CN114710273A - Secret key generating method for communication system - Google Patents

Abstract

The invention provides a key generation method of a communication system, which comprises four stages, wherein the first stage is a system initial stage, the second stage is a registration stage, the third stage is a verification stage, and the fourth stage is a key exchange stage. It is further proposed a key generation apparatus of a hardened communication system, the key generation apparatus comprising: a memory for storing computer-executed instructions; a processor for executing computer instructions stored in the memory to carry out the functional steps of the method as described above. By adopting the technical scheme of the invention, the safety between transmissions of the military communication system can be thoroughly solved, the local pretended identity is prevented from acquiring related information or being stolen during transmission, the communication efficiency can be improved, and the calculated amount is reduced.

Description

Secret key generating method for communication system

Technical Field

The present application relates to the field of network communication technologies, and in particular, to a method for generating a secret key of a communication system.

Background

The electronic communication combat capability of the military is continuously improved year by year in recent years, all system constructions are developed towards the direction of comprehensive communication combat, the importance of the military in all communication transmission is examined, a safer data exchange mechanism is required to be built under the existing communication system architecture, and the basic safety requirement is improved.

For the key exchange mechanism, there have been many international documents providing different design architectures, but the requirement of the military communication system for emphasizing the special customization of multiple security certificates cannot be met. In view of the above situation, a key mechanism for enhancing military communication system is based on military communication, and utilizes the characteristics of short encryption key, fast processing speed, etc. of random packet cryptosystem and elliptic curve cryptosystem to design a key switch mechanism meeting the basic requirements for enhancing identity authentication security, so as to achieve the following advantages.

1. In order to make the data transmission process have a non-repudiation mechanism, an identity authentication mechanism is built in the system, so that the dependence on a third-party authentication center can be reduced, and registered users in the system can perform mutual identity authentication by utilizing public parameters in an off-line manner.

2. When both communication parties transmit information in an open environment, data can be transmitted in a ciphertext mode, and human tampering and stealing are prevented. A secret key mechanism of a reinforced military communication system utilizes a communication secret key exchange mechanism of a random knapsack cryptosystem, thereby improving the complexity and the cracking difficulty of the secret key and reinforcing the integrity and the safety of data transmission.

The method has the advantages that the elliptic curve cryptosystem is used, the characteristics of short secret key length and low calculation complexity are achieved, and compared with other asymmetric second-time algorithms, the method has the characteristics of higher safety and high running speed in the same secret key length, the benefit of personnel identity is improved, and the integrity and non-repudiation of data of both communication parties are strengthened.

Disclosure of Invention

The invention discloses a secret key generation method of a communication system, which belongs to a secret key generation mechanism of a reinforced communication system, and is based on an elliptic curve cryptosystem and a random backpack cryptosystem and combined with reinforced identity authentication, namely a secret key exchange transmission mechanism.

According to an aspect of the present invention, there is provided a key generation method of a communication system, the method comprising:

the first stage is the initial stage of the system:

setting various initial conditions of an AS (application server) of a data management certificate center, and selecting a safe elliptic curve in a limited domain;

the second stage is a registration stage:

each user sends its own identity information and private key (id)_A,d_A) Handling registration id using secure means or in person to data management credential center (AS)_ASignature, id of_AFor user U_AIdentity information of d_AIs a private key;

data management credential center AS receives U_ASelecting a private key d according to the system_AData management credential center AS calculates U using knapsack cryptosystem_APublic key E_A；

AS authentication U_AAnd id_ACorrectness of the relationship between;

the third stage is a verification stage:

user U_AAnd U_BMutually verifying identity information and a timestamp of the other party;

the fourth stage is a key exchange stage:

the users UA and UB calculate their communication keys SKA and SKB and exchange them with each other.

According to an aspect of the present invention, the method for generating a secret key of an enhanced communication system includes:

selecting a prime number q greater than 3;

selecting two positive integers a, b smaller than q, satisfying that y is x³+ ax + b (modq), where mod is the remainder of q by b, where x is greater than or equal to 0 and less than or equal to q;

let P be a point on the elliptic curve E and P be a point on the order α, where α is 4P₁·p₂+1，p1＝2p₃+1、p₂＝2p₄+1, wherein p₁、p₂、p₃、p₄Are all large prime numbers; and p is₁、p₂、p₃、p₄Discarded after the calculation;

data management credential center AS computes public key Q_ASThen Q is_AS＝s_ASP, wherein s_ASIs a private key.

According to an aspect of the present invention, the key generation method of the enhanced communication system specifically includes, in the registration stage:

data management credential center AS receives U_ASelecting private key d according to system_ACalculating U by using knapsack password system_APublic key (E)_A)；

1) Firstly, randomly selecting n-dimensional vector d_AAnd d is_AiAre all positive integers, and are not limited to the integer,

d_A＝(d_A1,…,d_Ai,…,d_An)、d_A1＝max(d_Ai)；

2) then randomly selecting two prime numbers y_AAnd m_A，∑_Ai＝1 ⁿd_Ai<m_A<2d_A1

3) Computing vector J_A＝(j_A1,…,j_Ai,…,j_An) Wherein j is_Ai≡y_A*d_Ai(mod m_A)、Ai＝1,…,n；

4) Will j_AiAsymmetric grouping is carried out, and the left part and the right part are distinguished at the h-th position from left to right to form p_AiAnd z_Ai；

5) Selecting a positive integer t_ASatisfy (p)_A+t_A+*z_Ai)<2^h-1, i.e. represents p_AiNo carry;

6) let u_Ai＝p_Ai+t_A*z_Ai、Ai＝1,…,n；

7) Randomly selecting two prime numbers r_AAnd f_ASatisfy r_A>∑_Ai＝1 ⁿ u_Ai，f_A>∑_Ai＝1 ⁿ z_AiAnd calculating a formula by using a residue theorem:

EID(id_A)＝E_A＝(e_A1,e_A2,…,e_An) Wherein 0 is not more than e_Ai≤r_Af_A–1；

y_Ai≡u_Ai(mod r_A)、y_Ai≡z_Ai(mod f_A) Wherein A is_i＝1,…,n；

8) Secret key r_A，f_A，t_A，y_A ^-1，m_AWherein y is_A ^-1Is y_AModulo element of (D), and publish E_A。

AS authentication U_AAnd id_AThe correctness of the relation between the u and the u is calculated_Ai，p_Ai，j_Ai，d_Ai；

1)u_Ai＝c(mod r_A)、z_Ai＝c(mod f_A)；

2)p_Ai＝u_Ai–t_A·z_Ai；

3)j_Ai＝p_Ai·2^n-h+z_Ai；

4)d_Ai＝y_A ^-1·j_Ai(mod m_A)；

5) Using an initial superseding sequence s_ASAnd calculating and solving a plaintext x.

According to an aspect of the present invention, in the key generation method of the communication system, the verification stage specifically includes:

first, U_ASelecting a random binary vector X_A＝(X_A1||…||X_Ai) And a random number b_AAnd a time stamp t_AAs a corresponding parameter, we can calculate the registration certificate Y_A，T_AObtaining U_ASignature S of_A；

1)Y_A＝id_A·d_AP; p is a random prime number;

2)T_A＝(∑_j＝1 ^l x_Ai·h_Bj)·p，h_Bjis U_BA verification value of (a);

U_Ausing time stamps t_AAnd U_BIdentity information id_BExecution of operation f (Y) of the compact function_A||t_A||T_A||id_B) Calculating S_A＝G_A+f(Y_A||t_A||T_A||id_B)·(∑_j＝1 ^l x_Ai·h_Bj) P, wherein G_AIs a base point with the order of alpha on the elliptic curve, and p is a random prime number;

finally, U_ASending (id)_A||Y_A||t_A||S_A||T_A) To U_B；

Same, U_BSelecting a random binary vector X_B＝(X_B1||…||X_Bi) Time stamp t_BAs a corresponding parameter, the public key is then derived from Y_B、T_BObtaining a signature S_BThe following were used:

1)Y_B＝id_B·d_B·p；

2)T_B＝(∑_j＝1 ^l x_Bi·h_Aj)·p，h_Ajis U_AA verification value of (a);

3)S_B＝G_B+f(Y_B||t_B||T_B||id_A)·(∑_j＝1 ^l x_Bi·h_Aj) P, wherein G_BIs a base point with the order of alpha on the elliptic curve, and p is a random prime number;

information (id)_B||Y_B||t_B||S_B||T_B) Is sent to U in the same way_A。

According to an aspect of the present invention, in the key generation method of the enhanced communication system, the key exchange stage specifically includes:

before generating session key, U_AAnd U_BAuthentication is required (id)_A||Y_A||t_A||S_A||T_A) And (id)_B||Y_B||t_B||S_B||T_B)，U_ATo U_BSending (id)_A||Y_A||t_A||S_A||T_A)，U_BTo U_ASending (id)_B||Y_B||t_B||S_B||T_B)；

Verification was performed as follows:

1)S_B+Y_B+id_B·Q_AS≡f(Y_B||t_B||T_B||id_A)·T_B；

2)S_A+Y_A+id_A·Q_AS≡f(Y_A||t_A||T_A||id_B)·T_A；

thus U is_AAnd U_BComputing their communication key SK_AAnd SK_BThe formula is as follows:

3)SK_A＝(∑_j＝1 ^l x_Ai·h_Bj)·T_B；

4)SK_B＝(∑_j＝1 ^l x_Bi·h_Aj)·T_A；

and SK is demonstrated in the following equation_AAnd SK_BAre the same:

SKA＝SKB＝∑j＝1l xAi·hBj)·(∑j＝1l xBi·hAj)·P；

is UA and UB verify that SKB and SKA received from shared key are equal, respectively? If the two values are equal, the verification is successful, and if the two values are not equal, the current communication connection is abandoned.

According to another aspect of the present invention, there is also provided a key generation apparatus of a communication system, the key generation apparatus including: a memory for storing computer-executed instructions; a processor for executing computer instructions stored in the memory to carry out the functional steps of the method as described above.

By adopting the technical scheme of the invention, the safety between transmissions of the military communication system can be thoroughly solved, the local pretended identity is prevented from acquiring related information or being stolen during transmission, the communication efficiency can be improved, and the calculated amount is reduced.

Drawings

Fig. 1 is a schematic diagram of a key exchange protocol provided in an embodiment of the present application;

fig. 2 is a schematic diagram illustrating a registration phase of a key generation method according to an embodiment of the present disclosure;

fig. 3 is a schematic diagram illustrating a verification phase of a key generation method according to an embodiment of the present disclosure;

fig. 4 is a diagram illustrating an example of a communication key exchange phase of a key generation method according to an embodiment of the present application;

fig. 5 is a schematic diagram of a key exchange protocol flow provided in an embodiment of the present application.

Fig. 6 is a block diagram of a key generation apparatus according to an embodiment of the present application.

Detailed Description

In the solutions provided in the embodiments of the present application, the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.

In order to better understand the technical solutions, the technical solutions of the present application are described in detail below with reference to the drawings and specific embodiments, and it should be understood that the specific features in the embodiments and examples of the present application are detailed descriptions of the technical solutions of the present application, and are not limitations of the technical solutions of the present application, and the technical features in the embodiments and examples of the present application may be combined with each other without conflict.

The symbols used in this application and their physical meanings are shown in table 1.

TABLE 1

Sequence of	(symbol)	Description of the invention
			1	AS	Data management center
2	UA、UB	User A and user B
			3	E(Fq)	Elliptic curve
4	α	Order on elliptic curve (order)
			5	G	Order on the elliptic curve isBase point of alpha
6	QAS	Data management credential center (AS) public key
			7	SAS	Data management credential center (AS) private key
8	idA、idB	UA、UBIdentity information id of
			9	mA,yA,rA,fA	UARandom parameter of
10	mB,yB,rB,fB	UBRandom parameter of
			11	EA、EB	UA、UBPublic key
12	hA、hB	UA、UBVerification value
			13	SKB、SKA	UAAnd UBShared secret key
14	h>>n-h	h number of bits is greater than n-h number of bits

Elliptic curve cryptography is an open encryption algorithm based on elliptic curve mathematics. Elliptic curve cryptography requires substantially fewer system parameters and key lengths than other public key encryption methods. There are many slight differences in form, but all rely on the widely recognized difficulty of having to solve elliptic curve dispersion versus mathematical problems, corresponding to a finite field elliptic curve group, which is prior art.

General formula y for elliptic curves²+a xy+by＝x³+cx²+ dx + e, where a, b, c, d, e are prime numbers. In elliptic curves, the dot addition operation is particularly defined if q is a prime number greater than 3, as in Galois Field E (G)_q) Wherein x is an x-axis coordinate, y is a y-axis coordinate, and the formula of the elliptic curve is as follows:

y²＝x³+ ax + b (mod q), where x is greater than or equal to 0 and less than or equal to q, a, b are positive integers less than q and 4a³+27b²mod q is not equal to 0. In addition, an infinite origin O is also defined, and if a straight line intersects the elliptic curve at three points, the sum of the three points is an infinite point O. Suppose two points A (x)₁,y₁) And B (x)₂,y₂) In elliptic curve group E (F)_q) The dot addition operation is as follows:

A+O＝O+A＝A

if x₁＝x₂,y₁＝-y₂,A＝(x₁,y₁),B＝(x₂,y₂)＝(x₁–y₁) When the sum of A + B is O

If A is not equal to B, then A + B ═ x₃,y₃). Wherein (x)₃,y₃) The calculation is as follows:

x₃is constantly equal to lambda²-x₁–x₂(mod q)

y is always equal to λ (x)₁–x₃)–y₁(mod q)

The key exchange protocol was first proposed in 1976 by Diffie and Hellman, two scholars of public key cryptography. Through the key exchange protocol, the two parties can safely negotiate the conversation key, the privacy of the communication information at this time is ensured, and the safety property of the conversation key is based on the discrete pair mathematic problem. The algorithm is illustrated as follows: a

First, two public parameters are set, assuming a large prime number p and g is the original root of the modulus p, two parties of communication establish a session key.

A randomly selecting prime number X, and calculating X ═ g^xmod p, then send to B.

B randomly selecting prime number Y, and calculating Y ═ g^ymod p, then send to A.

(II) A receives y sent by B, and calculates the key of conversation by using the selected prime number y

K_xy＝(Y)^xmod p＝(g^y)^xmod p＝g ^xymod p

After both parties finish the key agreement, the same conversation key K is obtained without knowing the prime number selected by the other party.

Even if an attacker steals X and Y, it is not feasible for the attacker to compute the session key K because of the split log-split problem (X and Y cannot be derived from X and Y), and the key exchange protocol flow chart is shown in fig. 5.

The random knapsack system cryptosystem means that given a natural number sequence B ═ B, …, B, …, B) and a number S, it has been proved that an NP-Complete problem can not be solved in polynomial time, but the problem of unpacking the knapsack in many specific number sequences is simple, so most of them are not NP-Complete problem, and we are called easy-to-solve knapsack number sequences.

Therefore, the scholars in the following propose a new knapsack cryptosystem, and firstly, the random cryptosystem proposed by the scholars applies addition and modular subtraction to solve the problem of the super-increment series, so as to resist the tool for directly solving the knapsack problem under the condition that the attacker can not master the private key, for example, means such as low-density attack and the like, and applies a technology instead of confusion to reduce the redundancy of the system.

The calculation method is as follows:

key generation phase

1. Randomly selecting n-dimensional vector B ═ (B)₁,…,b_i,…,b_n) Wherein b is max (b)_i)、b_iAre all positive integers and must not be repeated.

2. Randomly selecting two prime numbers m and w, wherein sigmaⁿ _i＝1b<m<2b₁。

3. Calculating vector D ═ D₁,…,d_i,…,d_n) Wherein d is_i＝w·b_i(mod m)、i＝1,…,n。

4. Will d_iPerforming an asymmetric grouping, dividing the j-th bit into left and right parts from left to right to form e_iAnd v_iRespectively having j bits and n-j bits, and j>>n–j,d＝e+v。

5. Selecting a positive integer t satisfying (e)_i+t·v_i)<2^j1, i.e. meaning e has no carry, let u_i＝e_i+t·v_i、i＝1,…,n。

6. Randomly selecting two prime numbers p and q to satisfy p>∑ⁿ _i＝1u_i，q>∑ⁿ _i＝1v_iUsing the remainder theorem formula:

(1)A＝(a₁,a₂,…,a_n) Wherein 0 is not less than a_i≤(p·q-1)。

(2)a_i＝u_i(mod p)＝v_i(mod q), where i ═ 1.

(3) Privacy is p, q, t, w^-1M, wherein w^-1Is the negation element of w.

(II) encryption phase

1. Converting information x into binary n carry (x) ═ x₁,x₂,…,x_n,x_i∈(0,1)。

2. General information (x)₂＝x₁,x₂,…,x_nWith public key a ═ a₁,a₂,…,a_n) And (5) encrypting.

3.c＝a₁x₁+a₂x₂+…+a_nx_n。

(III) decryption stage

1. Calculate u ═ c (mod p), v ═ c (mod q).

2. And e-u-t.v is calculated.

3. Calculating d as e.2^n-j+v。

4. Calculating y as w^-1·d(mod m)。

5. And (5) calculating and solving the plaintext x by using the initial super-increment sequence B.

Fig. 1 shows a key mechanism of a hardened communication system according to the present invention. The method comprises the following four stages, wherein the first stage is a system initial stage, the second stage is a registration stage, the third stage is a verification stage, the fourth stage is a key exchange stage, and the symbol table is shown in table 1.

Stage 1, system initialization. Firstly, setting each initial condition of AS of data management certificate center, selecting a safe elliptic curve E (F) in a limited domain_q) The method comprises the following steps:

1.a prime number q greater than 3 is selected.

2. Selecting two positive integers a, b smaller than q, satisfying that y is x³+ ax + b (mod q), where mod is the remainder of q by b. Wherein x is 0 or more and q or less.

3. Let P be a point on the elliptic curve E and P be a point on the order α, where α is 4P₁·p₂+1, where p1 ═ 2p₃+1、p₂＝2p₄+1, wherein p₁、p₂、p₃、p₄Are all large prime numbers.

4.p₁、p₂、p₃、p₄And discarded after the calculation.

5. Data management credential center AS computes public key Q_ASThen Q is_AS＝s_ASP wherein s_ASIs a private key.

Stage 2, registration stage

The registration phase is shown in FIG. 2, with each user (U)_A) The identity information and the private key (id) of the user are combined_A,d_A) Handling registration id using secure means or in person to data management credential center (AS)_AAnd each user (U)_A) The public key of the data management certificate center AS is known, and only the data management certificate center AS knows the corresponding private key.

Data management credential center AS computing user (U)_A) Private key program, as shown in FIG. 2 (user U)_BThe same applies to the method).

1. Data management credential center AS receives U_ASelecting a private key d according to the system_AAnd will (id)_A,d_A) Transmitting to data management certificate center AS, which calculates U by using knapsack password system_APublic key (E)_A)。

1) First randomly selecting n-dimensional vectors, and d_AiAre all positive integers.

d_A＝(d_A1,…,d_Ai,…,d_An)、d_A1＝max(d_Ai)

2) Then randomly selecting two prime numbers y_AAnd m_A，∑_Ai＝1 ⁿd_Ai<m_A<2d_A1

3) Computing a vector where j_Ai≡y_A*d_Ai(mod m_A) 1, …, n and J_A＝(j_A1,…,j_Ai,…,j_An)

4) Will j_AiAsymmetric grouping is carried out, and the left part and the right part are distinguished at the h-th position from left to right to form p_AiAnd z_Ai。

5) Selecting a positive integer t_ASatisfy (p)_A+t_A+*z_Ai)<2^h-1, i.e. represents p_AiThere is no carry.

6) Let u_Ai＝p_Ai+t_A*z_Ai、Ai＝1,…,n

7) Randomly selecting two prime numbers r_AAnd f_ASatisfy r_A>∑_Ai＝1 ⁿ u_Ai，f_A>∑_Ai＝1 ⁿ z_AiAnd calculating a formula by using a residue theorem:

EID(id_A)＝E_A＝(e_A1,e_A2,…,e_An) Wherein 0 is not more than e_Ai≤r_Af_A–1

y_Ai≡u_Ai(modr_A)、y_Ai≡z_Ai(mod f_A) Wherein A is_i＝1,…,n

8) Secret key r_A，f_A，t_A，y_A ^-1，m_AWherein y is_A ^-1Is y_AModulo element of (D), and publish E_A。

AS authentication U_AAnd id_AThe correctness of the relation between the u and the u is calculated_Ai，p_Ai，j_Ai，k_Ai

1)u_Ai＝c(mod r_A)、z_Ai＝c(mod f_A)

2)p_Ai＝u_Ai–t_A·z_Ai

3)j_Ai＝p_Ai·2^n-h+z_Ai

4)k_Ai＝y_A ^-1·j_Ai(mod m_A)

5) Using an initial superseding sequence s_ASAnd calculating and solving a plaintext x.

Stage 3, verification stage

Suppose U_AAnd U_BSecret communication needs to be established, as shown in fig. 3:

1. first, U_ASelecting a random binary vector X_A＝(X_A1||…||X_Ai) And a random number b_AAnd a time stamp t_AAs corresponding parameters. We can compute the registration certificate Y_A，T_AObtaining U_ASignature S of_A。

5)Y_A＝id_A·d_A·p

6)T_A＝(∑_j＝1 ^l x_Ai·h_Bj)·p

2.U_AUsing time stamps t_AAnd U_BIdentity information id_BOperation f (Y) of the executed compact function_A||t_A||T_A||id_B) Calculating S_A＝G_A+f(Y_A||t_A||T_A||id_B)·(∑_j＝1 ^l x_Ai·h_Bj)·p

3. Finally, U_ASending (id)_A||Y_A||t_A||S_A||T_A) To U_B。

4. Same, U_BSelecting a random binary vector X_B＝(X_B1||…||X_Bi) Time stamp t_BAs corresponding parameters. Then the public key is changed from Y_B、T_BObtaining a signature S_BThe following were used:

1)Y_B＝id_B·d_B·p

2)T_B＝(∑_j＝1 ^l x_Bi·h_Aj)·p

3)S_B＝G_B+f(Y_B||t_B||T_B||id_A)·(∑_j＝1 ^l x_Bi·h_Aj)·p

5. thus, the information (id)_B||Y_B||t_B||S_B||T_B) And sent to U in the same manner_A。

Phase 4, communication key exchange phase

Before generating session key, U_AAnd U_BRequires authentication (id)_A||Y_A||t_A||S_A||T_A) And (id)_B||Y_B||t_B||S_B||T_B) Are respectively driven from U_AAnd U_BAnd (5) sending. The verification equation is shown in FIG. 3

1. First, the following formula is used for verification:

1)S_B+Y_B+id_B·Q_AS≡f(Y_B||t_B||T_B||id_A)·T_B

2)S_A+Y_A+id_A·Q_AS≡f(Y_A||t_A||T_A||id_B)·T

2. thus U is_AAnd U_BCalculate their communication key SK_AAnd SK_B. The formula is as follows:

5)SK_A＝(∑_j＝1 ^l x_Ai·h_Bj)·T_B

6)SK_B＝(∑_j＝1 ^l x_Bi·h_Aj)·T_A

3. and SK is demonstrated in the following equation_AAnd SK_BAre the same:

SK_A＝SK_B＝∑_j＝1 ^l x_Ai·h_Bj)·(∑_j＝1 ^l x_Bi·h_Aj)·P

U_Aterminal and U_BThe terminals respectively verify the received shared secret key SK_BAnd SK_AIs it equal? If the two are equal, the verification is successful, and if the two are not equal, the current communication connection is abandoned.

Referring to fig. 6, an embodiment of the present application provides a key generation apparatus, including:

a memory 301 for storing instructions for execution by at least one processor;

the processor 302 is configured to execute the instructions stored in the memory to perform the above-mentioned method steps proposed by the present invention.

Further, an embodiment of the present application provides a computer-readable storage medium, which stores computer instructions, and when the computer instructions are executed on a computer, the computer instructions cause the computer to perform the above-mentioned method steps proposed by the present invention.

As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.

Claims (7)

1.A method for key generation in a communication system, comprising:

the first stage is the initial stage of the system:

setting various initial conditions of an AS (application server) of a data management certificate center, and selecting a safe elliptic curve in a limited domain;

the second stage is a registration stage:

each user sends its own identity information and private key (id)_A,d_A) Handling registration id using secure means or in person to data management credential center (AS)_ASignature, id of_AFor the user U_AIdentity information of d_AIs a private key;

data management credential center AS receives U_ASelecting a private key d according to the system_AData management credential center AS calculates U using knapsack cryptosystem_APublic key E_A；

AS authentication U_AAnd id_ACorrectness of the relationship between;

the third stage is a verification stage:

user U_AAnd U_BMutually verifying identity information and a timestamp of the other party;

the fourth stage is a key exchange stage:

user U_AAnd U_BCalculate their communication key SK_AAnd SK_BAnd are interchanged with each other.

2.A key generation method of a communication system according to claim 1, characterized by:

the initial stage of the system specifically comprises:

selecting a prime number q greater than 3;

selecting two positive integers a, b smaller than q, satisfying that y is x³+ ax + b (mod q), where mod is the remainder of q by b, where x is greater than or equal to 0 and less than or equal to q;

let P be a point on the elliptic curve E and P be a point on the order α, where α is 4P₁·p₂+1，p1＝2p₃+1、p₂＝2p₄+1, wherein p₁、p₂、p₃、p₄Are all large prime numbers; and p is₁、p₂、p₃、p₄Discarded after the calculation is finished;

data management credential center AS computes public key Q_ASThen Q is_AS＝s_ASP, wherein s_ASIs a private key.

3. The key generation method of a communication system according to claim 2, characterized in that:

the registration stage specifically includes:

data management credential center AS receives U_ASelecting a private key d according to the system_ACalculating U by using knapsack password system_APublic key (E)_A)；

1) Firstly, randomly selecting n-dimensional vector d_AAnd d is d_AiAre all positive integers, and are not limited to the integer,

d_A＝(d_A1,…,d_Ai,…,d_An)、d_A1＝max(d_Ai)；

2) then randomly selecting two prime numbers y_AAnd m_A，∑_Ai＝1 ⁿd_Ai<m_A<2d_A1

3) Calculating vector J_A＝(j_A1,…,j_Ai,…,j_An) Wherein j is_Ai≡y_A*d_Ai(mod m_A)、Ai＝1,…,n；

4) Will j_AiPerforming asymmetric grouping, and distinguishing left and right parts at h-th position from left to right to form p_AiAnd z_Ai；

5) Selecting a positive integer t_ASatisfy (p)_A+t_A+*z_Ai)<2^h-1, i.e. represents p_AiNo carry;

6) let u_Ai＝p_Ai+t_A*z_Ai、Ai＝1,…,n；

7) Randomly selecting two prime numbers r_AAnd f_ASatisfy r_A>∑_Ai＝1 ⁿu_Ai，f_A>∑_Ai＝1 ⁿz_AiAnd calculating a formula by using a residue theorem:

EID(id_A)＝E_A＝(e_A1,e_A2,…,e_An) Wherein 0 is not more than e_Ai≤r_Af_A–1；

y_Ai≡u_Ai(mod r_A)、y_Ai≡z_Ai(mod f_A) Wherein A is_i＝1,…,n；

8) Secret key r_A，f_A，t_A，y_A ^-1，m_AWherein y is_A ^-1Is y_AModulo element of (D), and publish E_A。

AS authentication U_AAnd id_AThe correctness of the relation between the u and the u is calculated_Ai，p_Ai，j_Ai，d_Ai；

1)u_Ai＝c(mod r_A)、z_Ai＝c(mod f_A)；

2)p_Ai＝u_Ai–t_A·z_Ai；

3)j_Ai＝p_Ai·2^n-h+z_Ai；

4)d_Ai＝y_A ^-1·j_Ai(mod m_A)；

5) Using an initial superseding sequence s_ASAnd calculating and solving a plaintext x.

4. A key generation method of a communication system according to claim 3, characterized by:

the verification stage specifically comprises:

first, U_ASelecting a random binary vector X_A＝(X_A1||…||X_Ai) And a random number b_AAnd a time stamp t_AAs a corresponding parameter, we can compute the registration credential Y_A，T_AObtaining U_ASignature S of_A；

1)Y_A＝id_A·d_AP; p is a random prime number;

2)T_A＝(∑_j＝1 ^lx_Ai·h_Bj)·p，h_Bjis U_BA verification value of (a);

U_Ausing a time stamp t_AAnd U_BIdentity information id_BExecution of operation f (Y) of the compact function_A||t_A||T_A||id_B) Calculating S_A＝G_A+f(Y_A||t_A||T_A||id_B)·(∑_j＝1 ^lx_Ai·h_Bj) P, wherein G_AIs a base point with the order of alpha on the elliptic curve, and p is a random prime number;

finally, U_ASending (id)_A||Y_A||t_A||S_A||T_A) To U_B；

Same, U_BSelecting a random binary vector X_B＝(X_B1||…||X_Bi) Time stamp t_BAs a corresponding parameter, the public key is then derived from Y_B、T_BObtaining a signature S_BThe following were used:

1)Y_B＝id_B·d_B·p；

2)T_B＝(∑_j＝1 ^lx_Bi·h_Aj)·p，h_Ajis U_AA verification value of (a);

3)S_B＝G_B+f(Y_B||t_B||T_B||id_A)·(∑_j＝1 ^lx_Bi·h_Aj) P, wherein G_BIs on an elliptic curveA base point with an order of alpha, and p is a random prime number;

information (id)_B||Y_B||t_B||S_B||T_B) Is sent to U in the same way_A。

5. The key generation method of a communication system according to claim 4, wherein:

the key exchange phase specifically comprises:

before generating session key, U_AAnd U_BRequires authentication (id)_A||Y_A||t_A||S_A||T_A) And (id)_B||Y_B||t_B||S_B||T_B)，U_ATo U_BSending (id)_A||Y_A||t_A||S_A||T_A)，U_BTo U_ASending (id)_B||Y_B||t_B||S_B||T_B)；

Verification was performed as follows:

1)S_B+Y_B+id_B·Q_AS≡f(Y_B||t_B||T_B||id_A)·T_B；

2)S_A+Y_A+id_A·Q_AS≡f(Y_A||t_A||T_A||id_B)·T_A；

thus U is_AAnd U_BCalculate their communication key SK_AAnd SK_BThe formula is as follows:

1)SK_A＝(∑_j＝1 ^lx_Ai·h_Bj)·T_B；

2)SK_B＝(∑_j＝1 ^lx_Bi·h_Aj)·T_A；

and SK is demonstrated in the following equation_AAnd SK_BAre the same:

SK_A＝SK_B＝∑_j＝1 ^lx_Ai·h_Bj)·(∑_j＝1 ^lx_Bi·h_Aj)·P

U_Aterminal and U_BThe terminals respectively verify the received shared secret key SK_BAnd SK_AIs it equal? If the two are equal, the verification is successful, and if the two are not equal, the current communication connection is abandoned.

6. A key generation apparatus of a communication system, characterized by:

the key generation apparatus includes:

a memory for storing computer-executed instructions;

a processor for executing computer instructions stored in the memory to perform the method steps of any of claims 1-5.

7. A computer-readable storage medium characterized by:

the computer-readable storage medium stores computer instructions which, when executed on a computer, cause the computer to perform the method steps of any of claims 1-5.

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