TWI408938B - Flexible multi - digit signature method - Google Patents

Abstract

A multiple digital signature method with flexibility is applied to a network system with a system center and many user devices, and includes the following steps: performing a system key generation procedure to generate a number of system public keys, performing a first multiple digital signature generation procedure for obtaining a first multiple digital signature; performing a signature validation procedure to confirm whether the multiple digital signature is a legal signature; and performing a multiple digital signature generation procedure to produce a multiple digital signature; then, the multiple digital signature sends to the next user device issuing the signature request and repeatedly performing the signature validation procedure until all the user devices issuing signature requests generate corresponding multiple digital signatures.

Description

Flexible multi-digit signature method

The invention relates to a digital signature method, in particular to a multi-digit signature method with elastic and dynamic adjustment order.

In the era of developed Internet technology, the use of the network to transmit documents to be signed is widely used by enterprises, and a document to be signed may often require multiple members to sign together. Therefore, the technology of multiple digital signatures has been developed for application. herein.

The way of signing through digital signatures is indeed an effective and economical way to provide considerable convenience and save on paper costs, but in order to save money, for a confidential document to be signed, network transmission always exists. Risks, therefore, as in the Republic of China Patent Bulletin No. 424371, the relevant research results or patents have been proposed in the "Methods of Signing Group Signs When Passing Group Messages in Insecure Communication Channels", in an attempt to resolve multiple digital signatures. Technical security issues, however, these technologies are still accompanied by quite a few shortcomings. For example, the technology proposed in the Republic of China Patent Bulletin No. 424371 needs to complete the broadcast action before the multi-digit signing, which will increase the signature. The cost, and the order of its document delivery is fixed, and it can not be flexibly applied to various situations. In addition, the algorithm has a complexity of O ( n ), and there is still considerable room for improvement in computing time.

Accordingly, it is an object of the present invention to provide a flexible multi-digit signature method for a network system having a system center and a plurality of client devices, comprising the steps of: assembling the system center to Executing a system key generation program and generating a plurality of system public keys; assembling the system center to receive signature generation requests of N client devices, and cooperating with the client device to perform a first multiple digit The signature generation program obtains a first multiple digit signature, wherein N>1, and the client device is one of N client devices that issue a signature generation request; the user terminal device is assembled to receive the multiple The digital signature is executed and a signature verification procedure is executed to confirm whether the multiple digital signature is a legal signature; the system center and the client device are assembled to execute a multi-digit signature generation program and generate a multi-digit signature generation program Renumbering the signature, and then sending the multi-digit signature to the next client device that issues the signature generation request; and assembling the next client device that issues the signature generation request The signature verification program determines whether to execute the multi-digit signature generation program according to the result of the signature verification program, until all the client devices that issue the signature generation request generate corresponding multi-digit signatures; wherein the system The key generation program includes: assembling the system center to select a first system public key p , a second system public key q , and the third system public key g , wherein the second system discloses the gold The key q can be divisible by ( p -1), and the third system public key is obtained by the first system public key p and the second system public key as a modulo operation; The system center calculates a fourth system public key y _i according to a user private key x _i , the first system public key p , and the third system public key g .

The above and other technical contents, features and advantages of the present invention will be apparent from the following detailed description of the preferred embodiments.

Referring to Figure 1, a preferred embodiment of the flexible multi-digit signature method of the present invention is suitable for implementation in a network system. The network system includes a plurality of client devices 8 respectively corresponding to each user and a system center 9 connected to the client devices, and the embodiment includes: a system key generation program 1, a first multiple The digital signature generation program 2, a signature verification program 3, and a multi-digit signature generation program 4.

After the network system is completed, the system center 9 executes the system key generation program 1 to generate a plurality of system public keys, and then, when the system center 9 receives the first user n via the corresponding user When the end device N 8 issues a signature generation request, the system center 9 and the client device N 8 jointly execute the first multiple digit signature generation program 2 until a first multiple digit signature SIG _{N is} generated. The user equipment N 8 is sent to the next client device N+1 8 that issues a signature generation request to the system center 9 via the network, and the user equipment N+1 8 receives the first multiple digit number sign. After the SIG _N , the signature verification program 3 will be executed to verify whether the first multiple digit signature SIG _N is a valid signature, and if so, the multi-digit signature generation procedure 4 is continued, and if not, then The multi-digit signature method of the embodiment is suspended. Finally, when the first multi-digit signature SIG _N is a valid signature, the client device N+1 8 and the system center 9 jointly execute the multi-digit signature. Chapter 4 generates program 4 to generate a corresponding multi-digit sign Chapter SIG _{N +1} , and then send the signature SIG _{N +1} to the next client device N+2 8 that issues a signature generation request to the system center 9, and is repeatedly executed by the client device N+2 8 The signature verification program 3 and the multi-digit signature generation program 4 until all the client devices 8 that issue the signature generation request to the system center 9 complete the generation of the corresponding signature.

The steps to perform each procedure are explained below:

System key generation program 1

Referring to FIG. 1 and FIG. 2, sub-step 11 is when the system center 9 selects two large prime integers as a first system public key p and a second system public key q , wherein the second The system public key q can be divisible by ( p -1).

Sub-step 12 that the system select a center 9 of the first public key system is a primitive root of p (primitive element) g as a public key system, the third, and in accordance with the disclosed equation (F .1) calculating a fourth system Key:

Where mod is a modulo operator, x _i is a user private key, and y _{i is} the fourth system public key.

Sub-step 13 is that the system center 9 exposes the first to fourth system public keys so that each user on the network system can obtain the system public keys via the corresponding client device 8.

First multiple digit signature generation program 2

Referring to FIG. 1 and FIG. 3, after the system center 9 completes the system key generation program 1, when the system center 9 receives the signature generation request sent by the first user n via the corresponding client device N8, The system center 9 will execute the first multi-digit signature generation program 2, and the steps are as follows: sub-step 21 is that the user equipment N 8 randomly selects a first parameter k1 and a second parameter t , and sends the System Center 9.

Sub-step 22 is that after the system center 9 receives the first parameter k ₁ and the second parameter t , a first signature element r ₁ and a first are calculated according to the equations ( F . 2 ) and ( F . 3 ) respectively. Two signature elements T :

T ≡ g ^t (mod p ).....( F .3)

Where mod is a modulo operator, p is the first system public key, and g is the third system public key.

Then, the system center 9 sends the first signature element r ₁ and the second signature element T to the client device N 8 .

Sub-step 23 is that after the user equipment N 8 randomly selects a third signature element m ₁ , a fourth signature element m and a fifth signature element s ₁ : m _{1 are} calculated according to the equation ( F . 4 ). + tT ≡ x ₁ mr ₁ + k ₁ s ₁ (mod q ).....( F .4)

Where mod is a modulo operator, t is the second parameter, T is the second signature element, x _{1 is} the user private key of the user n, r _{1 is} the first signature element, k ₁ For the first parameter, q is the public key for the second system.

Sub-step 24 is that the client device N 8 transmits a first multiple digit signature SIG _N = ( r ₁ , T , m ₁ , m , s ₁ ) including the first to fifth signature elements via the network. The next user equipment N+1 8 that issues a signature generation request to the system center 9 is issued.

Signature verification procedure 3

Referring to FIG. 1 and FIG. 4, when the client device N+1 8 receives the first multiple digit signature SIG _N sent by the client device N 8 , the signature verification program 3 is executed.

Sub-step 31 that the client device N + 1 8 according to the equation (F .5) to verify the digital signature of the first multi-SIG _N digital signature, or other multi whether a valid signature:

Where R ₀ =1, s ₀ =1, R ₁ ≡ r ₁ (mod p ).

If the equation (F .5) was established the client device N + 1 8 continue the multiple digital signature generator 4, when the equation (F .5) is not satisfied aborts multiple digital signature method according to the present embodiment of the embodiment.

Multi-digit signature generation program 4

Referring to FIG. 1 and FIG. 5, sub-step 41 is that the user equipment N+1 8 randomly selects a first parameter k _i (the following i ranges of values are i =1, 2, . . . , N , N +1 ,...) and sent to the system center 9.

Sub-step 42 is that the system center 9 receives the first parameter k _i and calculates a temporary signature element r _i according to the equation ( F. 2):

Where mod is a modulo operator, p is the first system public key, and g is the third system public key.

Then, the system center 9 sends the temporary signature element r _i to the client device N+1 8.

Sub-step 43 is that the user equipment N+1 8 randomly selects a third parameter. Then, according to Equation (F .6) calculating a fourth signature elements m:

Where mod is a modulo operator, x _{i is} the user private key of the user n, r _{i is} the temporary signature element, k _{i is} the first parameter, and q is the second system public key. And a first signature element R _i and s _i the fifth signature element based on the equation _{(F .6) R i -1,} s i -1, to the equation (F .7), (F .8 ) get: R _i ≡ R _{i -1} r _i (mod p ).....( F .7)

s _i ≡ r _i s _{i -1} (mod q ).....( F .8)

Sub-step 44 that the client device N + 1 8 Equation (F .9) calculating a third signature element according to m _i:

Where mod is a modulo operator, For the third parameter, r _i is a temporary signature element, and q is the second system public key.

Sub-step 45 is that the client device N+1 8 will include a multi-digit signature SIG _i =( R _i , T , m _i , m , s _i ) including the first to fifth signature elements, i =1 ,2,... N , N +1,...

It is transmitted via the network to the next client device N+2 8 that issues a signature generation request to the system center 9.

It can be found that, in the embodiment, when a multi-digit signature method is implemented, it is not necessary to perform a broadcast operation in advance to notify all users on the network system, and at the same time, the embodiment does not limit all directions. The system center proposes the order in which the signature generates the user equipment of the demand. Therefore, in different situations, the system center can flexibly adjust the transmission order of the multiple digit signature, that is, for the Nth user equipment. In this case, the next client device N+1 is not necessarily the next-order client device, and the system center can flexibly decide to transmit the multi-digit signature corresponding to the Nth client device to the network. A client device that presents a request to the system center and has not generated a corresponding multi-digit signature; finally, according to the above embodiment, it can be found that all user devices that request the request can generate corresponding multiples according to the order of new dynamic adjustments in the system. Digital signature, therefore, the algorithm complexity of the present invention is O (1), which can greatly simplify the multi-digit signature side compared to the prior art. The cost of performing the calculation of the method, as described above, can indeed achieve the object of the present invention.

The above is only the preferred embodiment of the present invention, and the scope of the invention is not limited thereto, that is, the simple equivalent changes and modifications made by the scope of the invention and the description of the invention are All remain within the scope of the invention patent.

1‧‧‧System Key Generation Program

11~13‧‧‧substeps

2‧‧‧First multiple digital signature generation procedure

21~24‧‧‧Substeps

3‧‧‧ Signature verification procedure

31‧‧‧Substeps

4‧‧‧Multiple digital signature generation procedures

41~45‧‧‧Substeps

8‧‧‧Customer device

9‧‧‧System Center

1 is a flow chart of a flexible multi-digit signature method of the present invention; FIG. 2 is a flowchart of a system key generation program; FIG. 3 is a flow chart of a first multi-digit signature generation program; A flow chart of a signature verification procedure; and a flow chart of a multi-digit signature generation procedure of FIG.

1‧‧‧System Key Generation Program

2‧‧‧First multiple digital signature generation procedure

3‧‧‧ Signature verification procedure

4‧‧‧Multiple digital signature generation procedures

8‧‧‧Customer device

9‧‧‧System Center

Claims (14)

A flexible multi-digit signature method for a network system having a system center and a plurality of client devices, comprising the steps of: assembling the system center to execute a system key generation program and generating a majority a system public key; the system center is configured to receive a signature generation request of the N client devices, and the user equipment i is configured to execute a first multiple digit signature generation program and obtain a first Multi-digit signature, where N>1, and the client device i is one of N client devices that issue a signature generation request; the user equipment i +1 is assembled to receive the multi-digit signature and execute a signature verification procedure to confirm whether the multiple digit signature is a legal signature; assembling the system center with the client device i +1 to execute a multiple digit signature generation program and generate a multiple digit Signing, and then sending the multi-digit signature to the next client device that issues the signature generation request; and assembling the next client device that issues the signature generation request to repeatedly execute the signature verification program, and rooting The result of the signature verification program determines whether the multi-digit signature generation program is executed until all the client devices that issue the signature generation request generate corresponding multi-digit signatures; wherein the system key generation program includes: assembly The system center selects a first system public key p , a second system public key q , and a third system public key g , wherein the second system public key q can be ( p -1) Divisible, and the third system public key g is obtained by the first system public key p and the second system public key q as a modulo operation; and the system center is assembled according to one The user private key x _i , the first system public key p , and the third system public key g calculate a fourth system public key y _i . According to the flexible multi-digit signature method described in claim 1, wherein the system key generation program further comprises assembling the system center to disclose the system disclosure keys in the network system. According to the flexible multi-digit signature method described in claim 1 of the patent application scope, the fourth system public key y _{i is} calculated as follows: Where mod is a modulo operator. According to the flexible multi-digit signature method described in claim 1, wherein the first multi-digit signature generation program includes: assembling the user equipment i to randomly select a first parameter k ₁ And a second parameter t is sent to the center of the system; the system center is assembled to receive the first parameter k ₁ and the second parameter t , and according to the first parameter k ₁ , the second parameter t , The first system public key p and the third system public key g respectively calculate a first signature element r ₁ and a second signature element T ; and assemble the client device i to receive the After the first signature element r ₁ and the second signature element T , a third signature element m _{1 is} randomly selected, and according to the first parameter k ₁ , the second parameter t , and the second system disclosure gold The key q , the first signature element r ₁ , the second signature element T , and the user private key x _{1 of the} client device i calculate a fourth signature element m and a fifth signature element s ₁ . The flexible multi-digit signature method according to claim 4, wherein the first multi-digit signature generation program further comprises assembling the client device i to include one to fifth The first multi-digit signature of the signature element is sent to the next client device i +1 that issues a signature generation request to the system center. According to the flexible multi-digit signature method described in claim 4, wherein the first signature element r ₁ and the second signature element T are calculated as follows: T ≡ g ^t (mod p ) where mod is a modulo operator, p is the first system public key, g is the third system public key, k _{1 is} the first parameter, t is the first Two parameters. According to the flexible multi-digit signature method described in claim 4, wherein the fourth signature element m and the fifth signature element s _{1 are} calculated as follows: m ₁ + tT ≡ x ₁ mr ₁ + k ₁ s ₁ (mod q ) where mod is a modulo operator, t is the second parameter, T is the second signature element, x _{1 is} the user private key of the user n, r ₁ is The first signature element, k _{1 is} the first parameter, and q is the second system public key. According to the flexible multi-digit signature method described in claim 1, wherein the signature verification procedure is for the client device i +1 to verify the legitimacy of the multi-digit signature according to the following equation: Where R ₀ =1, s ₀ =1, R ₁ ≡ r ₁ (mod p ). According to the flexible multi-digit signature method described in claim 1, wherein the multi-digit signature generation process includes: the user equipment i +1 to randomly select a first parameter k _i , and Sending to the system center; assembling the system center to receive the first parameter k _i , and calculating a temporary signature element according to the first system public key p and the third system public key g r _i ; the user equipment i +1 is assembled to randomly select a third parameter And according to the user private key x _i of the client device i +1 , the temporary signature element r _i , the first parameter k _i , the second system public key q calculates a fourth signature element m : the user equipment i +1 is assembled, a first signature element R _i and the fifth signature element s _{i are} calculated; and the user equipment i +1 is assembled according to the third parameter The temporary signature element r _i and the second system public key q are used to calculate a third signature element m _i . According to the flexible multi-digit signature method of claim 9, wherein the multi-digit signature generation program further comprises assembling the client device i +1 to include the first to fifth The multi-digit signature of the signature element is sent to the next client device that issues a signature generation request to the system center. According to the flexible multi-digit signature method described in claim 9 of the patent application scope, the four-signature element m is calculated as follows: Where mod is a modulo operator, x _{i is} the user private key of the client device i +1, r _{i is} the temporary signature element, k _{i is} the first parameter, and q is the second system Public key, i = 1, 2, ..., N , N +1, .... According to the flexible multi-digit signature method described in claim 9 of the patent application scope, the first signature element R _{i is} calculated as follows: R _i ≡ R _{i -1} r _i (mod p ) wherein mod is A modulo operator, r _{i is} the temporary signature element, p is the first system public key, i = 1, 2, ..., N , N +1, .... According to the flexible multi-digit signature method described in claim 9 of the patent application scope, the fifth signature element s _{i is} calculated as follows: S _i ≡ r _i s _{i -1} (mod q ) wherein mod is A modulo operator, r _{i is} the temporary signature element, q is the second system public key, i = 1, 2, ..., N , N +1, .... According to the flexible multi-digit signature method described in claim 9 of the patent application scope, the third signature element m _{i is} calculated as follows: Where mod is a modulo operator, For the third parameter, r _i for the temporary signature elements, q is the second public key system.