TWI408938B - Flexible multi - digit signature method - Google Patents
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本發明是有關於一種數位簽章方法,特別是指一種具彈性可動態調整順序之多重數位簽章方法。The invention relates to a digital signature method, in particular to a multi-digit signature method with elastic and dynamic adjustment order.
網路科技發達的時代,利用網路傳送待簽署文件以廣為被企業所使用,而一份待簽署文件往往可能需要多位成員共同簽署,因此,多重數位簽章的技術被開發出來以應用於此。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.
透過數位簽章的方式的確是一種可以提供相當方便、且節省紙張成本的有效且經濟的方式,但是在方便省錢之餘,對於一份待簽署的機密文件而言,網路傳輸卻始終存在著風險性,因此,如同中華民國專利公告號424371所發表的「在不安全通訊通道傳遞群體訊息時簽署群體簽章的方法」等相關研究成果或是專利紛紛被提出,企圖解決多重數位簽章技術的安全性問題,然而,該等技術卻依然伴隨著相當多的缺點,例如:中華民國專利公告號424371所提出之技術在進行多重數位簽署前需先完成廣播動作,此舉將會增加簽署成本,而且其公文傳遞的順序是固定的,較無法彈性應用於各種情況,此外,該技術的演算法複雜度為O (n ),在運算時間上仍有相當大的改善空間。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.
因此,本發明之目的,即在提供一種具彈性之多重數位簽章方法,適用於一具有一系統中心及多數個用戶端裝 置之網路系統,其包含下列步驟:組配該系統中心,以執行一系統金鑰產生程序並產生多數個系統公開金鑰;組配該系統中心,以接收N個用戶端裝置之簽章產生請求,且配合組配用戶端裝置以執行一第一多重數位簽章產生程序並得到一第一多重數位簽章,其中N>1,且用戶端裝置為N個發出簽章產生請求之用戶端裝置其中之一;組配用戶端裝置,以接收該多重數位簽章並執行一簽章驗證程序,以確認該多重數位簽章是否為一合法簽章;組配該系統中心與該用戶端裝置,以執行一多重數位簽章產生程序並產生一多重數位簽章,然後將該多重數位簽章送至下一個發出簽章產生請求之用戶端裝置;及組配下一個發出簽章產生請求之用戶端裝置重複執行該簽章驗證程序,並根據該簽章驗證程序之結果判斷是否執行該多重數位簽章產生程序,直到所有發出簽章產生請求之用戶端裝置皆產生對應之多重數位簽章;其中,該系統金鑰產生程序包括:組配該系統中心,以選取一第一系統公開金鑰p 、一第二系統公開金鑰q ,及該第三系統公開金鑰g ,其中,該第二系統公開金鑰q 可以被(p -1)整除之,且該第三系統公開金鑰係由該第一系統公開金鑰p 及該第二系統公開金鑰作一模數運算而得到;及組配該系統中心,以根據一用戶私密金鑰x i 、該第一系統公開金鑰p ,及該第三系統公開金鑰g 計算出一第四系統公 開金鑰y i 。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 .
有關本發明之前述及其他技術內容、特點與功效,在以下配合參考圖式之一個較佳實施例的詳細說明中,將可清楚的呈現。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.
參閱圖1,本發明之具彈性之多重數位簽章方法之一較佳實施例,是適用於以一網路系統來實現。該網路系統包括多數個分別對應每一用戶之用戶端裝置8及一與該等用戶端裝置連接之系統中心9,而本實施例包含:一系統金鑰產生程序1、一第一多重數位簽章產生程序2、一簽章驗證程序3,及一多重數位簽章產生程序4。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.
當該網路系統建置完成之後,該系統中心9會執行該系統金鑰產生程序1以產生多數個系統公開金鑰,然後,當該系統中心9接收到第一個用戶n經由對應之用戶端裝置N 8發出簽章產生請求時,該系統中心9及該用戶端裝置N 8會共同執行該第一多重數位簽章產生程序2,直到一第一多重數位簽章SIG N 產生之後,該用戶端裝置N 8經由網路送至下一個向該系統中心9發出簽章產生請求之用戶端裝置N+1 8,該用戶端裝置N+1 8接收到該第一多重數位簽章SIG N 之後,將執行該簽章驗證程序3以驗證該第一多重數位簽章SIG N 是否為合法的簽章,若是,則繼續執行該多重數位簽章產生程序4,若否,則中止本實施例之多重數位簽章方法,最後,當該第一多重數位簽章SIG N 為合法的簽章時,該用戶端裝置N+1 8與該系統中心9共同執行該多重數位簽 章產生程序4以產生一對應之多重數位簽章SIG N +1 ,然後將該簽章SIG N +1 送至下一個向該系統中心9發出簽章產生請求之用戶端裝置N+2 8,並由該用戶端裝置N+2 8重複執行該簽章驗證程序3及該多重數位簽章產生程序4,直到所有向該系統中心9發出簽章產生請求之用戶端裝置8皆完成產生對應之簽章。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.
以下將分別說明每一程序之執行步驟:The steps to perform each procedure are explained below:
聯合參閱圖1、2,子步驟11是當該系統中心9選取二個大質數(Large prime integer)作為一第一系統公開金鑰p 及一第二系統公開金鑰q ,其中,該第二系統公開金鑰q 可以被(p -1)整除之。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).
子步驟12是該系統中心9選取一該第一系統公開金鑰p
之原根(primitive element)g
作為一第三系統公開金鑰,並根據方程式(F
.1)計算出一第四系統公開金鑰:
其中,mod為一模數運算子,x i 為一用戶私密金鑰,y i 為該第四系統公開金鑰。Where mod is a modulo operator, x i is a user private key, and y i is the fourth system public key.
子步驟13是該系統中心9將該第一至第四系統公開金鑰公開,使得該網路系統上的每一用戶皆可經由對應之用戶端裝置8取得該等系統公開金鑰。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.
聯合參閱圖1、3,當該系統中心9完成該系統金鑰產生程序1之後,當該系統中心9接收第一位用戶n經由對 應之用戶端裝置N 8所發出之簽章產生請求時,該系統中心9將執行該第一多重數位簽章產生程序2,執行步驟如下:子步驟21是該用戶端裝置N 8隨機選取一第一參數k1及一第二參數t ,並送至該系統中心9。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.
子步驟22是該系統中心9接收該第一參數k 1
及該第二參數t
之後,依據方程式(F
.2)、(F
.3)分別計算出一第一簽章元素r 1
及一第二簽章元素T
:
T ≡g t (modp ).....(F .3) T ≡ g t (mod p ).....( F .3)
其中,mod為一模數運算子,p 為該第一系統公開金鑰,g 為該第三系統公開金鑰。Where mod is a modulo operator, p is the first system public key, and g is the third system public key.
然後,該系統中心9將該第一簽章元素r 1 及該第二簽章元素T 送至該用戶端裝置N 8。Then, the system center 9 sends the first signature element r 1 and the second signature element T to the client device N 8 .
子步驟23是該用戶端裝置N 8隨機選取一第三簽章元素m 1 之後,根據方程式(F .4)計算出一第四簽章元素m 及一第五簽章元素s 1 :m 1 +tT ≡x 1 mr 1 +k 1 s 1 (modq ).....(F .4)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)
其中,mod為一模數運算子,t 為該第二參數,T 為該第二簽章元素,x 1 為該用戶n之用戶私密金鑰,r 1 為該第一簽章元素,k 1 為該第一參數,q 為該第二系統公開金鑰。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.
子步驟24是該用戶端裝置N 8將一包括第一至第五簽章元素之第一多重數位簽章SIG N =(r 1 ,T ,m 1 ,m ,s 1 )經由網路傳送至下一個向該系統中心9發出簽章產生請求之用戶端裝置N+1 8。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.
聯合參閱圖1、4,當該用戶端裝置N+1 8接收到該用戶端裝置N 8所送出之第一多重數位簽章SIG N 時,便會執行該簽章驗證程序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.
子步驟31是該用戶端裝置N+1 8根據方程式(F
.5)以驗證該第一多重數位簽章SIG N
或是其他多重數位簽章是否為一合法簽章:
其中,R 0 =1、s 0 =1、R 1 ≡r 1 (modp )。Where R 0 =1, s 0 =1, R 1 ≡ r 1 (mod p ).
若方程式(F .5)成立則該用戶端裝置N+1 8繼續執行該多重數位簽章產生程序4,若方程式(F .5)不成立則中止本實施例之多重數位簽章方法。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.
聯合參閱圖1、5,子步驟41是該用戶端裝置N+1 8隨機選取一第一參數k i (以下i 的數值範圍皆為i =1,2,...,N ,N +1,...),並送至該系統中心9。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.
子步驟42是該系統中心9接收該第一參數k i
,依據方程式(F
.2)計算出一暫存簽章元素r i
:
其中,mod為一模數運算子,p 為該第一系統公開金鑰,g 為該第三系統公開金鑰。Where mod is a modulo operator, p is the first system public key, and g is the third system public key.
然後,該系統中心9將該暫存簽章元素r i 送至該用戶端裝置N+1 8。Then, the system center 9 sends the temporary signature element r i to the client device N+1 8.
子步驟43是該用戶端裝置N+1 8隨機選取一第三參數之後,根據方程式(F
.6)計算出一第四簽章元素m
:
其中,mod為一模數運算子,x i 為該用戶n之用戶私密金鑰,r i 為該暫存簽章元素,k i 為該第一參數,q 為該第二系統公開金鑰。且一第一簽章元素R i 及該第五簽章元素s i 是根據方程式(F .6)中的R i -1 、s i -1 ,以方程式(F .7)、(F .8)得到:R i ≡R i -1 r i (modp ).....(F .7)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 (modq ).....(F .8) s i ≡ r i s i -1 (mod q ).....( F .8)
子步驟44是該用戶端裝置N+1 8根據方程式(F
.9)計算出一第三簽章元素m i
:
其中,mod為一模數運算子,為該第三參數,r i 為一暫存簽章元素,q 為該第二系統公開金鑰。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.
子步驟45是該用戶端裝置N+1 8將一包括該第一至第五簽章元素之多重數位簽章SIG i =(R i ,T ,m i ,m ,s i ),i =1,2,...N ,N +1,...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,...
經由網路傳送至下一個向該系統中心9發出簽章產生請求之用戶端裝置N+2 8。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.
由上述可以發現,在本實施例中要實現一多重數位簽章方法時,並不需要事先進行一廣播動作以知會該網路系統上之所有用戶,同時,本實施例並無限定所有向該系統中心提出簽章產生需求之用戶端裝置之順序,因此,在不同的情況下,該系統中心可以彈性的調整該多重數位簽章之傳遞順序,也就是說,對於第N個用戶端裝置而言,其 下一個用戶端裝置N+1並不一定是其下一順位之用戶端裝置,該系統中心可以彈性決定將第N個用戶端裝置對應之多重數位簽章傳遞至網路中任一個向系統中心提出需求且尚未產生對應之多重數位簽章的用戶端裝置;最後,依照上述實施例可以發現,所有提出需求之用戶端裝置可依照該系統中新動態調整之順序產生對應之多重數位簽章,因此,本發明之演算法複雜度為O (1),相較於先前技術而言可以大幅簡化多重數位簽章方法之執行運算成本,綜上所述,故確實能達成本發明之目的。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.
惟以上所述者,僅為本發明之較佳實施例而已,當不能以此限定本發明實施之範圍,即大凡依本發明申請專利範圍及發明說明內容所作之簡單的等效變化與修飾,皆仍屬本發明專利涵蓋之範圍內。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‧‧‧系統金鑰產生程序1‧‧‧System Key Generation Program
11~13‧‧‧子步驟11~13‧‧‧substeps
2‧‧‧第一多重數位簽章產生程序2‧‧‧First multiple digital signature generation procedure
21~24‧‧‧子步驟21~24‧‧‧Substeps
3‧‧‧簽章驗證程序3‧‧‧ Signature verification procedure
31‧‧‧子步驟31‧‧‧Substeps
4‧‧‧多重數位簽章產生程序4‧‧‧Multiple digital signature generation procedures
41~45‧‧‧子步驟41~45‧‧‧Substeps
8‧‧‧用戶端裝置8‧‧‧Customer device
9‧‧‧系統中心9‧‧‧System Center
圖1是本發明具彈性之多重數位簽章方法之流程圖;圖2是一系統金鑰產生程序之流程圖;圖3是一第一多重數位簽章產生程序之流程圖;圖4之一簽章驗證程序之流程圖;及圖5之一多重數位簽章產生程序之流程圖。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‧‧‧系統金鑰產生程序1‧‧‧System Key Generation Program
2‧‧‧第一多重數位簽章產生程序2‧‧‧First multiple digital signature generation procedure
3‧‧‧簽章驗證程序3‧‧‧ Signature verification procedure
4‧‧‧多重數位簽章產生程序4‧‧‧Multiple digital signature generation procedures
8‧‧‧用戶端裝置8‧‧‧Customer device
9‧‧‧系統中心9‧‧‧System Center
Claims (14)
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TW98145915A TWI408938B (en) | 2009-12-30 | 2009-12-30 | Flexible multi - digit signature method |
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TW98145915A TWI408938B (en) | 2009-12-30 | 2009-12-30 | Flexible multi - digit signature method |
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TWI408938B true TWI408938B (en) | 2013-09-11 |
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Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO1996039765A1 (en) * | 1995-06-05 | 1996-12-12 | Certco Llc | Multi-step digital signature method and system |
TW200836118A (en) * | 2008-03-21 | 2008-09-01 | Univ Chang Gung | User authentication method, system and computer system with atm ic-card system |
US20090164793A1 (en) * | 2007-12-19 | 2009-06-25 | Fujitsu Limited | Digital signature system and digital signing method |
TW200952438A (en) * | 2008-06-11 | 2009-12-16 | Microsoft Corp | Techniques for performing symmetric cryptography |
-
2009
- 2009-12-30 TW TW98145915A patent/TWI408938B/en not_active IP Right Cessation
Patent Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO1996039765A1 (en) * | 1995-06-05 | 1996-12-12 | Certco Llc | Multi-step digital signature method and system |
US20090164793A1 (en) * | 2007-12-19 | 2009-06-25 | Fujitsu Limited | Digital signature system and digital signing method |
TW200836118A (en) * | 2008-03-21 | 2008-09-01 | Univ Chang Gung | User authentication method, system and computer system with atm ic-card system |
TW200952438A (en) * | 2008-06-11 | 2009-12-16 | Microsoft Corp | Techniques for performing symmetric cryptography |
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