_i), wherein i epsilon [1, n+m ], m is a confusion margin, and m is more than or equal to 0;
the sender sends { A, (x_i, f_i) } |i E [1, n+m ] to the receiver;
the receiver uses the A and n groups of data pairs (x_i, f_i) to calculate the coefficient of the dimension-reduced unitary polynomial, namely n plaintext values;
the receiving party uses m groups of data to verify n plaintext values obtained, if the verification is met, a successful signal of receiving is sent to the sending party, otherwise, a failed signal of receiving is sent to the sending party;
and if the sender receives the receiving success signal in the preset time period, the next n plaintext values are sent.
2. The method for encrypted data transmission based on a dimensionality reduction polynomial as claimed in claim 1, wherein,
the method for retransmitting the current n plaintext values comprises the following steps:
regenerating n+m groups of reduced-dimension unitary polynomial variable values and polynomial value data pairs (x '_i, f' _i);
{ A, (x '_i, f' _i) } |i ε [1, n+m ] is sent to the receiver.
3. A data encryption transmission method based on a dimensionality reduction polynomial as claimed in claim 1 or 2,
the method for the sender and the receiver to agree on the initial binary polynomial comprises the following steps:
the sender generates an initial unitary polynomial, and the highest degree of the initial unitary polynomial does not exceed N;
the sender generates more than N groups of variable value and initial unitary polynomial value data pairs, and sends the data pairs to the receiver, and the receiver calculates an initial unitary polynomial;
the receiving party generates a plurality of groups of variable value and initial unitary polynomial value data pairs, and sends the variable value and initial unitary polynomial value data pairs to the sending party, and the sending party verifies that the data pairs are correct, and if the data pairs are not correct, the sending party sends a resolving success signal, otherwise, the sending party sends a resolving failure signal;
if the solution fails, the sender regenerates the initial unitary polynomial;
regenerating more than N groups of variable values and initial unitary polynomial value data pairs, and sending the data pairs to a receiver until the receiver successfully calculates;
the sender uses another variable to generate a plurality of coefficient unitary polynomials, the highest degree of the coefficient unitary polynomials is not more than N, and the coefficient unitary polynomials are multiplied by the coefficients of the initial unitary polynomials to be used as the coefficients of the single polynomials of the initial unitary polynomials;
and generating a plurality of groups of variable values and coefficient unitary polynomial value data pairs for each coefficient unitary polynomial respectively, and sending the variable values and the coefficient unitary polynomial value data pairs to a receiver until the receiver calculates all coefficient unitary polynomials.
4. A data encryption transmission method based on a dimensionality reduction polynomial as claimed in claim 3, characterized in that,
after the sender selects the dimension reduction value A, substituting the dimension reduction value A into an initial binary polynomial to generate a variable value and a unitary polynomial value data pair, and marking the variable value and the unitary polynomial value data pair as (x_0, f_0);
the sender sends { (x_0, f_0), (x_i, f_i) } |i epsilon [1, n+m ], n+m+1 group data pairs to the receiver;
after the receiver receives the data, the dimension reduction value A is calculated by using (x_0, f_0) and an initial binary polynomial;
the receiving side uses the calculated dimension reduction value A and n groups of data pairs (x_i, f_i) to calculate the coefficient of the dimension reduction unitary polynomial, namely n plaintext values.
5. The method for encrypted transmission of data based on a dimensionality reduction polynomial as claimed in claim 4,
the sender sends data pairs corresponding to k x n plaintext values to the receiver together;
the receiver uses the first data pair to calculate the dimension-reduction value A, and uses the subsequent n data pairs to recover n plaintext values;
subsequently verifying the subsequent data pairs one by one until data pairs which do not match the recovered n plaintext values appear;
and repeatedly calculating a dimension reduction value A by using the unmatched data, and recovering n plaintext values by using the subsequent n data pairs until all the data pairs are used.
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| NTRU型多密钥全同态加密方案的优化;车小亮 等;《工程科学与技术》;全文 * |
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