CN116846558A - Data encryption method, system, electronic equipment and medium based on RSA algorithm - Google Patents

Abstract

This application discloses a data encryption method, system, electronic device and medium based on the RSA algorithm. The technical field to which it belongs is data security technology. The data encryption method based on the RSA algorithm includes: if a data encryption request is received, determining the target data corresponding to the data encryption request, and obtaining the modulus n of the RSA algorithm from a third-party platform; determining whether the modulus n is There are only 2 prime factors greater than 1 and less than n; among them, the 2 prime factors include prime factor p and prime factor q; if the modulus n has only 2 prime factors greater than 1 and less than n, then determine Whether the numerical similarity between the prime factor p and the prime factor q meets the preset requirements; if it meets the preset requirements, use the modulus n to perform a data encryption operation based on the RSA algorithm on the target data. This application can reduce the complexity of detecting the security of modulus n and improve the execution efficiency of using RSA algorithm to encrypt data.

Description

Data encryption method, system, electronic equipment and media based on RSA algorithm

Technical field

This application relates to the field of data security technology, and in particular to a data encryption method, system, electronic equipment and media based on the RSA algorithm.

Background technique

The RSA algorithm was proposed by Ron Rivest, Adi Shamir, and Leonard Adleman. According to number theory, it is relatively simple to find two large prime numbers, but it is extremely difficult to factor their product, so the product can be disclosed as an encryption key. The RSA algorithm system is constructed based on Euler's theorem of number theory, and its security relies on the difficulty of factorizing large numbers. The biggest threats facing RSA mainly come from the continuous improvement of computing power and the continuous improvement of factorization algorithms. In order to improve the security of the RSA algorithm, it is necessary to ensure that the selected modulus n is the product of secure prime numbers p and q of specified sizes. In related technologies, the Camenisch–Michels protocol is usually used to detect the security of the modulus n, but the pseudo- Primeness testing requires many calculation operations, high computational overhead, and low execution efficiency.

Therefore, how to reduce the complexity of detecting the security of modulus n and improve the execution efficiency of encrypting data using the RSA algorithm is a technical problem that those skilled in the art currently need to solve.

Contents of the invention

The purpose of this application is to provide a data encryption method, system, electronic equipment and media based on the RSA algorithm, which is used to solve the technology of how to reduce the complexity of detecting the security of modulus n and improve the execution efficiency of using the RSA algorithm to encrypt data. question.

In order to solve the above technical problems, this application provides a data encryption method based on the RSA algorithm. The data encryption method based on the RSA algorithm includes:

If a data encryption request is received, the target data corresponding to the data encryption request is determined, and the modulus n of the RSA algorithm is obtained from the third-party platform;

Determine whether the modulus n has only two prime factors greater than 1 and less than n; wherein, the two prime factors include prime factor p and prime factor q;

If there are only two prime factors greater than 1 and less than n in the modulus n, determine whether the numerical similarity between the prime factor p and the prime factor q meets the preset requirements;

If the preset requirements are met, the modulus n is used to perform a data encryption operation based on the RSA algorithm on the target data.

Optionally, determine whether the modulus n has only two prime factors greater than 1 and less than n, including:

Select m random values ρ _i from the target set;

Determine whether the random value ρ _i is the quadratic remainder of the modulus n; if so, add the square root of the random value ρ _i to the verifier set; if not, add 0 to the verifier set ;

Determine whether the number of non-zero elements in the verifier set is greater than a preset number, and obtain the first judgment result;

Determine whether the modulus n is a positive odd number and not a prime number or a prime power, and obtain a second judgment result;

If the first judgment result and the second judgment result are both yes, it is determined that the modulus n has only two prime factors greater than 1 and less than n;

If the first judgment result and the second judgment result are not both yes, it is judged that the modulus n does not meet the safety requirements.

Optionally, add the square root of the random value ρ _i to the verifier set, including:

A square root is randomly selected from all square roots of the random value ρ _i and added to the verifier set.

Optionally, before selecting m random values ρ _i from the target set, it also includes:

Calculate the value of m according to the statistical safety parameter κ; where,

Correspondingly, before judging whether the number of non-zero elements in the verifier set is greater than the preset number, it also includes:

Set the preset number to 3m/8.

Optionally, determine whether the numerical similarity between the prime factor p and the prime factor q meets preset requirements, including:

Determine whether the digit difference or numerical difference between the prime factor p and the prime factor q is less than a preset value;

If so, it is determined that the numerical similarity between the prime factor p and the prime factor q meets the preset requirements;

If not, it is determined that the numerical similarity between the prime factor p and the prime factor q does not meet the preset requirements.

Optionally, determine whether the numerical similarity between the prime factor p and the prime factor q meets the preset requirements, including:

The GPS signature algorithm is used to determine whether the numerical similarity between the prime factor p and the prime factor q meets the preset requirements.

Optional, also includes:

If the prime factor p and the prime factor q do not exist in the modulus n, or the numerical similarity between the prime factor p and the prime factor q does not meet the preset requirements, then it is determined that the modulus n Does not meet security requirements.

This application also provides a data encryption system based on the RSA algorithm, which includes:

A modulus acquisition module, used to determine the target data corresponding to the data encryption request if a data encryption request is received, and obtain the modulus n of the RSA algorithm from a third-party platform;

A quantity judgment module, used to judge whether the modulus n has only two prime factors greater than 1 and less than n; wherein the two prime factors include the prime factor p and the prime factor q;

A similarity judgment module, used to judge whether the numerical similarity between the prime factor p and the prime factor q meets the preset requirements if there are only two prime factors greater than 1 and less than n in the modulus n;

An encryption module, configured to use the modulus n to perform a data encryption operation based on the RSA algorithm on the target data if the numerical similarity meets the preset requirements.

This application also provides a storage medium on which a computer program is stored. When the computer program is executed, the steps of performing the above data encryption method based on the RSA algorithm are implemented.

This application also provides an electronic device, including a memory and a processor. A computer program is stored in the memory. When the processor calls the computer program in the memory, it implements the steps of performing the above-mentioned RSA algorithm-based data encryption method. .

This application provides a data encryption method based on the RSA algorithm, which includes: if a data encryption request is received, determining the target data corresponding to the data encryption request, and obtaining the modulus n of the RSA algorithm from a third-party platform; judging the Whether the modulus n has only 2 prime factors greater than 1 and less than n; among them, the 2 prime factors include prime factor p and prime factor q; if the modulus n has only 2 prime factors greater than 1 and less than n factor, then determine whether the numerical similarity between the prime factor p and the prime factor q meets the preset requirements; if it meets the preset requirements, use the modulus n to perform data encryption based on the RSA algorithm on the target data. operate.

After receiving the data encryption request, this application obtains the modulus n of the RSA algorithm from the third-party platform, and determines whether the modulus n has only two prime factors that comply with the rules of 1<p<n and 1<q<n. If there are only 2 prime factors greater than 1 and less than n in the modulus n, continue to determine whether the numerical similarity of the prime factor p and the prime factor q meets the preset requirements. If the numerical similarity meets the preset requirements, use the module Number n performs a data encryption operation based on the RSA algorithm on the target data. This application detects the security of the modulus n from the two dimensions of the number of prime factors of the modulus n and the numerical similarity of the prime factors, and can efficiently and low-costly avoid the security problems that may be caused by n provided by a third party. Therefore, this application can reduce the complexity of detecting the security of modulus n and improve the execution efficiency of using RSA algorithm to encrypt data. This application also provides a data encryption system based on the RSA algorithm, a storage medium and an electronic device, which have the above beneficial effects and will not be described again here.

Description of the drawings

In order to explain the embodiments of the present application more clearly, the drawings required to be used in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, As far as workers are concerned, other drawings can also be obtained based on these drawings without exerting creative work.

Figure 1 is a flow chart of a data encryption method based on the RSA algorithm provided by an embodiment of the present application;

Figure 2 is a schematic structural diagram of a data encryption system based on the RSA algorithm provided by an embodiment of the present application.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments These are part of the embodiments of this application, but not all of them. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of this application.

Please refer to Figure 1 below. Figure 1 is a flow chart of a data encryption method based on the RSA algorithm provided by an embodiment of the present application.

Specific steps may include:

S101: If a data encryption request is received, determine the target data corresponding to the data encryption request, and obtain the modulus n of the RSA algorithm from the third-party platform;

Among them, this embodiment can be applied to electronic devices with the function of using the RSA algorithm to encrypt data. After receiving the data encryption request, the target data corresponding to the data encryption request can be determined, and the data encrypted using the RSA algorithm can also be obtained from a third-party platform. The required modulus n.

S102: Determine whether the modulus n has only two prime factors greater than 1 and less than n; if so, enter S103; if not, end the process;

Among them, the purpose of this step is to determine whether the modulus n provided by the third-party platform has only two prime factors greater than 1 and less than n. The above two prime factors include the prime factor p and the prime factor q. If the modulus n does not satisfy the condition that there are only two prime factors greater than 1 and less than n, then the modulus n is judged to be unsafe.

S103: If there are only two prime factors greater than 1 and less than n in the modulus n, determine whether the numerical similarity between the prime factor p and the prime factor q meets the preset requirements;

Among them, this step is based on the fact that the modulus n has only two prime factors p and q that are greater than 1 and less than n. At this time, the similarity of the prime factors p and q can be judged. This step can determine whether the numerical similarity between the prime factor p and the prime factor q meets the preset requirements; specifically, it can be determined whether the digit difference or the numerical difference between the prime factor p and the prime factor q is less than Preset numerical value; if yes, it is determined that the numerical similarity between the prime factor p and the prime factor q meets the preset requirements; if not, it is determined that the numerical similarity between the prime factor p and the prime factor q does not meet the preset requirements Default requirements.

S104: If the preset requirements are met, use the modulus n to perform a data encryption operation based on the RSA algorithm on the target data.

If the numerical similarity between the prime factor p and the prime factor q meets the preset requirements, the modulus n can be used to perform a data encryption operation based on the RSA algorithm on the target data to obtain ciphertext data.

This embodiment obtains the modulus n of the RSA algorithm from the third-party platform after receiving the data encryption request, and determines whether the modulus n has only two prime factors that conform to the rules of 1<p<n and 1<q<n. If there are only 2 prime factors greater than 1 and less than n in the modulus n, continue to determine whether the numerical similarity of the prime factor p and the prime factor q meets the preset requirements. If the numerical similarity meets the preset requirements, use the module Number n performs a data encryption operation based on the RSA algorithm on the target data. This embodiment detects the security of the modulus n from the two dimensions of the number of prime factors of the modulus n and the numerical similarity of the prime factors. It can efficiently and low-costly avoid the security problems that may be caused by n provided by a third party. . Therefore, this embodiment can reduce the complexity of detecting the security of modulus n and improve the execution efficiency of encrypting data using the RSA algorithm.

As a feasible implementation, this embodiment can determine the number of prime factors of modulus n in the following manner: select m random values ρ _i from the target set; determine whether the random value ρ _i is the modulus The quadratic remainder of n; if yes, add the square root of the random value ρ _i to the verifier set; if not, add 0 to the verifier set; determine the number of non-zero elements in the verifier set Whether it is greater than the preset number, the first judgment result is obtained; it is judged whether the modulus n is a positive odd number, and the modulus n is not a prime number or a power of a prime number, the second judgment result is obtained; if the first judgment result and the third If the two judgment results are both yes, then it is judged that the modulus n has only 2 prime factors greater than 1 and less than n; if the first judgment result and the second judgment result are not both yes, then it is judged that the Modulo n does not meet security requirements. Specifically, if the modulus n is a positive odd number and the modulus n is not a prime number or a prime power, then the second judgment result is yes; if the modulus n is not a positive odd number, or the modulus n is a prime number or a prime power, then the second judgment result is yes. 2. The judgment result is no. The above target set is a subset of the set that satisfies the Jacobian symbol of 1.

In the above process, a random value ρ _i can have multiple square roots, so a square root can be randomly selected from all the square roots of the random value ρ _i and added to the verifier set.

Furthermore, before selecting m random values ρ _i from the target set, the value of m can also be calculated based on the statistical security parameter κ; where, Correspondingly, before judging whether the number of non-zero elements in the verifier set is greater than the preset number, the preset number can also be set to 3m/8 (that is, 0.375 _m ). Statistical security parameters refer to constraining the probability of an attacker deviating from the protocol (without being discovered) during online interactions.

As a feasible implementation, the numerical similarity of the prime factor p and the prime factor q can be determined in the following way: using the GPS (Girault-Poupard-Stern) signature algorithm to determine the numerical similarity of the prime factor p and the prime factor q. Whether the similarity meets the preset requirements. The GPS signature algorithm is an existing algorithm in this field. For details on the implementation process, see the paper On theFly Authentication and Signature Schemes Based on Groups of Unknown Order.

As a feasible implementation, if the prime factor p and the prime factor q do not exist in the modulus n, or the numerical similarity between the prime factor p and the prime factor q does not meet the preset requirements , then it is determined that the modulus n does not meet the safety requirements. If the modulus n does not meet the security requirements, the above data encryption request can be rejected and no encryption operation is performed on the target data.

The processes described in the above embodiments are described below through examples in practical applications.

In related technologies, the Camenisch–Michels protocol is usually used to detect the security of modulus n. However, the pseudoprimality test in the above method requires many calculation operations, has high computational overhead, and has low execution efficiency, and the core of the Camenisch–Michels protocol It is a pseudo-primality proof, which is combined with zero-knowledge proofs such as discrete logarithms and composite numbers. It involves many and complex operations and communications and is not easy to understand. The implementation and security analysis of the protocol are difficult. Therefore, the above related technologies have high computational overhead, low efficiency, and are not easy to implement and analyze.

This embodiment provides a method for proving the security of RSA modulus n. This method generates parameters p, q and n based on the Joy08 protocol, where p and q are not controlled by human intervention, realizing the cryptographic security of p, q and n. , verify the RSA modulus n through the GRSB modulus test algorithm to detect whether it has exactly one pair of p and q values, and use the GPS signature algorithm to verify whether the prime factors p and q are similar in size. The technical solution of the present invention can efficiently and at low cost avoid the security problems that may be caused by n provided by a third party. The Joy08 protocol is a common protocol in this field for generating RSA algorithm parameters p, q and n. Its specific implementation process can be found in the paper RSA Moduli with a Predetermined Portion: Techniques and Applications.

This example uses the following symbols:

(a)a|b means a and b are connected in series, where a and b are bit strings.

(b) Indicates the space size of c, that is, the minimum number of bits required to write c, where c is an integer.

(c) Express/> A string of all zeros.

(d)[A] represents the set {0,1,...,A-1}, Represents a set of natural numbers.

(e) Represents uniform random sampling from X, where X is a finite set.

As a feasible implementation, the safe generation method of p, q and n is as follows:

Using the Joy08 protocol, generate a pair of prime numbers (p, q), the bit string of whose product n = pq has a known fixed pattern π (such as the string FFF....FFF), so that (p, q) is not controlled , and then achieve the cryptographic security of n. The central idea is as follows:

① Form a string x:=π|ρ, where ρ is a random bit string.

② Generate a prime number p, and

③Increase q until it is a prime number.

The Joy08 protocol can achieve bit strings of length s Part of the fixed pattern string N _H =π:

Given lengths s, s ₀ , κ, the bit string length of prime number p |p| ₂ =ss ₀ , the bit string length of prime number q |q| ₂ =s ₀ , fixed pattern bit string N _H (length is κ, is the high-order part of n-bit string form).

The bit string N _L (is the low-order part of the n-bit string form), RSA modulus n (the bit string length of n |n| ₂ = s): |n| ₂ =|pq| ₂ =|N _H |N _L | ₂ .

① Randomly select an integer p ₀ , bit string length |p ₀ | ₂ = ss ₀ , definition:

② Use a recursive method to define the triplet (d _i , u _i , vi ₎ , d _i represents the first auxiliary generation parameter, u _i represents the second auxiliary generation parameter, _vi represents the third auxiliary generation parameter, i=0, 1,2…;

(d ₀ ,u ₀ ,v ₀ )=(p ₀ ,0,1)

(d _-1 ,u _-1 ,v _-1 )=(q ₀ ,1,0)

③Use a recursive method to define the triplet (x _i , y _i , z _i ), _xi represents the first generation parameter, _yi represents the second generation parameter, z _i represents the third generation parameter, i=0,1,2 ...;

(x ₀ ,y ₀ ,z ₀ )=(0,0,[N _H 2 ^s-κ mod p ₀ ]+2 ^s-κ-1 );

If the triplet (x _i ,y _i ,z _i ) satisfies |z _i -x _i y _i |<2 ^s-κ-1 , then add it to the list If it is not satisfied, jump out of the recursive definition and terminate the loop.

④From list Find a (x _i ,y _i ,z _i ) that satisfies the following conditions:

p＝p ₀ + _xi

q＝q ₀ +y _i

Make p and q both prime numbers. If the search fails, return to step ① and start again.

⑤Output n=(p ₀ +x _i )(q ₀ +y _i ), N _L =nmod2 ^s-κ . In order to make smooth numbers related to prime factors p and q of n (such as p-1, q+1, etc.) rarer, it is preferable to select a modulus n that is 62% larger than the preset normal value. n can achieve higher security by satisfying additional short redundancy (such as: SHA(n)mod2 ²⁴ =0), but it requires greater resource overhead.

As a feasible implementation method, the process of verifying that n has exactly two prime factors p and q is as follows:

This embodiment uses the Goldberg-Rey Zin-Sagga-Baldimtsi (GRSB) modulus test to verify that n has exactly two prime factors. GRSB is an existing prime factor verification method in this field. The specific implementation process can be found in the paper EfficientNoninteractive Certification of RSA Moduli and Beyond.

(a) Define the following symbols:

①J _n represents the set that satisfies the Jacobian symbol of 1 a subset of .

②QR _n represents the subset composed of the quadratic remainder of module n in J _n .

③κ is a statistical safety parameter.

(b)GRSB modulus test protocol:

①The prover P and the verifier V both let

②The verifier V selects m random values ρ _i ∈J _n and sends them to P to wait for proof.

③The prover P checks whether each ρ _i is a quadratic remainder modulo n (that is, whether it belongs to QR _n and satisfies ρ _i ² modn=ρ _i ), if it belongs to QR _n , the prover P returns the square root of ρ _i σ _i to V, otherwise P returns σ _i =0 to V (P is randomly selected among the four square roots of ρ _i one).

④Verifier V verifies whether n is a positive odd number and not a prime number or a prime power, otherwise the protocol fails.

⑤The verifier checks whether there are at least 3m/8 non-zero σ _i , and each non-zero σ _i satisfies σ _i ² =ρ _i modn. If so, n has exactly two prime factors, otherwise the protocol fails.

As a feasible implementation method, the process of verifying that the prime factors p and q are similar in size is as follows:

This embodiment uses the Girault-Poupard-Stern (GPS) signature algorithm to verify that the prime factors p and q are similar in size.

The GPS algorithm consists of four parts: setting, key generation, signature, and verification:

(a)GPS.Setup(λ)—→pp:

Set the protocol public parameters (the public parameters, pp):

①Set integers A, B, S.

②Hash function h:{0,1}*-→[B].

to achieve security level λ. Among them, the security level λ is a measurement of the security strength that an encryption primitive (such as a ciphertext or a hash function) can achieve, and its unit is usually bit.

(b)GPS.Keygen(pp)—→(sk,pk)：

The signer chooses two safe prime numbers p, q, n=pq. Select element The order satisfying g can be divisible by pq (if and only if gcd(g-1,n)=gcd(g+1,n)=1),/> Indicates that g belongs to a group. Signer's private key Public key pk:=g ^s .

(c)GPS.Sign(pp,sk,msg)-→σ：

①

②x＝g ^r modn;

③c=h(msg,x);

④y＝r+c·sk;

⑤ If y ≥ A, use the new r value to return to step ① and start again.

Where msg is plain text information, generating signature σ = (x, c, y).

(d)GPS.Verify(pp,pk,msg,σ)-→{valid,invalid}, valid means the verification result is valid, invalid means the verification result is invalid:

Validator V checks the following scopes:

x>0 and x∈[n]and c∈[B]and y∈[A+(B-1)(S-1)];

If any of the above range of check items fails, the signature is invalid, otherwise the verifier V continues to calculate:

Represents the hash output result of (msg,x),/> and x represents the public key. if/> and/> Then σ is valid, otherwise it is invalid.

This embodiment uses the Joy08 protocol, the GRSB modulus test algorithm, and the GPS signature algorithm to realize the cryptographic security of the RSA modulus n, and realize the modulus n-digit string with low overhead. Parts are fixed to specified pattern strings to prevent third-party human intervention, with fewer calculation operations, low calculation costs, and high execution efficiency. The communication complexity of the protocol in this embodiment is lower than that of the Camenisch-Michels protocol, which is simpler and easier to understand. The implementation and security analysis of the protocol are relatively easy.

This embodiment is based on the Joy08 protocol, the GRSB modulus test algorithm, and the GPS signature algorithm. It constructs a corresponding technical solution for the issue of how to prove the security of the RSA modulus n, and provides a simpler and more efficient RSA module based on number theory knowledge. The number-n security proof method allows the prover and verifier to implement the verification function with fewer operations and communications. This embodiment provides security proof for RSA modulus n, and can be applied to RSA encrypted communication and other aspects.

Please refer to Figure 2. Figure 2 is a schematic structural diagram of a data encryption system based on the RSA algorithm provided by an embodiment of the present application. The system may include:

The modulus acquisition module 201 is used to determine the target data corresponding to the data encryption request if a data encryption request is received, and obtain the modulus n of the RSA algorithm from the third-party platform;

The quantity judgment module 202 is used to judge whether the modulus n has only two prime factors greater than 1 and less than n; wherein the two prime factors include the prime factor p and the prime factor q;

The similarity judgment module 203 is used to judge whether the numerical similarity between the prime factor p and the prime factor q meets the preset requirements if there are only two prime factors greater than 1 and less than n in the modulus n;

The encryption module 204 is configured to use the modulus n to perform a data encryption operation based on the RSA algorithm on the target data if the numerical similarity meets the preset requirements.

This embodiment obtains the modulus n of the RSA algorithm from the third-party platform after receiving the data encryption request, and determines whether the modulus n has only two prime factors that conform to the rules of 1<p<n and 1<q<n. If there are only 2 prime factors greater than 1 and less than n in the modulus n, continue to determine whether the numerical similarity of the prime factor p and the prime factor q meets the preset requirements. If the numerical similarity meets the preset requirements, use the module Number n performs a data encryption operation based on the RSA algorithm on the target data. This embodiment detects the security of the modulus n from the two dimensions of the number of prime factors of the modulus n and the numerical similarity of the prime factors. It can efficiently and low-costly avoid the security problems that may be caused by n provided by a third party. . Therefore, this embodiment can reduce the complexity of detecting the security of modulus n and improve the execution efficiency of encrypting data using the RSA algorithm.

Further, the process of the quantity judgment module 202 judging whether the modulus n has only 2 prime factors greater than 1 and less than n includes: selecting m random values ρ _i from the target set; judging whether the random value ρ _i is the quadratic remainder of the modulus n; if yes, add the square root of the random value ρ _i to the verifier set; if not, add 0 to the verifier set; determine whether Whether the number of non-zero elements is greater than the preset number, the first judgment result is obtained; whether the modulus n is a positive odd number and not a prime number or a power of a prime number, the second judgment result is obtained; if the first judgment result and If the second judgment results are all yes, then it is judged that the modulus n has only 2 prime factors greater than 1 and less than n; if the first judgment result and the second judgment result are not both yes, then It is determined that the modulus n does not meet the safety requirements.

Further, the process of the quantity judgment module 202 adding the square root of the random value ρ _i to the verifier set includes: randomly selecting one square root from all the square roots of the random value ρ _i and adding it to the verifier set.

Further, before selecting m random values ρ _i from the target set, the quantity judgment module 202 is also used to calculate the value of m according to the statistical security parameter κ; where,

Correspondingly, before judging whether the number of non-zero elements in the verifier set is greater than the preset number, the number judgment module 202 is also used to set the preset number to 3m/8.

Further, the process of determining whether the numerical similarity between the prime factor p and the prime factor q meets the preset requirements by the similarity judgment module 203 includes: judging the digit difference between the prime factor p and the prime factor q or Whether the numerical difference is less than the preset value; if so, determine that the numerical similarity of the prime factor p and the prime factor q meets the preset requirements; if not, determine the numerical similarity of the prime factor p and the prime factor q The similarity does not meet the preset requirements.

Further, the process of the similarity judgment module 203 judging whether the numerical similarity of the prime factor p and the prime factor q meets the preset requirements includes: using the GPS signature algorithm to judge the numerical similarity of the prime factor p and the prime factor q. Whether the numerical similarity meets the preset requirements.

Furthermore, it also includes:

An error reporting module is used to determine if the prime factor p and the prime factor q do not exist in the modulus n, or the numerical similarity between the prime factor p and the prime factor q does not meet the preset requirements. The modulus n does not meet security requirements.

Since the embodiments of the system part correspond to the embodiments of the method part, please refer to the description of the embodiments of the method part for the embodiments of the system part, and will not be described again here.

This application also provides a storage medium on which a computer program is stored. When the computer program is executed, the steps provided in the above embodiments can be implemented. The storage medium may include: U disk, mobile hard disk, read-only memory (ROM), random access memory (Random Access Memory, RAM), magnetic disk or optical disk and other various media that can store program code.

This application also provides an electronic device, which may include a memory and a processor. A computer program is stored in the memory. When the processor calls the computer program in the memory, the steps provided in the above embodiments can be implemented. Of course, the electronic device may also include various network interfaces, power supplies and other components.

Each embodiment in the specification is described in a progressive manner. Each embodiment focuses on its differences from other embodiments. The same and similar parts between the various embodiments can be referred to each other. As for the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple. For relevant details, please refer to the description in the method section. It should be noted that for those of ordinary skill in the art, several improvements and modifications can be made to the present application without departing from the principles of the present application, and these improvements and modifications also fall within the protection scope of the claims of the present application.

It should also be noted that in this specification, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that these entities or operations There is no such actual relationship or sequence between operations. Furthermore, the terms "comprises," "comprises," or any other variation thereof are intended to cover a non-exclusive inclusion such that a process, method, article, or apparatus that includes a list of elements includes not only those elements, but also those not expressly listed other elements, or elements inherent to the process, method, article or equipment. Without further limitation, an element defined by the statement "comprises a..." does not exclude the presence of additional identical elements in a process, method, article, or device that includes the stated element.

Claims (10)

1. A data encryption method based on RSA algorithm, comprising:

if a data encryption request is received, determining target data corresponding to the data encryption request, and acquiring a modulus n of an RSA algorithm from a third-party platform;

judging whether the modulus n only has 2 quality factors which are more than 1 and less than n; wherein the 2 plasma factors include a plasma factor p and a plasma factor q;

if the modulus n only has 2 quality factors which are more than 1 and less than n, judging whether the numerical similarity of the quality factor p and the quality factor q meets the preset requirement;

and if the data meets the preset requirement, executing data encryption operation based on RSA algorithm on the target data by using the modulus n.

2. The RSA algorithm-based data encryption method according to claim 1, wherein determining whether the modulus n has only 2 prime factors greater than 1 and less than n comprises:

selecting m random values ρ from a target set _i ；

Judging the random value rho _i Whether the modulus n is twice the remainder; if yes, the random value rho is obtained _i Adding the square root of (2) to the verifier set; if not, adding 0 to the verifier set;

judging whether the number of non-zero elements in the verifier set is larger than a preset number or not to obtain a first judgment result;

judging whether the modulus n is positive odd number and is not prime number or prime power to obtain a second judging result;

if the first judging result and the second judging result are both yes, judging that the modulus n only has 2 quality factors which are more than 1 and less than n;

and if the first judging result and the second judging result are not equal, judging that the modulus n does not meet the safety requirement.

3. The RSA algorithm-based data encryption method according to claim 2, wherein the random value ρ is _i Adding to the verifier set a square root of (c) comprising:

from the random value ρ _i Randomly selected one of the square roots of (a) is added to the verifier set.

4. The method for encrypting data based on RSA algorithm according to claim 2, wherein m random values ρ are selected from the target set _i Before, still include:

calculating the value of m according to the statistical safety parameter kappa; wherein,

correspondingly, before judging whether the number of non-zero elements in the verifier set is greater than a preset number, the method further comprises:

the preset number is set to 3m/8.

5. The RSA algorithm-based data encryption method according to claim 1, wherein determining whether the numerical similarity of the quality factor p and the quality factor q meets a preset requirement comprises:

judging whether the digit difference or the numerical value difference between the quality factor p and the quality factor q is smaller than a preset numerical value;

if yes, judging that the numerical similarity of the quality factor p and the quality factor q meets the preset requirement;

if not, judging that the numerical similarity of the quality factor p and the quality factor q does not meet the preset requirement.

6. The RSA algorithm-based data encryption method according to claim 1, wherein determining whether the numerical similarity of the quality factor p and the quality factor q meets a preset requirement comprises:

and judging whether the numerical similarity of the quality factor p and the quality factor q meets the preset requirement or not by using a GPS signature algorithm.

7. The RSA algorithm-based data encryption method according to any one of claims 1 to 6, further comprising:

and if the modulus n does not have the quality factor p and the quality factor q, or the numerical similarity of the quality factor p and the quality factor q does not meet the preset requirement, judging that the modulus n does not meet the safety requirement.

8. A data encryption system based on RSA algorithm, comprising:

the module acquisition module is used for determining target data corresponding to the data encryption request if the data encryption request is received, and acquiring a module n of an RSA algorithm from a third-party platform;

the quantity judging module is used for judging whether the modulus n only has 2 quality factors which are more than 1 and less than n; wherein the 2 plasma factors include a plasma factor p and a plasma factor q;

the similarity judging module is used for judging whether the numerical similarity of the quality factor p and the quality factor q meets the preset requirement if the modulus n only has 2 quality factors which are more than 1 and less than n;

and the encryption module is used for executing data encryption operation based on RSA algorithm on the target data by utilizing the modulus n if the numerical similarity meets the preset requirement.

9. An electronic device comprising a memory and a processor, the memory having stored therein a computer program, the processor implementing the steps of the RSA algorithm-based data encryption method according to any one of claims 1 to 7 when the computer program in the memory is invoked by the processor.

10. A storage medium having stored therein computer executable instructions which when loaded and executed by a processor implement the steps of the RSA algorithm-based data encryption method according to any one of claims 1 to 7.