CN106911716B - RSA-Hill mixed encryption method based on plaintext random segmentation - Google Patents

RSA-Hill mixed encryption method based on plaintext random segmentation Download PDF

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CN106911716B
CN106911716B CN201710241961.5A CN201710241961A CN106911716B CN 106911716 B CN106911716 B CN 106911716B CN 201710241961 A CN201710241961 A CN 201710241961A CN 106911716 B CN106911716 B CN 106911716B
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CN106911716A (en
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杨宏宇
宁宇光
谢丽霞
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Civil Aviation University of China
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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
    • H04L63/045—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 hybrid encryption, i.e. combination of symmetric and asymmetric encryption
    • 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
    • H04L9/14—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using a plurality of keys or algorithms
    • 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
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters
    • H04L9/302—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters involving the integer factorization problem, e.g. RSA or quadratic sieve [QS] schemes

Abstract

An RSA-Hill mixed encryption method based on plaintext random segmentation. The generated Pascal matrix is used for replacing a secret key of a Hill password, a session secret key in a mixed encryption algorithm is transferred into a random division number of a plaintext, and then an RSA password is used for encrypting the session secret key. It can be observed from simulation experiments that the method provided by the invention meets the requirements for constructing a hybrid encryption method by randomly segmenting the plaintext, avoids the occurrence of the dummy problem, and realizes the encryption process of one-time pad, so that the method has better encryption efficiency and stronger attack resistance.

Description

RSA-Hill mixed encryption method based on plaintext random segmentation
Technical Field
The invention belongs to the technical field of computer network information security, and particularly relates to an RSA-Hill mixed encryption method based on plaintext random segmentation.
Background
In the long-term practice of cryptography, hybrid cryptography has been proposed and has been widely used because of its high performance efficiency. In hybrid encryption schemes, plaintext is often encrypted with a symmetric cipher and a session key is encrypted with a public key cipher. The hybrid encryption not only utilizes the advantages of public key cryptography to avoid the problem of key distribution, but also utilizes the advantages of symmetric cryptography to improve the processing speed of the method.
Cramer and Shoup first formally defined a hybrid encryption model in 2001 and proposed a KEM-DEM structural model. They divide the hybrid encryption into a Key Encapsulation Mechanism (KEM) module and a Data Encapsulation Mechanism (DEM) module. The KEM module encrypts a randomly generated session key K by using a public key of a receiver to obtain a ciphertext C of the session key0. DEM module adds plaintext M by using session key KAnd (5) encryption. At the same time, the authors mention that one of the key prerequisites for constructing a hybrid password is that the KEM module must be compatible with the DEM module, namely: the length of the session key K is equal to that of the symmetric cipher key in the DEM module.
Due to the formal definition of the hybrid password, a large amount of research is carried out by domestic and foreign scholars, but for many hybrid encryption schemes, the KEM-DEM structure cannot be simply applied, and the schemes also have better execution efficiency and safety. Such as: the DHAES model, the REACT model, and the FO model. Aiming at the situation, a brand-new scheme of the tag KEM-DEM is provided, a ciphertext generated by the DEM is used as a label in the tag KEM, and the security of a mixed cryptosystem is guaranteed while the two modules are associated. Due to the limitation of the hybrid password formalization structure, the password system conforming to the structure is less. Some cryptosystems cannot be combined with other cryptosystems into hybrid cryptosystems according to the KEM-DEM structure because of the form of the key (such as Hill cryptosystem) or the security.
The RSA cipher and Hill cipher construction of a hybrid cipher are still in the exploration phase. While Rahman et al propose that the Hill + + algorithm enhances the resistance of the Hill cipher to known plaintext attacks, Goel improves the security of the RSA cipher by way of the Hill cipher. Levenspeak proposes an RSA-Sign-Hill algorithm based on a finite field matrix construction technique. The key number k generated when the Hill cipher encryption matrix is generated is used as the session key in the algorithm, so that the session key is single, the algorithm for generating the encryption matrix is fixed and has higher cost, and the algorithm cannot resist known cipher analysis means such as plaintext attack and the like. The method focuses on improvement of the Hill password, but the Hill password belongs to classical passwords and is weak in safety. Meanwhile, the method still has the dummy problem, and although relevant researches solve the dummy problem, the safety of the Hill password is not substantially improved.
Disclosure of Invention
In order to solve the above problems, an object of the present invention is to provide an RSA-Hill hybrid encryption method based on plaintext random partitioning.
In order to achieve the above purpose, the RSA-Hill mixed encryption method based on plaintext random partitioning provided by the present invention comprises the following steps in sequence:
step 1) plaintext submitting stage: a user submits a plaintext to be encrypted, letters in the plaintext are converted into numbers according to a character table, and the number of characters in the digital plaintext is counted;
step 2) generating a plaintext random division number: determining the number k of plaintext random division numbers according to the counted number n of digital plaintext characters, and generating a group of plaintext random division numbers n according to the number k1，n2，…，nk；
Step 3) judging whether the plaintext random division number meets the conditions: judging the generated group of plaintext random division number n1，n2，…，nkWhether a condition is satisfied; if it is
Figure BDA0001269640200000021
If the conditions are met, entering the next step; otherwise, returning to the step 2) to regenerate a group of plaintext random division numbers;
step 4) implementing the plaintext segmentation: according to the generated group of plaintext random division numbers n1，n2，…，nkRandomly dividing the digital plaintext in the step 1) into k blocks, wherein the number of the divided digital plaintext characters in each block is ni，i＝1,2,…,k；
Step 5) generating a Pascal matrix stage: firstly, defining the order numbers 1,2, …, k of a Pascal matrix, then selecting a Pascal formula with different orders by a user according to needs, and finally generating the Pascal matrix;
step 6) plaintext encryption: carrying out encryption operation on the segmented digital plaintext obtained in the step 4) and the Pascal matrix with the corresponding order in the step 5) by adopting a Hill encryption algorithm to obtain an encrypted ciphertext column vector, and then converting the encrypted ciphertext column vector into a ciphertext row vector by transposition;
step 7) random number encryption stage: encrypting the plaintext random division number by using an RSA password to obtain an encrypted plaintext random division number, and finally combining the encrypted plaintext random division number and the encrypted ciphertext vector in the step 6) into a final ciphertext vector.
In step 2), there are two methods for determining the number k of plaintext random partitions: the first method is to manually set the numerical value of the fixed number k; the second method is to determine the numerical value of the number k according to the number of plaintext characters; selecting a second method for a smaller plaintext; whereas for larger plaintext the first method is chosen.
In step 5), the specific method for generating the Pascal matrix is as follows:
the method comprises the following steps: randomly dividing the number n according to the set of plaintext1，n2，…，nkDetermining the order of a Pascal matrix required by encryption; if a plaintext is randomly divided into niIf i is 1,2, …, k, the order of the Pascal matrix required to encrypt it is also ni；
Step two: determining an order using the Pascal formula; if the plaintext is randomly divided by niThe larger the size, the higher order Pascal formula is used, so that the Pascal matrix with the required order can be generated more quickly; and if the plaintext is randomly divided by the number niIf smaller, a lower-order Pascal formula is used;
step three: if a high-order Pascal formula is selected, the data of the first rows of the Pascal matrix are required to be generated line by line as the basis for generating the complete Pascal matrix, and then the complete Pascal matrix is generated according to the high-order Pascal formula.
The RSA-Hill mixed encryption method based on plaintext random division provided by the invention is characterized in that a generated Pascal matrix is used for replacing a secret key of a Hill password, a session secret key in a mixed encryption algorithm is transferred into a random division number of the plaintext, and then the RSA password is used for encrypting the secret key. It can be observed from simulation experiments that the method provided by the invention meets the requirements for constructing a hybrid encryption method by randomly segmenting the plaintext, avoids the occurrence of the dummy problem, and realizes the encryption process of one-time pad, so that the method has better encryption efficiency and stronger attack resistance.
Drawings
FIG. 1 is a flow chart of an RSA-Hill hybrid encryption method based on plaintext random partitioning according to the present invention;
FIG. 2 is a flow chart of a classical Hill encryption algorithm;
FIG. 3 is a graph comparing the time consumption for encrypting files of different sizes by different encryption algorithms.
Detailed Description
The following describes in detail the RSA-Hill hybrid encryption method based on plaintext random partition according to the present invention with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the RSA-Hill hybrid encryption method based on plaintext random partition provided by the present invention includes the following steps in sequence:
step 1) plaintext submitting stage: a user submits a plaintext to be encrypted, letters in the plaintext are converted into numbers according to a character table, and the number of characters in the digital plaintext is counted; for example: the letter Apple in the plain text is converted into numbers of 36,25,25,21 and 14, and the number of characters is 5;
step 2) generating a plaintext random division number: determining the number k of plaintext random division numbers according to the counted number n of digital plaintext characters, and generating a group of plaintext random division numbers n according to the number k1，n2，…，nk；
Step 3) judging whether the plaintext random division number meets the conditions: judging the generated group of plaintext random division number n1，n2，…，nkWhether a condition is satisfied; if it is
Figure BDA0001269640200000051
If the conditions are met, entering the next step; otherwise, returning to the step 2) to regenerate a group of plaintext random division numbers;
step 4) implementing the plaintext segmentation: according to the generated group of plaintext random division numbers n1，n2，…，nkRandomly dividing the digital plaintext in the step 1) into k blocks, wherein the number of the divided digital plaintext characters in each block is niI ═ 1,2, …, k; the plaintext is segmented according to the generated plaintext random segmentation number, so that the dummy problem can be effectively avoided; the dummy is caused by that the Hill password divides the plaintext with fixed length; when the plaintext length is not integral multiple of the order of the encryption matrix, the complete plaintext matrix can be combined only by supplementing the dummy; but problems withRegular division of plaintext in Hill ciphers has not been resistant to cryptanalysis measures such as known plaintext attacks. The invention ensures that the plaintext segmentation has no regularity, thereby ensuring the safety of a cryptosystem.
Step 5) generating a Pascal matrix stage: firstly, defining the order numbers 1,2, …, k of a Pascal matrix, then selecting a Pascal formula with different orders by a user according to needs, and finally generating the Pascal matrix;
step 6) plaintext encryption: carrying out encryption operation on the segmented digital plaintext obtained in the step 4) and the Pascal matrix with the corresponding order in the step 5) by adopting a Hill encryption algorithm to obtain an encrypted ciphertext column vector, and then converting the encrypted ciphertext column vector into a ciphertext row vector by transposition; because the Hill encryption algorithm is a matrix operation, the calculated result is a ciphertext column vector;
step 7) random number encryption stage: encrypting the plaintext random division number by using an RSA password to obtain an encrypted plaintext random division number, and finally combining the encrypted plaintext random division number and the encrypted ciphertext vector in the step 6) into a final ciphertext vector. Because of the plaintext random number n of divisions1，n2，…，nkIs key to decryption, so that the encryption and transmission of the key are fully guaranteed. The RSA cipher is a public key cipher system with high safety, and the encryption of the RSA cipher can ensure the safe transmission of the encrypted plaintext random division number in the channel.
In step 2), there are two methods for determining the number k of plaintext random partitions: the first method is to manually set the numerical value of the fixed number k; the second method is to determine the value of the number k from the number of plaintext characters, such as: k is n1/2. Selecting a second method for a smaller plaintext; whereas for larger plaintext the first method is chosen.
In step 5), the method for generating the Pascal matrix comprises the following steps:
step 5.1) defining the order of the Pascal matrix
The first step of the combined meaning proof of the Pascal formula and the general formula derived from the combined meaning is to arbitrarily take i (1 ≦ i ≦ k) elements in the set S, so the number of elements selected in the set S is not used to divide the order of the Pascal formula.
(1)
Figure BDA0001269640200000061
Defining the formula as 0-order Pascal formula;
(2)
Figure BDA0001269640200000062
defining the formula as a 1 st order Pascal formula;
(3)
Figure BDA0001269640200000063
defining the formula as a 2-step Pascal formula;
……
(4)
Figure BDA0001269640200000064
it is defined as a Pascal formula of order i.
Step 5.2) proof of the order i Pascal formula
Selecting i (1 ≦ i ≦ k) elements (x) in the set S1,x2,…,xi) Set division of k-combinations of set S into 2iAnd (4) collecting the seeds. By 1 representing xiIn the set S, x is represented by 0iNot in the set S. The division of the set S is therefore:
(1) (0,0, …,0) Note that none of the i elements are in the k-combination of set S, with
Figure BDA0001269640200000071
Indicating the size of the set S.
(2) (0, …,0,1,0,0, …,0) states that only one of the i elements is in the k-combination of the set S, and that this element is selected from
Figure BDA0001269640200000072
Is possible, so can use
Figure BDA0001269640200000073
Indicating the size of the set S.
(3) (1,0,0, …,0,1,1,0, …,0) indicates that j of the i elements are in the k-combination of the set S, and that this element is selected from
Figure BDA0001269640200000074
Is possible, so can use
Figure BDA0001269640200000075
Indicating the size of the set S.
(4) (1,1,1, …,1) indicates that i elements are all in the k-combination of the set S, and that this element is selected from
Figure BDA0001269640200000076
Possibly, can use
Figure BDA0001269640200000077
Indicating the size of the set S.
In summary, according to the double counting principle:
Figure BDA0001269640200000078
step 5.3) generating a Pascal matrix
The specific method comprises the following steps:
the method comprises the following steps: randomly dividing the number n according to the set of plaintext1，n2，…，nkDetermining the order of a Pascal matrix required by encryption; if a plaintext is randomly divided into niIf i is 1,2, …, k, the order of the Pascal matrix required to encrypt it is also ni；
Step two: determining an order using the Pascal formula; if the plaintext is randomly divided by niThe larger the size, the higher order Pascal formula is used, so that the Pascal matrix with the required order can be generated more quickly; and if the plaintext is randomly divided by the number niIf smaller, a lower-order Pascal formula is used;
step three: if a high-order Pascal formula is selected, the data of the first rows of the Pascal matrix are required to be generated line by line as the basis for generating the complete Pascal matrix, and then the complete Pascal matrix is generated according to the high-order Pascal formula.
(1) The scales of n in the Pascal formulas from 1 order to 2 order, 3 order, … order and i order are sequentially reduced, when a larger-order Pascal matrix needs to be generated, a relatively high-order Pascal formula can be utilized, so that the complexity of operation can be reduced;
(2) by applying the i-order Pascal formula when generating the Pascal matrix, the limitation of the number of rows can be eliminated. Namely: the data of the ith row of the Pascal matrix can be generated by depending on the data of the ith row which is not less than 1 and less than j. Therefore, the algorithm is more flexible and is suitable for more complex operating environment;
(3) when the i-order Pascal formula is used, due to the limitation of the value range of the formula, the previous i-row data must be given as the basis for generating the Pascal matrix with the required order.
In addition, the keys in the Hill encryption algorithm are randomly selected, but the keys are selected such that the encryption matrix is non-degenerate and the determinant is ± 1, the key space is:
Ai＝{Ai×i|i∈Z+,|Ai×i|＝±1}
key space AiThe encryption matrix is ensured to be reversible, and elements in the inverse matrix are all integers, so that a correct plaintext can be obtained when a decryption algorithm is carried out. And the value space of the Pascal matrix is:
Pi＝{Pi×i|i∈Z+}
namely:
Figure BDA0001269640200000081
the key space is reduced, and the Pascal matrix cannot be used as the key of the Hill password. However, in the RSA-Hill mixed encryption method, the key is not a Pascal matrix but a plaintext random division number, so that the Pascal matrix is used to replace the key of the Hill cipher, which has the advantage of avoiding a large amount of complex operations when generating the encryption matrix.
The real secret key in the RSA-Hill mixed encryption method based on plaintext random division provided by the invention is a plaintext random division number. Let n be the plaintext length, and the key space K be:
Figure BDA0001269640200000082
when the key space is K, the pseudo-random number generator can efficiently generate a random key for each encryption. The invention establishes a one-time pad hybrid cryptosystem based on a secret key space K.
FIG. 3 is a simulation of the method of the present invention. In the experiment, the encryption time consumption of plaintexts with different sizes is compared with the DES algorithm, the AES algorithm and the DES-RSA mixed encryption algorithm. As can be seen from FIG. 3, when the size of the plaintext is not larger than 3M, the encryption time consumption of the method of the invention is not much different from that of the DES algorithm and the DES-RSA hybrid encryption algorithm; when the size of the plaintext is larger than 4M, the encryption time of the method is larger than that of a DES algorithm and an AES algorithm, but is basically equivalent to that of a DES-RSA mixed encryption algorithm. The reason is that for large files, the order of the Pascal matrix required by the encryption of the method is higher, and the time consumption of matrix operation is correspondingly longer. The method of the present invention is suitable for encrypting less than 4M of plaintext.
Table 1 is a table of characters used in the method of the present invention;
table 2 shows the time taken to generate k Pascal matrices of different plaintext sizes in the method of the present invention.
TABLE 1
Figure BDA0001269640200000091
TABLE 2
Figure BDA0001269640200000092
Figure BDA0001269640200000101
As can be seen from comparison between fig. 1 and fig. 2, when the computer runs the method of the present invention, it is no longer necessary to generate a random matrix with a determinant of ± 1, and only a series of plaintext random division numbers need to be generated.

Claims (3)

1. A plaintext random segmentation based RSA-Hill mixed encryption method is characterized in that: the RSA-Hill mixed encryption method based on plaintext random segmentation comprises the following steps in sequence:
step 1) plaintext submitting stage: a user submits a plaintext to be encrypted, letters in the plaintext are converted into numbers according to a character table, and the number of characters in the digital plaintext is counted;
step 2) generating a plaintext random division number: determining the number k of plaintext random division numbers according to the counted number n of digital plaintext characters, and generating a group of plaintext random division numbers n according to the number k1，n2，…，nk；
Step 3) judging whether the plaintext random division number meets the conditions: judging the generated group of plaintext random division number n1，n2，…，nkWhether a condition is satisfied; if it is
Figure FDA0002244382750000011
If the conditions are met, entering the next step; otherwise, returning to the step 2) to regenerate a group of plaintext random division numbers;
step 4) implementing the plaintext segmentation: according to the generated group of plaintext random division numbers n1，n2，…，nkRandomly dividing the digital plaintext in the step 1) into k blocks, wherein the number of the divided digital plaintext characters of each block is equal to n in sequencei，i＝1,2,…,k；
Step 5) generating a Pascal matrix stage: firstly, defining the order numbers 1,2, …, k of a Pascal matrix, then selecting a Pascal formula with different orders by a user according to needs, and finally generating the Pascal matrix;
step 6) plaintext encryption: carrying out encryption operation on the segmented digital plaintext obtained in the step 4) and the Pascal matrix with the corresponding order in the step 5) by adopting a Hill encryption algorithm to obtain an encrypted ciphertext column vector, and then converting the encrypted ciphertext column vector into a ciphertext row vector by transposition;
step 7) random number encryption stage: encrypting the plaintext random division number by using an RSA password to obtain an encrypted plaintext random division number, and finally combining the encrypted plaintext random division number and the encrypted ciphertext vector in the step 6) into a final ciphertext vector.
2. The RSA-Hill hybrid encryption method based on plaintext random partitioning according to claim 1, wherein: in step 2), there are two methods for determining the number k of plaintext random partitions: the first method is to manually set the numerical value of the fixed number k; the second method is to determine the numerical value of the number k according to the number of plaintext characters; selecting a second method for a smaller plaintext; whereas for larger plaintext the first method is chosen.
3. The RSA-Hill hybrid encryption method based on plaintext random partitioning according to claim 1, wherein: in step 5), the specific method for generating the Pascal matrix is as follows:
the method comprises the following steps: randomly dividing the number n according to the set of plaintext1，n2，…，nkDetermining the order of a Pascal matrix required by encryption; if a plaintext is randomly divided into niIf i is 1,2, …, k, the order of the Pascal matrix required to encrypt it is also ni；
Step two: determining an order using the Pascal formula; if the plaintext is randomly divided by niThe larger the size, the higher order Pascal formula is used, so that the Pascal matrix with the required order can be generated more quickly; and if the plaintext is randomly divided by the number niIf smaller, a lower-order Pascal formula is used;
step three: if a high-order Pascal formula is selected, the data of the first rows of the Pascal matrix are required to be generated line by line and used as the basis for generating the complete Pascal matrix, and then the complete Pascal matrix is generated according to the high-order Pascal formula.
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