CN106533698A - RSA-based distributed threshold signature method and system - Google Patents

RSA-based distributed threshold signature method and system Download PDF

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Publication number
CN106533698A
CN106533698A CN201611160582.5A CN201611160582A CN106533698A CN 106533698 A CN106533698 A CN 106533698A CN 201611160582 A CN201611160582 A CN 201611160582A CN 106533698 A CN106533698 A CN 106533698A
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signature
component
private key
components
calculated
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杨国强
刘会议
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Beijing Sansec Technology Development Co Ltd
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Beijing Sansec Technology Development Co Ltd
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Priority to CN201611160582.5A priority Critical patent/CN106533698A/en
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
    • H04L9/3249—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using RSA or related signature schemes, e.g. Rabin scheme

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  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Computer And Data Communications (AREA)

Abstract

The present invention relates to an RSA-based distributed threshold signature method and system. The method comprises the following steps of generating a private key component di corresponding to a signature end, wherein i is an element of a set [1, n], and n represents a quantity of all signature ends and is greater than or equal to 3; initiating signature, and obtaining a signature component si according to the private key component di; sending a signature request to other signature ends joining in signature; acquiring signature components generated by other signature ends joining in signature according to the signature request; and obtaining a complete signature s according to the signature components of all signature ends joining in signature. The RSA-based distributed threshold signature method and system provided by the present invention has advantages of being widely used, being high in security, and being easy to implement.

Description

A kind of distributed Threshold Signature method and system based on RSA
Technical field
The present invention relates to information security field, more particularly to a kind of distributed Threshold Signature method and system based on RSA.
Background technology
Digital signature is the important part for ensureing RESEARCH OF CHAOS-BASED SECURITY COMMUNICATION, and current common digital signature scheme is logical Intelligent code key storage key information is crossed, when signature is needed, is coordinated by middleware and is called intelligent code key to complete to sign Name.
With the popularization of mobile Internet, increasing signature service progressively moves to mobile terminal, more user's choosings Select by intelligent movable equipment to carry out business operation, but traditional intelligent code key be difficult to play a role in mobile terminal, Mainly include following several respects reason：
1. intelligent code key is inconvenient to carry, and user needs to carry extra signature apparatus；
2. hardware interface cannot be docked, and mobile terminal cannot provide the interface of docking traditional intelligence cipher key；
3. middle unit development is difficult, and the middle unit development difficulty called for hardware is larger.
And existing digital signature technology usually needs the intervention of third party's certificate agency, the safety of signature is easily reduced Property, therefore, how under the premise of ensureing user easily, there is provided can be used in the high security digital signature technology of mobile terminal, It is the problem of urgent need to resolve instantly.
The content of the invention
The technical problem to be solved is for the deficiencies in the prior art, there is provided a kind of based on the distributed of RSA Threshold Signature method and system, Threshold Signature are the popularizations to ordinary numbers signature, its difference with ordinary numbers signature It is：Ordinary numbers signature is signed by signer complete independently, and Threshold Signature completes digital signature jointly by multiple members, and And each member for signing mutually is unaware of to respective secret information.
The technical scheme that the present invention solves above-mentioned technical problem is as follows：
A kind of distributed Threshold Signature method based on RSA, comprises the following steps：
Step 1, generates private key component d corresponding with signature endi, i ∈ [1, n], n are all signature end quantity, n >=3；
Step 2, initiates signature, according to the private key component diObtain signature components si；
Step 3, the signature end to other participation signatures send signature request；
Step 4, obtains the signature components that other described signature ends for participating in signature are generated according to the signature request；
Step 5, obtains full signature s according to the signature components at the whole signature ends for participating in signature.
The invention has the beneficial effects as follows：A kind of distributed Threshold Signature method based on RSA that the present invention is provided, by pre- The private key component at signature end is first generated, and after signature is initiated, participates in the signature end private key component respectively according to oneself of signature Respective signature components are generated, signature components are integrated into into complete signature finally, improve the security of signature, signature process It is simple and convenient, it is only necessary to which that interaction twice can just complete complete signature, by the flexible quantity and ginseng for arranging all signature ends With the quantity at the signature end of signature, in that context it may be convenient to realize the even multi-party distributed signature of both sides, can thus support Single server unit/terminal or the distributed signature of single server multiple terminals, while the present invention does not need third party's certificate agency Intervention, is not in complete private key in signature process, further increases the security of signature, and the present invention has application wide Advantage that is general, safe, being easily achieved.
On the basis of above-mentioned technical proposal, the present invention can also do following improvement.
Further, step 1 is specifically included：
Step 11, it is random to generate procatarxis subcomponent piAnd qi；
Step 12, according to procatarxis subcomponent piAnd qiIt is calculated component product N；
Step 13, carries out test for primality to component product N, if component product N is prime number, execution step 14, otherwise, execution step 11；
Step 14, according to procatarxis subcomponent piAnd qiIt is calculated the factor component of the rank of component product N
Step 15, randomly selects public key value e；
Step 16, by distributed detection, judge public key value e withIt is whether coprime, if coprime, Execution step 17, otherwise, execution step 15, wherein,
Step 17, according to describedPrivate key component d is calculated with public key value ei, i ∈ [1, n], n is complete Portion's signature end quantity, n >=3.
Using the beneficial effect of above-mentioned further scheme it is：By procatarxis subcomponent piAnd qiDescribed point is calculated directly The factor component of the rank of amount product NAnd according toPrivate key is obtained by Distributed Calculation with public key value e Component di, can avoid occurring complete private key d in signature process, further increase the safety of private key in signature process Property.
Further, step 2 is specifically included：
Step 21, obtains signature request m0；
Step 22, according to the m0It is calculated signature request information m, m=h (m0), h is the Hash for meeting signature agreement Function；
Step 23, according to signature request information m, the private key component diInstitute is calculated with component product N State signature components s at signature endi。
Further, according to below equation, component product N is calculated by Secure Multi-party Computation Protocols are distributed：
The factor component of the rank of component product N is calculated according to below equation
As i=1,
Work as i>When 1,
Further, according to below equation, the private key component d is calculated by Secure Multi-party Computation Protocols are distributedi：
Wherein, ciFor Lagrange interpolation coefficient.
Further, signature components s are calculated according to below equationi：
Wherein, ciFor Lagrange interpolation coefficient.
Further, full signature s is calculated according to below equation：
Wherein, t is the signature end quantity for participating in signature.
Another kind of technical scheme that the present invention solves above-mentioned technical problem is as follows：
A kind of distributed Threshold Signature system based on RSA, including：N signature end, n >=3, the signature end include：
Registering modules, for generating private key component d corresponding with end of signingi, i ∈ [1, n]；
Signature blocks, for initiating signature, according to the private key component diObtain signature components si, to other participation signatures The signature end send signature request, obtain the label that other described signature ends for participating in signature are generated according to the signature request Name component, obtains full signature s according to the signature components at the whole signature ends for participating in signature.
Further, the Registering modules are specifically included：
Signal generating unit, generates procatarxis subcomponent p for randomiAnd qi；
Computing unit, for according to procatarxis subcomponent piAnd qiComponent product N is calculated, and calculates the component The factor component of the rank of product NAnd according toPrivate key component d is obtained with public key value ei, wherein,
Detector unit, for carrying out test for primality to component product N, if component product N is not prime number, Perform signal generating unit, if component product N is prime number, perform computing unit calculate component product N rank because Subcomponent
Unit is chosen, for randomly selecting public key value e；
Judging unit, for by distributed detection, judge public key value e with it is describedIt is whether coprime, such as It is really coprime, then computing unit is performed according to describedPrivate key component d is calculated with public key value ei, otherwise, perform Choose unit.
Further, the signature blocks are specifically included：
First signature unit, for initiating signature, according to the private key component diObtain signature components si；
Communication unit, for sending signature request to the signature end of other participation signatures, and obtains other participation label The signature components that the signature end of name is generated according to the signature request；
Second signature unit, for obtaining full signature s according to the signature components at the whole signature ends for participating in signature.
The advantage of the additional aspect of the present invention will be set forth in part in the description, and partly will become from the following description Obtain substantially, or recognized by present invention practice.
Description of the drawings
Fig. 1 is a kind of schematic flow sheet of distributed Threshold Signature method based on RSA provided in an embodiment of the present invention；
A kind of flow chart of distributed Threshold Signature method based on RSA that Fig. 2 is provided for another embodiment of the present invention；
A kind of structure chart of distributed Threshold Signature system based on RSA that Fig. 3 is provided for another embodiment of the present invention.
Specific embodiment
The principle and feature of the present invention are described below in conjunction with accompanying drawing, example is served only for explaining the present invention, and It is non-for limiting the scope of the present invention.
As shown in figure 1, showing for a kind of flow process of the distributed Threshold Signature method based on RSA provided in an embodiment of the present invention It is intended to, the distributed Threshold Signature method includes：
S101, generates private key component d corresponding with signature endi, i ∈ [1, n], n are all signature end quantity, n >=3；
S102, initiates signature, according to private key component diObtain signature components si；
S103, the signature end to other participation signatures send signature request；
S104, obtains the signature components that other signature ends for participating in signature are generated according to signature request；
S105, obtains full signature s according to the signature components at the whole signature ends for participating in signature.
A kind of distributed Threshold Signature method based on RSA provided in above-described embodiment, by previously generating signature end Private key component, and after signature is initiated, the signature end for participating in signature generates respective label according to the private key component of oneself respectively Signature components are finally integrated into complete signature, improve the security of signature by name component, and signature process is simple and convenient, only Need to interact twice and can just complete complete signature, all quantity at signature end and the signature for participating in signature are set by flexible The quantity at end, in that context it may be convenient to realize the even multi-party distributed signature of both sides, can thus support single server monohapto End or the distributed signature of single server multiple terminals, and the intervention of third party's certificate agency is not needed, in signature process Be not in complete private key, further increase the security of signature, above-described embodiment have be widely used, it is safe, The advantage being easily achieved.
In another embodiment, as shown in Fig. 2 for another embodiment of the present invention provide it is a kind of based on the distributed of RSA The flow chart of Threshold Signature method, including 5 signature ends, respectively A, B, C, D and E, initiate signature request by signature end A, sign B and C participate in signature at name end, then the distributed Threshold Signature mode is comprised the following steps：
S201, signature end A generate procatarxis subcomponent p at randomiAnd qi；
S202, signature end A is according to procatarxis subcomponent piAnd qiIt is calculated component product N；
S203, signature end A carry out test for primality to component product N, if component product N is prime number, perform S204, no Then, perform S201；
S204, signature end A is according to procatarxis subcomponent piAnd qiIt is calculated the factor component of the rank of component product N
S205, signature end A randomly select public key value e；
S206, signature end A by distributed detection, judge public key value e andIt is whether coprime, if coprime, S207 is performed, otherwise, S205 is performed, wherein,
S207, signature end A according toPrivate key component d is calculated with public key value eA；
S208, signature end A generate signature request m0；
S209, signature end A is according to m0It is calculated signature request information m, m=h (m0), h is the Hash for meeting signature agreement Function；
S210, signature end A is according to signature request information m, private key component dAThe label at signature end are calculated with component product N Name component sA；
S211, signature end A send signature request information m to signature end B and signature end C；
S212, signature end B and signature end C generate signature components s according to signature request information m respectivelyBAnd sC；
S213, signature end A obtain sBAnd sC；
S214, signature end A is according to sA、sBAnd sCObtain full signature s.
Further, according to below equation, component product N is calculated by Secure Multi-party Computation Protocols are distributed：
The factor component of the rank of component product N is generated according to below equation
As i=1,
Work as i>When 1,
Further, according to below equation, by the distributed calculating private key component d of Secure Multi-party Computation ProtocolsA：
Wherein, cAFor Lagrange interpolation coefficient.
Further, signature components s are calculated according to below equationA：
Wherein, cAFor Lagrange interpolation coefficient.
Further, full signature s is calculated according to below equation：
In another embodiment, as shown in figure 3, for another embodiment of the present invention provide it is a kind of based on the distributed of RSA The structure chart of Threshold Signature system, the distributed Threshold Signature system include：4 signature ends, the respectively first signature end 300, Second signature end, the 3rd signature end and the 4th signature end, wherein, the first signature end 300 includes：
Registering modules 310, for generating private key component d corresponding with end of signing1；
Signature blocks 320, for initiating signature, according to private key component d1Obtain signature components s1, to other participation signatures Signature end sends signature request, obtains the signature components that other signature ends for participating in signature are generated according to signature request, according to ginseng Full signature s is obtained with the signature components at whole signature ends of signature.
Further, Registering modules 310 are specifically included：
Signal generating unit 311, generates procatarxis subcomponent p for randomiAnd qi；
Computing unit 312, for according to procatarxis subcomponent piAnd qiComponent product N is calculated, and calculates component product N Rank factor componentAnd according toPrivate key component d is obtained with public key value ei, wherein,
Detector unit 313, for carrying out test for primality to component product N, if component product N is not prime number, performs Signal generating unit 311, if component product N is prime number, performs the factor component that computing unit 312 calculates the rank of component product N
Unit 314 is chosen, for randomly selecting public key value e；
Judging unit 315, for by distributed detection, judge public key value e withIt is whether coprime, if mutually Element, then perform 312 basis of computing unitPrivate key component d is calculated with public key value ei, otherwise, perform and choose unit 314。
Further, signature blocks 320 are specifically included：
First signature unit 321, for initiating signature, according to private key component d1Obtain signature components s1；
Communication unit 322, for sending signature request to the signature end of other participation signatures, and obtains other participation signatures The signature components that generated according to signature request of signature end；
Second signature unit 323, for obtaining full signature s according to the signature components at the whole signature ends for participating in signature.
Those skilled in the art can be understood that, the second signature end, the 3rd signature end and the 4th signature end Concrete structure with first signature end 300 it is identical, interconnect each other, for convenience of description and succinctly, here is no longer Repeat.
Those skilled in the art can be understood that, for convenience of description and succinctly, the dress of foregoing description The specific work process with unit is put, the corresponding process in preceding method embodiment is may be referred to, be will not be described here.
In several embodiments provided herein, it should be understood that disclosed system and method, which can be passed through Its mode is realized.For example, system embodiment described above is only schematic, and for example, the division of module is only A kind of division of logic function, can have when actually realizing other dividing mode, such as multiple modules or unit can with reference to or Person is desirably integrated into another system, or some features can be ignored, or does not perform.In addition, it is shown or discussed it is mutual it Between coupling or direct-coupling or communication connection can be INDIRECT COUPLING or communication link by some interfaces, device or unit Connect, or electricity, machinery or other forms connections.
The foregoing is only presently preferred embodiments of the present invention, not to limit the present invention, all spirit in the present invention and Within principle, any modification, equivalent substitution and improvements made etc. should be included within the scope of the present invention.

Claims (10)

1. a kind of distributed Threshold Signature method based on RSA, it is characterised in that comprise the following steps：
Step 1, generates private key component d corresponding with signature endi, i ∈ [1, n], n are all signature end quantity, n >=3；
Step 2, initiates signature, according to the private key component diObtain signature components si；
Step 3, the signature end to other participation signatures send signature request；
Step 4, obtains the signature components that other described signature ends for participating in signature are generated according to the signature request；
Step 5, obtains full signature s according to the signature components at the whole signature ends for participating in signature.
2. distributed Threshold Signature method according to claim 1, it is characterised in that step 1 is specifically included：
Step 11, it is random to generate procatarxis subcomponent piAnd qi；
Step 12, according to procatarxis subcomponent piAnd qiIt is calculated component product N；
Step 13, carries out test for primality to component product N, if component product N is prime number, execution step 14, Otherwise, execution step 11；
Step 14, according to procatarxis subcomponent piAnd qiIt is calculated the factor component of the rank of component product N
Step 15, randomly selects public key value e；
Step 16, judge public key value e withWhether coprime, if coprime, execution step 17 otherwise, performs step Rapid 15, wherein,
Step 17, according to describedPrivate key component d is calculated with public key value ei, i ∈ [1, n], n are all signatures End quantity, n >=3.
3. distributed Threshold Signature method according to claim 2, it is characterised in that step 2 is specifically included：
Step 21, obtains signature request m0；
Step 22, according to the m0It is calculated signature request information m, m=h (m0), h is the hash function for meeting signature agreement；
Step 23, according to signature request information m, the private key component diThe signature is calculated with component product N Signature components s at endi。
4. distributed Threshold Signature method according to claim 2, it is characterised in that according to below equation, by safety In many ways calculate protocol distributed calculating component product N：
N = ( Σ i = 1 n p i ) * ( Σ i = 1 n q i ) ;
The factor component of the rank of component product N is calculated according to below equation
As i=1,
Work as i>When 1,
5. distributed Threshold Signature method according to claim 2, it is characterised in that according to below equation, by safety In many ways calculate the protocol distributed calculating private key component di：
Wherein, ciFor Lagrange interpolation coefficient.
6. the distributed Threshold Signature method according to any one of claim 2 to 5, it is characterised in that according to below equation Calculate signature components si：
s i = m c i * d i mod N ,
Wherein, ciFor Lagrange interpolation coefficient.
7. distributed Threshold Signature method according to claim 6, it is characterised in that calculate described complete according to below equation Whole signature s：
s = Π i = 1 t s i mod N ,
Wherein, t is the signature end quantity for participating in signature.
8. a kind of distributed Threshold Signature system based on RSA, it is characterised in that include：N signature end, n >=3, the signature End includes：
Registering modules, for generating private key component d corresponding with end of signingi, i ∈ [1, n]；
Signature blocks, for initiating signature, according to the private key component diObtain signature components si, to the institute of other participation signatures State signature end and send signature request, obtain the signature point that other described signature ends for participating in signature are generated according to the signature request Amount, obtains full signature s according to the signature components at the whole signature ends for participating in signature.
9. distributed Threshold Signature system according to claim 8, it is characterised in that the Registering modules are specifically included：
Signal generating unit, generates procatarxis subcomponent p for randomiAnd qi；
Computing unit, for according to procatarxis subcomponent piAnd qiComponent product N is calculated, and calculates component product N Rank factor componentAnd according toPrivate key component d is obtained with public key value ei, wherein,
Detector unit, for carrying out test for primality to component product N, if component product N is not prime number, performs Signal generating unit, if component product N is prime number, performs the Factor minute that computing unit calculates the rank of component product N Amount
Unit is chosen, for randomly selecting public key value e；
Judging unit, for judge public key value e with it is describedIt is whether coprime, if coprime, perform computing unit According to describedPrivate key component d is calculated with public key value ei, otherwise, perform and choose unit.
10. distributed Threshold Signature system according to claim 8, it is characterised in that the signature blocks are specifically included：
First signature unit, for initiating signature, according to the private key component diObtain signature components si；
Communication unit, for sending signature request to the signature end of other participation signatures, and obtains other participation signatures The signature components that the signature end is generated according to the signature request；
Second signature unit, for obtaining full signature s according to the signature components at the whole signature ends for participating in signature.
CN201611160582.5A 2016-12-15 2016-12-15 RSA-based distributed threshold signature method and system Pending CN106533698A (en)

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CN107294707A (en) * 2017-06-22 2017-10-24 四川思安特科技有限公司 A kind of cellphone shield signature key guard method
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CN110311881B (en) * 2018-03-27 2022-01-14 阿里健康信息技术有限公司 Authorization method, encryption method and terminal equipment
CN110311881A (en) * 2018-03-27 2019-10-08 阿里健康信息技术有限公司 A kind of authorization method, encryption method and terminal device
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