CN103259662A - Novel procuration signature and verification method based on integer factorization problems - Google Patents

Novel procuration signature and verification method based on integer factorization problems Download PDF

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CN103259662A
CN103259662A CN2013101574422A CN201310157442A CN103259662A CN 103259662 A CN103259662 A CN 103259662A CN 2013101574422 A CN2013101574422 A CN 2013101574422A CN 201310157442 A CN201310157442 A CN 201310157442A CN 103259662 A CN103259662 A CN 103259662A
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allograph
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CN103259662B (en
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禹勇
夏琦
倪剑兵
黄可
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a novel procuration signature and verification method based on integer factorization problems. The novel procuration signature and verification method based on the integer factorization problems includes the steps: before a network operates, firstly generating personal public keys and private keys by original signature people and procuration signature people, and issuing the public keys; when signature requests are provided, generating authorization letters by the original signature people, and calculating signature authorization based on a chameleon hash function and an ordinary digital signature algorithm, sending the signature authorization to the procuration signature people, carrying out validity verification on the received signature authorization by the procuration signature people, if the signature authorization is effective, generating the procuration signature based on collision property of the chameleon hash function, and digital signature does not need to be carried out on information, when a verifier receives the authorization letters and the procuration signature, firstly, verifying whether the authorization letters are effective or not, after the authorization letters are verified to be effective, and then verifying validity of the procuration signature. According to the application of the novel procuration signature and verification method based on the integer factorization problems, processing efficiency of the procuration signature is high, and the length of the procuration signature is short. The novel procuration signature and verification method based on the integer factorization problems is suitable for environments such as mobile networks and the wireless networks where computing power and network bandwidth are limited.

Description

A kind of new allograph and verification method based on the integer resolution problem
Technical field
The invention belongs to the network security technology field, relate to public key cryptography and digital signature, be specifically related to a kind of new allograph and verification method based on the integer resolution problem.
Background technology
Along with development of computer network with popularize, information security issue also becomes the social concern that common people pay close attention to, and in information world, how to realize authenticating, data integrity and non-repudiation become the emphasis that numerous scholars explore.Digital signature is as the digital substitute of handwritten signature, the natural broad research that has obtained password educational circles.Need based on different application in people's real life, numerous have the digital signature scheme of special purpose to be proposed in succession, and allograph is the important means that solves the signature authorises problem in the digital signature.To be an entity or colony entrust to a kind of behavior that another one entity or colony implement to some the signature rights of oneself to signature authorises, and this mandate is needing the occasion of commission order that important application is arranged such as mobile agent, Distributed Calculation, grid computing and wireless network etc.
In existing allograph method based on the integer resolution problem, adopt the string data mode to realize: original signature people is the certificate of entrustment (PKI that comprises the original signature people to generating at first, allograph people's PKI, the term of validity of authorizing and allograph message etc.) carry out digital signature, obtain signature authorises and (comprise certificate of entrustment, certificate of entrustment is signed) and send to the allograph people, the allograph people utilizes signature authorises and the private key of oneself, message in the certificate of entrustment is carried out digital signature, produce final allograph, and this allograph is made up of to information signature two parts signature authorises and the allograph people of original signature.
During the last ten years, Chinese scholars has been carried out deep research to allograph, has obtained great successes, comprises the discussion to security model, proposes new departure, to the analysis of existing scheme and improvement etc.Yet also there are following problem in the research of allograph and application:
(1) present allograph mostly utilizes bilinearity to designing, and the operand that bilinearity is right is big, and is many to the consumption of computational resource, can't be applied to the computing capability constrained environment;
(2) existing allograph based on the integer resolution problem is the signature authorises of original signature and allograph people two signatures of signature of message to be made of in essence, this makes that final allograph length is long, the transmission of allograph can consume more bandwidth, is not suitable for the limited network environment of bandwidth;
(3) existing several allograph method based on the integer resolution problem proves because rational security model and fail safe are not provided, cause to resist a kind of or two kinds of attacks in outside opponent, malicious agent signer, three types of attacks of malice original signature people, so existing several allograph method based on the integer resolution problem is generally dangerous.
Summary of the invention
Goal of the invention of the present invention is: at the problem of above-mentioned existence, provide the new allograph method based on the integer resolution problem that a kind of processing speed is fast, allograph length is short.
A kind of new allograph method based on the integer resolution problem of the present invention comprises the following steps:
Step 1: generate original signature people's private key, PKI, allograph people's private key, PKI;
Step 2: the allograph people generates interim PKI r according to its private key, PKI 1, and send to the original signature people;
Step 3: original signature people receives interim PKI r 1After, at first generating certificate of entrustment w, this certificate of entrustment w comprises original signature people's PKI, allograph people's PKI, the term of validity of mandate and the message m of allograph, selects integer t more at random 0, based on the cryptographic Hash h of the certificate of entrustment w calculating chameleon hash function that generates 2, and to described cryptographic Hash h 2Carry out digital signature, obtain certificate of entrustment w signature; And by safe lane signature authorises being sent to the allograph people, described signature authorises comprises certificate of entrustment w, certificate of entrustment signature, integer t 0
Step 4: the allograph people carries out validation verification to the signature authorises of receiving, if effectively, then execution in step 5;
Step 5: the allograph people verifies whether the allograph message m meets certificate of entrustment w, if, then:
Private key, PKI according to the allograph people generate interim PKI r 2
According to described interim PKI r 2, based on collision (certificate of entrustment w, the integer t of chameleon hash function 0Chameleon hash functional value and message m, random number t 1The chameleon hash functional value equate, be cryptographic Hash h 2) generation message m random number corresponding t 1
By certificate of entrustment signature, interim PKI r 2, random number t 1Constitute the allograph of message m under certificate of entrustment w.
Realize allograph of the present invention owing to the present invention is based on the collision of chameleon hash function, guaranteeing under the prerequisite that no key is revealed, its processing speed is fast, resource consumption is few, and final allograph is shorter than the length of existing Proxy Signature Scheme based on the integer resolution problem, allograph people of the present invention is based on the collision of chameleon hash function, only need find out the collision of given chameleon hash value (based on the cryptographic Hash of the chameleon hash function of certificate of entrustment w), just can generate allograph, and need not to calculate again signature to message m, shorten the length of existing allograph based on the integer resolution problem, reduced the amount of calculation of allograph generative process; And because the length of allograph of the present invention is short, the bandwidth that its transmission consumes is few, is specially adapted to the signature authorises business of resource-constrained wireless network environment.
Simultaneously, by the generative process of allograph of the present invention as can be known, its allograph has unforgeable, and this has just resisted malicious agent signer's attack; And under the prerequisite of the trapdoor of not knowing chameleon hash function of the present invention (trap door information), original signature people can't forge allograph, and this has just prevented malice original signature people's attack; The attack resource that has because of outside opponent is far fewer than malicious agent signer and malice original signature people, so since the present invention can resist malicious agent signer and malice original signature people's attack, then also can resist outside opponent's attack.
Further, in order to ensure allograph method validation of the present invention fail safe, in step 1, select the p that satisfies condition at random according to security parameter k 0≡ 3mod8, q 0The prime number p of ≡ 7mod8 0, q 0As original signature people's private key, and with p 0, q 0Product n 0As original signature people PKI.
In order further to improve fail safe of the present invention, allograph people's of the present invention private key, PKI can be:
Select two safe prime p at random according to security parameter k 1, q 1Private key for the allograph people; Get p 1, q 1Product be N1, select the multiplication group of integers
Figure BDA00003133921600031
On an integer λ (n 1) the element g on rank, described
Figure BDA00003133921600032
Integer
Figure BDA00003133921600033
Figure BDA00003133921600034
Then with described n 1, g is as allograph people's PKI.
The invention allows for a kind of signature verification method at allograph method of the present invention, comprise the following steps:
Whether the checking message m meets certificate of entrustment w, if not, then stops; Otherwise,
Based on message m, certificate of entrustment w, allograph, and whether allograph people's PKI, original signature people's PKI surveying agent signature is effective.
In sum, owing to adopted technique scheme, the invention has the beneficial effects as follows:
(1) length of allograph of the present invention is short, and the allograph processing speed is fast, and resource consumption is few;
(2) because the length of allograph of the present invention is short, the bandwidth that its transmission consumes is few, is specially adapted to the authorization activities of resource-constrained wireless network environment;
(3) the present invention is because Proxy Signature Scheme can be resisted original signature people's the attack of allograph people, the malice of outside opponent, malice, the theoretical proof fail safe of the present invention of deriving can be foretelling under the machine model stipulations at random to the integer resolution problem, and is safe.
Description of drawings
To illustrate by example and with reference to the mode of accompanying drawing, wherein:
Fig. 1 is allograph process flow diagram of the present invention;
Fig. 2 is that signature authorises of the present invention generates-verify flow chart;
Fig. 3 is that allograph of the present invention generates-verify flow chart.
Embodiment
Disclosed all features in this specification, or the step in disclosed all methods or the process except mutually exclusive feature and/or step, all can make up by any way.
Disclosed arbitrary feature in this specification (comprising any accessory claim, summary and accompanying drawing) is unless special narration all can be replaced by other equivalences or the alternative features with similar purpose.That is, unless special narration, each feature is an example in a series of equivalences or the similar characteristics.
With reference to Fig. 1, specific implementation process of the present invention is as follows:
Process 1, the key of original signature people Alice and allograph people Bob generates
(1.1) before the network operation, Alice selects the p that satisfies condition at random according to security parameter k 0≡ 3mod8 and q 0The prime number p of ≡ 7mod8 0And q 0, i.e. p 0For divided by 8 remainders being arbitrary prime number of 3, q 0For divided by 8 remainders being arbitrary prime number of 7, with p 0And q 0As the long-term private of Alice, and calculate prime number p 0And q 0Product n 0=p 0q 0PKI as Alice;
(1.2) Bob selects two safe prime p at random according to security parameter k 1, q 1And group
Figure BDA00003133921600041
On an integer λ (n 1) the element g on rank, the computationally secure prime number p 0And q 0Product n 1=p 1q 1, integer
Figure BDA00003133921600042
Figure BDA00003133921600048
With the Ka Mixieer function
Figure BDA00003133921600043
Select the group then
Figure BDA00003133921600044
Last element g.The PKI of Bob and private key are respectively (n 1, g) with (p 1, q 1).
So-called safe prime namely requires the prime number of selection according to security parameter, and security parameter is the security requirement that obtains agreement according to scheme, and a pre-determined parameter of describing fail safe is binary bits how long in order to determine safe prime.Security parameter is made as k among the present invention, and value is generally 512,768,1024 or 2048 etc.
Process 2, original signature people Alice licenses to allograph people Bob with signature capabilities
When Alice has the demand of signature information, but when busier or own need limited in one's ability license to Bob with signature capabilities because of self, the Alice calculating and sending gives its signature authorises to give Bob, and whether Bob mandate of checking Alice earlier before generating allograph is effective.With reference to Fig. 2, being implemented as follows of this process:
(2.1) when Alice need license to Bob with signature capabilities, at first generate certificate of entrustment w, this certificate of entrustment comprises the PKI of Alice, the PKI of Bob, the term of validity of mandate and the message m of allograph etc.;
(2.2) Bob selects temporary private
Figure BDA00003133921600045
And calculate interim PKI
Figure BDA00003133921600046
Interim PKI r 1Send to Alice;
(2.3) Alice receives interim PKI r 1After, utilize certificate of entrustment w and the private key (p of oneself 0, q 0) generate its signature authorises (w, t 0, s 0, a 0, b 0), and by safe lane signature authorises is sent to Bob; The implementation procedure that Alice generates signature authorises is as follows:
(2.3a) Alice selects integer t at random 0, the hash value of calculating chameleon hash (hash) function: H wherein 2(w, r 1) be to be input as w||r 1Hash function, operation is appended in symbol " || " expression, namely r 1Append after w; Again with hash value h 2The certificate of entrustment w that generates with Alice is as part territory hash function H 1Input, calculating section territory hash value h w=H 1(h 2, w);
(Partial-Domain Hash, PDH) size that refers to the hash function is a factor of modulus to so-called part territory hash function.Part territory hash function H among the present invention 1: { 0,1} *→ [h 1, h' 1) and
Figure BDA00003133921600049
Can be based on the consequence devised of Gentry, the distortion of the proposition of Gentry sees for details: C.Gentry.How to compress Rabin ciphertexts and signatures.In:Advances in Cryptology Crypto2004, LNCS3152, Springer-Verlag, 2004:179-200.
(2.3b) Alice calculates the Jacobi symbol, determines parameter a by the Jacobi symbol 0And b 0Value:
Figure BDA00003133921600051
Figure BDA00003133921600052
(2.3c) Alice utilizes the private key (p of oneself 0, q 0) to part territory hash value h wSign, obtain the signature value:
s 0 ≡ ( 2 - a 0 h w ) n 0 - p 0 - q 0 + 5 8 mod n 0
(2.3d) Alice by safe lane with its signature authorises (w, t 0, s 0, a 0, b 0) send to allograph people Bob.
(2.4) Bob receives signature authorises (w, the t of Alice 0, s 0, a 0, b 0) after, at first utilize certificate of entrustment w to calculate the hash value of chameleon hash function again
Figure BDA00003133921600054
, with the hash value
Figure BDA00003133921600055
With certificate of entrustment w as part territory hash function H 1Input, calculating section territory hash value h w * = h 1 ( h 2 * , w ) , formula is verified in check then s 0 2 ≡ 2 - a 0 2 h w * ( - 1 ) b 0 mod n 0 Whether set up, if the checking formula is set up, represent that then signature authorises is effective, enter process 3; Otherwise signature authorises is invalid.
Process 3, Bob generates allograph
Allograph people Bob verifies at first whether message m meets certificate of entrustment w, if do not meet, then stops, otherwise utilizes message m, the private key (p of oneself 1, q 1) and certificate of entrustment w calculate the allograph σ=(a of message m based on the collision of chameleon hash function 0, b 0, s 0, r 2, t 1).Last Bob sends to the verifier to certificate of entrustment w and allograph σ.With reference to Fig. 3, the specific implementation process that generates allograph σ is as follows:
(3.1) Bob at first checks message m whether to meet certificate of entrustment w, if do not meet, then exports engineering noise and termination; Otherwise, enter step (3.2);
(3.2) Bob selects random value
Figure BDA00003133921600058
With temporary private k 1Be updated to k 2, and calculate new interim PKI r 2 ≡ g k 2 mod n 1 ;
(3.3) Bob generates message m random number corresponding t based on the collision of the chameleon hash functional value of certificate of entrustment w and message m 1:
t 1 ≡ t 0 + ( k 2 - k 1 ) + 2 λ ( n 1 ) ( H 2 ( w , r 1 ) - H 3 ( m , r 2 ) ) mod λ ( n 1 ) ,
Wherein, t 0In step (2.3a), the integer that Alice selects at random, λ (n 1) be the Ka Mixieer function, by (the p of Bob 1, q 1) determine H 2(w, r 1) refer to be input as message w and interim PKI r 1General hash function, H 3(m, r 2) refer to be input as m||r 2Hash function;
(3.4) allograph of message m under certificate of entrustment w is σ=(a 0, b 0, s 0, r 2, t 1).
Process 4, the verifier verifies the validity of allograph σ
The verifier receives allograph σ=(a of Bob 0, b 0, s 0, r 2, t 1) after, whether surveying agent's signature sigma is the effective allograph of message m under certificate of entrustment w.With reference to Fig. 3, being implemented as follows of this process:
(4.1) verifier at first checks message m whether to meet certificate of entrustment w, if do not meet, then exports engineering noise and termination; Otherwise, enter step (4.2);
(4.2) verifier utilizes allograph σ to calculate chameleon hash function
Figure BDA00003133921600061
With the hash value With certificate of entrustment w as part territory hash function H 1Input, calculating section territory hash value
Figure BDA00003133921600063
(4.3) verifier checks the checking formula
Figure BDA00003133921600064
Whether set up, if set up, represent that then allograph is effective; Otherwise allograph is invalid.
The present invention is not limited to aforesaid embodiment.The present invention expands to any new feature or any new combination that discloses in this manual, and the arbitrary new method that discloses or step or any new combination of process.

Claims (7)

1. the new allograph method based on the integer resolution problem is characterized in that, comprises the following steps:
Step 1: generate original signature people's private key, PKI, allograph people's private key, PKI;
Step 2: the allograph people generates interim PKI r according to its private key, PKI 1, and send to the original signature people;
Step 3: original signature people receives interim PKI r 1After, at first generate certificate of entrustment w, select integer t more at random 0, based on the cryptographic Hash h of the certificate of entrustment w calculating chameleon hash function that generates 2, and to described cryptographic Hash h 2Carry out digital signature, obtain certificate of entrustment w signature; And by safe lane signature authorises being sent to the allograph people, described signature authorises comprises certificate of entrustment w, certificate of entrustment signature, integer t 0
Step 4: the allograph people carries out validation verification to the signature authorises of receiving, if effectively, then execution in step 5;
Step 5: the allograph people verifies whether the allograph message m meets certificate of entrustment w, if, then:
Private key, PKI according to the allograph people generate interim PKI r 2
According to described interim PKI r 2, generate message m random number corresponding t based on the collision of chameleon hash function 1, the collision of described chameleon hash function is: the chameleon hash functional value of certificate of entrustment w, integer t0 and message m, random number t 1The chameleon hash functional value equate, be cryptographic Hash h 2
By certificate of entrustment signature, interim PKI r 2, random number t 1Constitute the allograph of message m under certificate of entrustment w.
2. the method for claim 1 is characterized in that, in the described step 1,
Select the p that satisfies condition at random according to security parameter k 0≡ 3mod8, q 0The prime number p of ≡ 7mod8 0, q 0As original signature people's private key, and with p 0, q 0Product n 0As original signature people PKI.
3. method as claimed in claim 1 or 2 is characterized in that, in the described step 1,
Select two prime number p at random according to security parameter k 1, q 1Private key for the allograph people;
Get described p 1, q 1Product be n 1, select the multiplication group of integers
Figure FDA00003133921500011
On an integer λ (n 1) the element g on rank, described λ ( n 1 ) = 2 p 1 * q 1 * , Integer p 1 * = p 1 - 1 2 , q 1 * = q 1 - 1 2 , Then with described n 1, g is as allograph people's PKI.
4. method as claimed in claim 3 is characterized in that, in the described step 2, the allograph people is from the addition group of integers
Figure FDA00003133921500015
The middle random number k of selecting 1As temporary private, and calculate interim PKI
Figure FDA00003133921500016
5. method as claimed in claim 3 is characterized in that, in the step 3, obtains described certificate of entrustment w signature and comprises the following steps:
Original signature people is according to integer t 0, the cryptographic Hash of calculating chameleon hash function , H wherein 2(w, r 1) be to be input as w||r 1Hash function, operation is appended in symbol " || " expression; Again with cryptographic Hash h 2With certificate of entrustment w as part territory hash function H 0Input, obtain part territory cryptographic Hash h w=H 1(h 2, w);
Original signature people determines parameter a based on the Jacobi symbol 0And b 0Value:
Figure FDA00003133921500021
Original signature people is based on its private key (p 0, q 0) to part territory cryptographic Hash h wSign, obtain signature value s 0: s 0 ≡ ( 2 - a 0 h w ) n 0 - p 0 - q 0 + 5 8 mod n 0 ;
By parameter a 0, b 0, s 0Constitute described certificate of entrustment w signature;
In the then described step 4, validation verification is:
The allograph people calculates the cryptographic Hash of chameleon hash function again based on certificate of entrustment w
Figure FDA00003133921500024
With described cryptographic Hash
Figure FDA00003133921500025
With certificate of entrustment w as part territory hash function H 1Input, calculating section territory cryptographic Hash h h * = H 1 ( h 2 * , w ) , By check checking formula s 0 2 ≡ 2 - a 0 2 h w * ( - 1 ) b 0 mod n 0 Whether become Rob Roy to finish validation verification;
In described step 5, generate message m random number corresponding t 1Be specially:
The allograph people selects random number
Figure FDA00003133921500028
With temporary private k 1Be updated to k 2, generate new interim PKI r 2 ≡ g k 2 mod n 1 , Random number t then 1For:
t 1 ≡ t 0 + ( k 2 - k 1 ) + 2 λ ( n 1 ) ( H 2 ( w , r 1 ) - H 3 ( m , r 2 ) ) mod λ ( n 1 ) ,
H wherein 3(m, r 2) be to be input as m||r 2Hash function.
6. based on the signature verification method of the allograph method of claim 1, it is characterized in that, comprise the following steps:
Whether the checking message m meets certificate of entrustment w, if not, then stops; Otherwise,
Based on certificate of entrustment w, allograph, and whether allograph people's PKI, original signature people's PKI surveying agent signature is effective.
7. based on the signature verification method of the allograph method of claim 6, it is characterized in that, comprise the following steps:
Step S1: whether the check message m meets certificate of entrustment w, if then stop; Otherwise, execution in step S2;
Step S2: according to the random number t of the chameleon hash function in message m, the allograph 1, and allograph people's PKI n 1, g, interim PKI r 2Calculate the chameleon hash function
Figure FDA000031339215000211
With described cryptographic Hash
Figure FDA000031339215000212
With certificate of entrustment w as part territory hash function H 1Input, calculating section territory cryptographic Hash
Figure FDA000031339215000213
Again based on original signature people's PKI n 0And allograph, check checking formula
Figure FDA00003133921500031
Whether set up, if represent that then allograph is effective; Otherwise allograph is invalid.
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