CN102045164A - Key exposure free chameleon digital signature method based on ID (Identity) - Google Patents
Key exposure free chameleon digital signature method based on ID (Identity) Download PDFInfo
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- CN102045164A CN102045164A CN2009101932017A CN200910193201A CN102045164A CN 102045164 A CN102045164 A CN 102045164A CN 2009101932017 A CN2009101932017 A CN 2009101932017A CN 200910193201 A CN200910193201 A CN 200910193201A CN 102045164 A CN102045164 A CN 102045164A
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Abstract
The invention relates to a chameleon digital signature method based on ID (Identity). A special chameleon hashing function with three trap doors and an equal-index knowledge certification technology are adopted in the method to realize key exposure free chameleon digital signature based on ID under the condition that the bilinear Diffie-Hellman problem is supposed to be difficult. The invention solves the problem that the advantage of simple key management based on ID by utilizing a cryptosystem can not be realized because the chameleon digital signature method based on ID does not exists in the background art.
Description
Technical field
The present invention relates to information security field.Especially, the present invention relates to the method that a kind of Chameleon digital signature that leaks based on the no key of identity generates and verifies.
Background technology
Digital signature is a kind of basic information security technology, at aspects such as authentication, data integrity, non-repudiation and anonymities important application is arranged, particularly the encryption key distribution in secure communication of network has important effect in the systems such as authentication and ecommerce, E-Government.Digital signature is to realize the important tool of authentication.
The generation of digital signature and checking need the signature private key and the verification public key of signer.The signature private key of signer is only known by signer.The verification public key of signer then is disclosed.The generation of digital signature need be used the signature private key of signer and the digital content of being signed.The checking of digital signature then is to use verification public key to confirm that signer has corresponding signature private key.The security requirement digital signature of digital signature should be forged, and does not promptly have anyone or equipment of signature private key all can not forge a digital signature.Signature private key has the important function of unique sign signer identity, and digital signature should not leaked the useful information of signature private key.
Usually verification public key is a character string at random, is difficult to the holder of the concrete PKI of identification.The method of infrastructure is bound PKI and PKI holder's identity so people use public-key, and has set up trust systems.Huge and the complexity of PKIX has been brought no small expense on the public key management, in order to address this problem, people propose to use significant character string as PKI, promptly based on the cryptographic system of identity, this system nature is bound identity and PKI, reduce the expense of public key management, be subjected to people's favor.Particularly from calendar year 2001 based on after computing having been proposed practical cryptographic algorithm based on identity, received the concern that continues based on the cryptographic system of identity.
Common digital signature has the broad sense verifiability, and promptly anyone can verify that whether certain signature is the signature to certain particular message.This characteristic has very usefulness in some cases, such as the issue of overt propaganda product.But in a lot of other are used, particularly when protecting signer or recipient's privacy, do not wish to allow everyone can both verify that message/signature is right.This has just produced the contradiction between the broad sense verifiability and privacy in the digital signature system.For example, certain signer has been signed a bidding documents and has been gone to submit a tender, the marked price of bidding documents belongs to privacy information usually, this moment, this signer was just wished the not openly checking of its signature, otherwise its competitor just can confirm that certain marked price belongs to this signer really by its bidding documents, to such an extent as to can with the later competition of this signer in be on a good wicket.Also have many other examples to highlight above-mentioned contradiction, need to design special digital signature for this reason and solve problem.
Chaum and Van Antwerpen have proposed undeniable signature and have solved the problems referred to above.Because the checking of signature must just can be finished by the cooperation of signer, so signature does not satisfy the broad sense verifiability.Further, signer can determine to sign and only just can be verified under certain condition or can only be verified by certain specific entity.
Krawcayk and Rabin have proposed the chameleon signature and have come more effective addressing the above problem.The chameleon measured digital signature generation method of signing, that is: first Hash is signed again.Wherein the chameleon hash function is used to calculate the message cryptographic Hash.The chameleon hash function is a kind of unidirectional trapdoor hash function, and the owner of trap door information can calculate a collision of input at random effectively; And do not having under the situation of trap door information, function is a crash-resistant.The chameleon signature can provide non-repudiation and non-transferability simultaneously as undeniable signature, but with respect to the latter, the former can simpler, realization more efficiently.More accurate, the chameleon signature is a nonreciprocal, and does not relate to complicated zero-knowledge proof, and this is the basis that traditional undeniable signature is realized.Though there is noninteractive undeniable signature, the realization of chameleon signature is more simple.
In some initial designed chameleon signature schemes, if the verifier forges a signature, and signer has obtained forging a signature, and signer just can utilize the collision calculation of this chameleon hash function to go out verifier's private key, causes verifier's key to leak.Though this characteristic can prevent effectively that the verifier from forging a signature, but the third party may forge a signature because believe the danger that the verifier dare not emit private key to reveal, and then believe that certain signature is that signer is signed really, thereby weakened the not transferability of signature.
People such as Chen Xiaofeng do not have the chameleon hash function that key leaks based on bilinearity completely to having proposed first, and new departure has well solved this problem.Subsequently, people such as Ateniese has proposed more no keys based on the difference hypothesis and has revealed the chameleon hash functions.People such as Ateniese point out that the promise scheme of traditional single trapdoor can't be used for constructing the chameleon hash function that no key is revealed; Have only the promise scheme of two trapdoors can be used for designing chameleon hash function that no key reveals or based on the chameleon hash function of identity.
Yet there is not the chameleon endorsement method of revealing based on the no key of identity at present, thereby can't use the chameleon signature that carries out high level of security based on the system of identity in practice, have to rely on the support of traditional PKIX, perhaps transfer to use the lower scheme of some level of securitys that can not prevent that key from revealing.
From the above, the Chameleon digital signature method that the no key of having announced in the prior art based on identity is revealed does not exist.We wish to provide a kind of Chameleon digital signature scheme, enable based on identity, can solve the key leakage problem simultaneously, have public key management characteristic easily.
Summary of the invention
The object of the present invention is to provide a kind of implementation method of the Chameleon digital signature scheme of revealing based on the no key of identity, solve and not have the Chameleon digital signature method of revealing based on the no key of identity in the background technology, can not utilize based on the system public key management of identity advantage easily.
For achieving the above object, the invention provides a kind of implementation method of the Chameleon digital signature scheme of revealing based on the no key of identity: disclosed system parameters is set; Signature private key and disclosed verification public key that signer has are set; Trapdoor private key and disclosed chameleon PKI that the verifier has are set; Signer uses signature private key and chameleon PKI to calculate the Chameleon digital signature of digital content; The verifier uses the disclosed verification public key of signer, chameleon PKI and trapdoor private key to verify the correctness of Chameleon digital signature; Signer is denied the chameleon signature that the verifier generates to trusted third party.
1) disclosed system parameters comprises: clearance D iffie-Hellman group G
1, group G
1Generator P, the rank of generator P are big prime number q, cyclic group G
2, group G
2Rank also be big prime number q, the collisionless hash function H:{0 of universe, 1}
*→ G
1, to mapping Function e: G
1* G
1→ G
2, the PKI P of trusted third party
Pub=sP, wherein s is the private key of trusted third party; The Digital Signature Algorithm based on identity of any one safety (JG, JE, JS, JV).
Wherein about group G
1, G
2, be difficult to the bilinear Diffie-Hellman problem of computing e.
Wherein An Quan Digital Signature Algorithm refers to that this algorithm has unforgeable under adaptability selection message attack.
2) the signature private key x that has of signer
SGenerate by algorithm JE.According to Digital Signature Algorithm (JG, JE, JS, difference JV), signature private key and verification public key can have various form.
3) the trapdoor private key that has of verifier is x
R=sQ
R, disclosed chameleon PKI is Q
R=H (R).
4) signer uses signature private key and chameleon PKI to calculate digital content
The step of Chameleon digital signature as follows:
(1) signer is selected random integers
(2) generate Bit String I;
(3) calculate chameleon Hash Value H;
(4) use signature private key x
S, use Digital Signature Algorithm JS, to chameleon Hash Value H signature, obtain the signature value
(5) use chameleon PKI Q
R, the PKI P of trusted third party
Pub, integer α to the mapping Function e, calculates group G
1Element α P and group G
2Element e (α P
Pub, Q
R);
(6) signer series connection α P, e (α P
Pub, Q
R), δ, chameleon signature (α P, e (the α P of formation digital content m
Pub, Q
R), δ).
Wherein the computational methods of chameleon Hash Value H are at clearance D iffie-Hellman group G
1Last calculating H=α P+mH (I).
Wherein Bit String I comprises the temporal information that signer identity information, verifier's identity information and signer and verifier make an appointment.
5) verifier uses the disclosed verification public key of signer, chameleon PKI and trapdoor private key to verify the Chameleon digital signature of digital content m (α P, e (α P
Pub, Q
R), the step of correctness δ) is as follows:
(1) verifier uses first element α P and the private key sQ of trapdoor private key to signature
RCalculate e (α P, sQ
R);
(2) compare e (α P
Pub, Q
R) with step (1) in the value e (α P, the sQ that calculate
R) whether identical, if difference then think this signature for false, otherwise continue to judge;
(3) verifier generates Bit String I;
(4) use message m to calculate mH (I);
(5) verifier uses first element of signature and calculates resulting mH (I) and calculate chameleon Hash Value H=α P+mH (I)
(6) verifier uses disclosed verification public key y
S, chameleon Hash Value H, the correctness of coming certifying signature δ according to the defined proof procedure of digital signature verification algorithm JV.Think signature if signature verification is failed for false, otherwise think that signature is true.
6) signer to trusted third party deny that the verifier generates about message m
*Chameleon signature (α * P, e (α * P
Pub, Q
R), step δ) is as follows:
(1) whether trusted third party's checking chameleon signature satisfies following attribute:
-verifier submits α * P, e (α * P to trusted third party
Pub, Q
R) contain same integer α
*Evidence;
-trusted third party recomputates Bit String I, m*H (I), H=α * P+m*H (I), uses the identity S of signer, verifies δ according to the defined proof procedure of digital signature verification algorithm JV, can be by checking.
(2) if trusted third party thinks that the chameleon signature that the verifier submits to satisfies above-mentioned two attributes, then require signer to deny the chameleon signature, otherwise assert that directly the chameleon signature is for false.
(3) signer denies that to trusted third party the process of chameleon signature is as follows:
-signer is showed chameleon signature value (α P, e (α P to trusted third party
Pub, Q
R), δ);
-signer shows that to trusted third party the message m or the m that gives information are group element H/g
αWith H (y
R, I) be the knowledge proof of the discrete logarithm at the end;
-signer produces evidence to prove (α P, e (α P to trusted third party
Pub, Q
R) contain identical integer α;
(4) if signer provides message m, trusted third party checks the message m that the chameleon signature is signed
*Different with m, but H=g
αH (y
R, I)
m, and signer (α P, e (the α P that provide
Pub, Q
R) contain identical integer α evidence reliable through checking, just can judge that the chameleon signature is vacation;
(5) m if signer does not give information, trusted third party checks
And (α P, e (α P that signer provides
Pub, Q
R) contain identical integer α evidence reliable through checking, the m that signer provides is group element H/g
αWith H (y
R, I) reliable through checking for the knowledge proof of the discrete logarithm at the end, just can judge that the chameleon signature is vacation.
The present invention has the following advantages:
The present invention is based on the hypothesis of bilinear Diffie-Hellman problem hard, constructed the Chameleon digital signature scheme that no key is revealed based on identity, this scheme can be utilized the advantage that does not need PKIX based on the system of identity, make things convenient for the management of key, and had higher efficient.
The implementation method based on the Chameleon digital signature scheme of identity that no key provided by the invention is revealed is applicable to fields such as electronic bidding, electronic auction, copyright protection, copyright be false proof.
Description of drawings
The Chameleon digital signature scheme implementation method block diagram that Fig. 1 reveals for no key based on identity
Embodiment
Copyright protection with software is the concrete enforcement of example explanation this programme.The software copyright owner is the signer of this programme, and the consumer of software is the verifier of this programme.Enforcement by this programme, the software copyright owner can sign the chameleon signature for digital product, the consumer of software can be by the authenticity of checking chameleon Signature Confirmation digital product, yet come from the not transferability of chameleon signature, the consumer can't prove that its used product is a certified products to anyone, carries out the secondary sale thereby make digital product can not duplicated by the consumer.Specific implementation process is as follows:
1) everyone and consumer of software copyright has following disclosed system parameters:
The Digital Signature Algorithm based on identity of-safety (JG, JE, JS, JV): can be chosen to be the Digital Signature Algorithm of Cha-Cheon, signature length 1024 bits, the parameter of this signature algorithm (E, p, q, k, P, G based on identity
1) as follows:
E：y
2＝x
3+1
p＝
1005585594745694782468051874865438459560952436544
4295033292671082791323022555160232602838231103021
8299615970507030097306168828238323448310057449840
09826581
q＝
1675975991242824637446753124775730765934920727574
0491722154451804652205037591933721004730385171703
0499359950845050162176948047063872413850095749733
4971097
k＝2
P＝(x，y)
x＝
2218248283148307312060782604701661398038778976686
8776087296524683183375451964436704312239069091547
2603013162873873034608314248613358036757769762946
5320989
y＝
4515056003532170177558482288850754893020739301430
3695723827477100680433208082449098697164691334340
9487874330444808136912136808585726273940504926721
5539276
G
1=＜P 〉, be a group of P generation;
Computing e is adopted the Miller algorithm
G
2Be GF (p
2) on subgroup, q rank, generator be e (P, P).
Open parameter G in the-chameleon signature scheme
1, G
2, to computing e, G
1Generator P, prime number q with based on the Digital Signature Algorithm of identity (JG, JE, JS, JV) relevant parameter in is identical.
The collisionless hash function H of-universe can adopt SHA-256 earlier the input bit string to be carried out hash in this concrete enforcement, and then to Hash Value mould q, acquisition value x is this value substitution elliptic curve equation y
2=x
3+ ax+b, if can solve y, then obtain H output (x, y); Otherwise repeat said process with i series connection input bit string, obtain x
i, wherein i successively value { 1,2,3...} is up to solving y
iTill, obtain H and be output as (x
i, y
i).
The PKI P of-trusted third party
Pub=sP, s are trusted third party's private key.
2) the signature private key x that has of the software copyright owner
SGenerated based on the Digital Signature Algorithm of identity by Cha-Cheon, PKI is this copyright owner's a identity information.
3) the trapdoor private key that has of consumer is x
R=sQ
R, the identity information R that disclosed chameleon PKI is the consumer.
4) the software copyright owner obtains the digital finger-print of this software product to the computing of software product operation SHA-256 hash, carries out mould q computing afterwards and obtains message m to be signed.The software copyright owner moves following steps afterwards:
(1) signer is selected random integers
(2) use the possessory identity information of software copyright, consumer's identity information, the disclosed time of putting on the shelf of digital product generates Bit String I;
(3) use universe collisionless function calculation chameleon Hash Value H=α P+mH (I);
(4) use signature private key x
S, use Digital Signature Algorithm JS, to chameleon Hash Value H signature, obtain the signature value
(5) use chameleon PKI R to calculate Q
R=H (R), integer α, the PKI P of trusted third party
Pub, calculate α P and e (α P
Pub, Q
R);
(6) the software copyright owner α P that connects, e (α P
Pub, Q
R), δ, chameleon signature (α P, e (the α P of formation digital product
Pub, Q
R), δ), and issue simultaneously with digital product, the digital product time of putting on the shelf.
5) consumer uses owner's identity information of software product, the identity information of use oneself and Chameleon digital signature (α P, e (the α P that the trapdoor private key is verified digital product
Pub, Q
R), the step of correctness δ) is as follows:
(1) consumer calculates e (α P, sQ with the trapdoor private key to first element α P that signs
R);
(2) second element e (the α P that relatively signs
Pub, Q
R) with the e (α P, the sQ that calculate
R) whether identical, if difference then think this signature for false, otherwise continue to judge;
(3) use the possessory identity of software copyright, consumer's identity information, the disclosed time of putting on the shelf of digital product generates Bit String I;
(4) consumer obtains the digital finger-print of this software product to not comprising the software product operation SHA-256 hash computing of signature, carries out mould q computing afterwards and obtains message m to be signed.
(5) consumer calculates mH (I);
(5) consumer uses first element of signature and calculates resulting mH (I) and calculate chameleon Hash Value H=α P+mH (I)
(6) consumer uses copyright owner's identity S, chameleon Hash Value H, the correctness of coming certifying signature δ according to the defined proof procedure of digital signature verification algorithm JV.Think signature if signature verification is failed for false, otherwise think that signature is true.
6) the software copyright owner denies the incidental chameleon signature of the digital product about consumer oneself generation or change (α * P, e (the α * P that consumer person generates to trusted third party
Pub, Q
R), the step of authenticity δ) is as follows:
(1) trusted third party verifies whether pseudo-chameleon signature satisfies following attribute:
-consumer submits α * P, e (α * P to trusted third party
Pub, Q
R) contain identical α
*Evidence;
-trusted third party recomputates the digital finger-print of digital product, obtains message m after the mould q
*, recomputate Bit String I, m*H (I), H=α * P+m*H (I),
Use disclosed copyright owner's identity S, verify δ according to the defined proof procedure of digital signature verification algorithm JV, can be by checking.
(2) if trusted third party thinks that the chameleon signature of submitting to satisfies above-mentioned two attributes, then require the software copyright owner to deny the chameleon signature, otherwise assert that directly the chameleon signature is for false.
(3) the software copyright owner denies that to trusted third party the process of chameleon signature is as follows:
-software copyright the owner shows chameleon signature value (α P, e (α P to trusted third party
Pub, Q
R), δ);
-software copyright the owner shows that to trusted third party the message m or the m that gives information are that group element mH (I) is the knowledge proof of the discrete logarithm at the end with H (I);
-software copyright the owner produces evidence to prove α P and e (α P to trusted third party
Pub, Q
R) contain identical integer α;
(4) if the software copyright owner provides message m, trusted third party checks the message m that needs the chameleon of checking true and false signature to be signed
*Different with m, but H=α P+mH (I), and signer (α P, e (the α P that provide
Pub, Q
R) contain identical integer α evidence reliable through checking, the chameleon signature that just can judge submission is for false, product is forgery;
(5) m if the software copyright owner does not give information, trusted third party check α P ≠ α * P, and signer (α P, e (the α P that provide
Pub, Q
R) contain identical integer α evidence reliable through checking, the m that signer provides is group element H/g
αWith H (y
R, I) reliable through checking for the knowledge proof of the discrete logarithm at the end, just can judge the chameleon signature for false, product is forgery.
Claims (6)
1. one kind generates and the Chameleon digital signature method based on identity of checking digital content, comprising:
Be used to calculate the step of disclosed system parameters;
Be used for the signature private key that compute signature person has and the step of disclosed verification public key;
Be used to calculate the trapdoor private key that the verifier has and the step of disclosed chameleon PKI;
Being used for signer uses signature private key and chameleon PKI to calculate the step of the Chameleon digital signature of digital content;
Being used for the verifier uses the disclosed verification public key of signer, chameleon PKI and trapdoor private key to verify the step of the correctness of Chameleon digital signature;
Be used for signer and deny the step of the chameleon signature that the verifier generates to trusted third party;
It is characterized in that:
Wherein said disclosed system parameters comprises: clearance D iffie-Hellman group G
1, group G
1Generator P, the rank of generator P are big prime number q; Cyclic group G
2, group G
2Rank also be big prime number q; To mapping Function e: G
1* G
1→ G
2The collisionless hash function H:{0 of universe, 1}
*→ G
1The Digital Signature Algorithm based on identity of any one safety (JG, JE, JS, JV); The PKI P of trusted third party
Pub=sP, wherein s is the private key of trusted third party; The signature private key x that wherein said signer has
SGenerate its verification public key Q by algorithm JE
S=H (S), S are the signer identity; The trapdoor private key that wherein said verifier has is x
R=sQ
R, disclosed chameleon PKI Q
R=H (R), R are verifier's identity; When wherein said signer used signature private key and chameleon PKI to calculate the Chameleon digital signature of digital content, the message of being signed was
Signer is selected random integers
Generate Bit String I, calculate chameleon Hash Value H, the computational methods of this chameleon Hash Value H relate to Bit String I, message m, generator P, integer α.
2. a kind of Chameleon digital signature method that generates and verify digital content according to claim 1, the computational methods that it is characterized in that described chameleon Hash Value H are H=α P+mH (I)).
3. a kind of the generation and the Chameleon digital signature method of checking digital content according to claim 1 is characterized in that described Bit String I comprises temporal information or sequence number information that signer identity information, verifier's identity information and signer and verifier consult.
4. a kind of Chameleon digital signature method that generates and verify digital content according to claim 2 is characterized in that the Chameleon digital signature that described signer uses signature private key and chameleon PKI to calculate digital content generates as follows:
(1) signer uses signature private key x
S, use Digital Signature Algorithm JS, to chameleon Hash Value H signature, obtain the signature value
(2) signer uses chameleon PKI Q
R, the PKI P of trusted third party
Pub, integer α to the mapping Function e, calculates group G
1Element α P and group G
2Element e (α P
Pub, Q
R);
(3) signature about message m of signer generation is (α P, e (α P
Pub, Q
R), δ).
5. a kind of the generation and the Chameleon digital signature method of checking digital content according to claim 4, when it is characterized in that described verifier uses the disclosed verification public key of signer, chameleon PKI and trapdoor private key to verify the correctness of Chameleon digital signature according to following steps:
(1) verifier at first utilizes first element α P and the private key sQ of signature
RCalculate e (α P, sQ
R);
(2) second element e (the α P that relatively signs
Pub, Q
R) with claim 5 step (1) in the value e (α P, the sQ that calculate
R) whether identical, if difference then think this signature for false, otherwise continue to judge;
(3) verifier generates Bit String I;
(4) use message m to calculate mH (I);
(5) verifier uses first element of signature and calculates resulting mH (I) and calculate chameleon Hash Value H=α P+mH (I)
(6) verifier uses the identity S of signer, and the chameleon Hash Value H of gained in claim 5 step (5) is according to the correctness of coming certifying signature δ based on the defined proof procedure of the digital signature verification algorithm JV of identity.Think signature if signature verification is failed for false, otherwise think that signature is true.
6. a kind of the generation and the Chameleon digital signature method of checking digital content according to claim 5 is characterized in that described signer denies chameleon signature (α * P, e (the α * P that the verifier generates to trusted third party
Pub, Q
R), in the time of δ), can deny the chameleon signature to trusted third party by following step:
(1) signer is to part chameleon signature value (α P, e (the α P of trusted third party's displaying about message m
Pub, Q
R)), message m and α P and e (α P
Pub, Q
R) have the evidence of identical integer α, perhaps show part chameleon signature value (g about message m to trusted third party
α,
), message m is that group element H-α P is knowledge proof and the α P and e (the α P of the elliptic curve discrete logarithm at the end with H (I)
Pub, Q
R) have the evidence of identical integer α;
(2) if signer provides message m, if the message that the chameleon signature that the inspection verifier of trusted third party provides is signed is different with m, H=α P+mH (I), and checking α P and e (α P
Pub, Q
R) have and regard as behind the evidence of identical integer α correctly, just can judge that the chameleon signature of submitting to trusted third party is vacation; The m if signer does not give information, trusted third party check α P ≠ α * P, and checking m is that group element H-α P regards as correctly behind the knowledge proof of elliptic curve discrete logarithm at the end, verify α P and e (α P
Pub, Q
R) have and regard as behind the evidence of identical integer α correctly, just can judge that the chameleon signature of submitting to trusted third party is vacation.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US10326753B2 (en) | 2016-06-23 | 2019-06-18 | International Business Machines Corporation | Authentication via revocable signatures |
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| CN102256247A (en) * | 2011-06-17 | 2011-11-23 | 西安电子科技大学 | Universal construction for safely and effectively switching authentication scheme in wireless network |
| CN102256247B (en) * | 2011-06-17 | 2014-06-04 | 西安电子科技大学 | Universal construction for safely and effectively switching authentication scheme in wireless network |
| CN104219047A (en) * | 2013-05-31 | 2014-12-17 | 华为技术有限公司 | A signature verification method and apparatus |
| CN104219047B (en) * | 2013-05-31 | 2017-12-15 | 华为技术有限公司 | A kind of method and apparatus of signature verification |
| CN107172586A (en) * | 2017-05-19 | 2017-09-15 | 北京航空航天大学 | Mobile terminal network localization method based on block chain |
| CN110071812A (en) * | 2019-04-29 | 2019-07-30 | 电子科技大学 | A kind of editable can link, the ring signatures method of non-repudiation |
| CN110071812B (en) * | 2019-04-29 | 2021-06-08 | 电子科技大学 | Editable, linkable and non-repudiatable ring signature method |
| CN114710298A (en) * | 2022-06-02 | 2022-07-05 | 深圳天谷信息科技有限公司 | Method, device, equipment and medium for batch signature of documents based on chameleon Hash |
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