CN113849861A - Proxy digital signature method based on elliptic curve - Google Patents

Proxy digital signature method based on elliptic curve Download PDF

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CN113849861A
CN113849861A CN202111108592.5A CN202111108592A CN113849861A CN 113849861 A CN113849861 A CN 113849861A CN 202111108592 A CN202111108592 A CN 202111108592A CN 113849861 A CN113849861 A CN 113849861A
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proxy
signature
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elliptic curve
private key
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廖大见
查明明
封宇谦
丁颖
金文杰
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Jiangsu Ocean University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/60—Protecting data
    • G06F21/64—Protecting data integrity, e.g. using checksums, certificates or signatures
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/30—Authentication, i.e. establishing the identity or authorisation of security principals
    • G06F21/45—Structures or tools for the administration of authentication
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
    • G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
    • G06F7/722—Modular multiplication

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Abstract

The invention discloses an elliptic curve-based proxy digital signature method, which comprises the following specific steps: s1: initializing the process; s2: a delegation process; s3: a generation process of the proxy key; s4: a verification process of the proxy key; in the proxy signature scheme of the present invention, proxy signatures
Figure DDA0003273405000000011
Private key k containing BBAnyone else does not know the private key kBSo neither can masquerade as B, nor can B repudiate his signature; authorization parameter sA≡e1kA+k1(modn) includes the original signer's private key kAOnly B authorized by a can generate a valid proxy signature. The method is suitable for temporary and short-term proxy authorization(ii) a The method is suitable for different conditions of the verifiers each time; the verification procedure is simple; other people in the method cannot impersonate, and different roles in the scheme cannot impersonate mutually.

Description

Proxy digital signature method based on elliptic curve
Technical Field
The invention relates to the field of proxy signatures, in particular to a proxy digital signature method based on an elliptic curve.
Background
Under the era background of the rapid development of the internet, the social informatization degree is increasingly high. The communication among people is more and more internationalized, and the human really enters the 'information age'. Information on the internet is chaotic and complicated, potential risk factors such as counterfeiting or tampering exist, and the electronic signature system is paid more attention to and perfected, so that the information security on the internet is maintained. The proxy signature is a special digital signature, and in the special digital signature system, two main bodies are required: original signers and proxy signers. The original signer passes the information to a third party (proxy signer) which creates a proxy signature based on various public parameters including its private key, the original signer's public key and randomly selected parameters.
Proxy signatures require three parties to participate; the private key of the original signer A is kAThe public key is PA＝kAP; the proxy signer is B, the private key is kBThe public key is PB＝kBP; c denotes a proxy signature verifier. The overall process of the document "elliptic curve-based proxy signature scheme" is summarized below:
1. initializing the process;
(1) let E be set up in a finite field FqThe above elliptic curve, P belongs to E and the order of the point P is n;
(2) a randomly selects a positive integer kA，0＜kAN as private key; public key is PA＝kAP；
(3) Disclosing coefficient parameters { E, n, PA}。
2. A delegation process; a, carrying out the following operations:
(1) randomly selecting a positive integer k0，0＜k0< n, calculate Q0＝k0P＝(x0，y0)，x0，y0∈Fq；
(2) Calculating r0≡x0 mod n，σ≡kA+r0k0 mod n；
(3) A will be σ and Q0Respectively communicated to B privately and publicly.
B is receiving sigma and Q0Thereafter, the validity of the delegation information is verified. Verifying sigma P ═ PA+r0Q0Wherein Q is0＝(x0，y0)，r0≡x0mod n. If the equation holds, then σ and Q0May act as a proxy signing key pair.
3. A generation process of the proxy signature; b, carrying out the following steps:
(1) randomly selecting a positive integer k, wherein k is more than 0 and less than n, and calculating kP (x, y) and r ≡ x mod n;
(2) calculating s ≡ k-1(m+rσ)mod n；
(3) Will { m, r, s, Q0It is sent to C.
4. A verification process of the proxy signature; c, verification:
(1) calculating c ≡ s-1 mod n，u1≡mc mod n，u2≡rc mod n；
(2) Calculating u1P+u2(PA+r0Q0)＝P′＝(x′，y′)；
(3) This proxy signature is valid if x' ≡ rc mod n.
In the scheme, anyone can not obtain the private key of the original signer A, and the private key can be ensured according to the elliptic curve discrete logarithm problem; in this scenario original signer a can revoke the signature authority of proxy signer B by declaring Q0 invalid; but s ≡ k generated during generation of the proxy signature-1The private key of the proxy signer B is not contained in the (m + r sigma) mod n, and the signature can be denied by the B, so that the signature cannot be denied; therefore, the elliptic curve based proxy digital signature method is provided.
Disclosure of Invention
The present invention is directed to provide a proxy digital signature method based on elliptic curve to solve the problems of the background art mentioned above.
In order to achieve the purpose, the invention provides the following technical scheme: a proxy digital signature method based on elliptic curve includes the following steps:
s1: initializing the process;
s11: let E be set up in a finite field FqThe above elliptic curve, P belongs to E and the order of the point P is n;
s12: a randomly selects a positive integer kA，0＜kAN as private key; public key is PA＝kAP；
S13: b randomly selecting positive integer kB，0＜kBN as private key; public key is PB＝kBP；
S14: disclosing coefficient parameters { E, n, PA，PB}；
S2: a delegation process; a pair of request information mAThe following operations were carried out:
s21: a randomly selects k1，0＜k1< n, calculate YA＝k1P＝(xA，yA)；
S22: calculating rA≡xAmod n、e1＝h(mA,rA)、sA≡e1kA+k1(mod n)；
S23: will (m)A,YA,sA) To B, (Y)A，sA) Is to A to mAA signature of the authorization information of (2); b accept (m)A,YA,sA) Then, first calculate rA≡xA mod n、e1＝h(mA,rA) (ii) a Then verifying sAP＝PAe1+YAIf yes, the authorization is established;
s3: a generation process of the proxy signature; b pair of signature information mBThe following operations were carried out:
s31: computing
Figure BDA0003273404980000031
S32: randomly selecting a positive integer k2，0＜k2< n, calculate YB＝k2PB＝(xB，yB)；
S33: calculating rB＝xB mod n、e2＝h(mB,rB)、s≡xe2+k2(mod n)；
S34: will (m)A,mB,YA,YBS) to C;
s4: a verification process of the proxy signature; c, verification:
s41: calculating rA≡xA mod n，rB≡xB mod n，e1＝h(mA,rA),e2＝h(mB,rB)；
S42: verification of xPB＝YB+e2(YA+e1PA) (ii) a If the equation is true, then the proxy signature generated by B is valid, and if the equation is false, then it is invalid.
As a preferred embodiment of the present invention, a represents an original signer; the B represents a proxy signer; the C represents a proxy signature verifier.
The invention has the beneficial effects that:
1. suitable for temporary, short-term proxy authorization;
2. the method is suitable for different conditions of the verifiers each time;
3. the verification procedure is simple;
4. other people in the method cannot impersonate, and different roles in the scheme cannot impersonate mutually.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The following detailed description of the preferred embodiments of the present invention, taken in conjunction with the accompanying drawings, will make the advantages and features of the invention more readily understood by those skilled in the art, and thus will more clearly and distinctly define the scope of the invention.
Example (b): referring to fig. 1, the present invention provides a technical solution: a proxy digital signature method based on elliptic curve includes the following steps:
s1: initializing the process; a represents the original signer; b represents a proxy signer; c represents a proxy signature verifier;
s11: let E be set up in a finite field FqThe above elliptic curve, P belongs to E and the order of the point P is n;
s12: a randomly selects a positive integer kA，0＜kAN as private key; public key is PA＝kAP；
S13: b randomly selecting positive integer kB，0＜kBN as private key; public key is PB＝kBP；
S14: disclosing coefficient parameters { E, n, PA，PB}；
S2: a delegation process; a pair of request information mAThe following operations were carried out:
s21: a randomly selects k1，0＜k1< n, calculate YA＝k1P＝(xA，yA)；
S22: calculating rA≡xA mod n、e1＝h(mA,rA)、sA≡e1kA+k1(mod n)；
S23: will (m)A,YA,sA) To B, (Y)A，sA) Is to A to mAA signature of the authorization information of (2); b accept (m)A,YA,sA) Then, first calculate rA≡xA mod n、e1＝h(mA,rA) (ii) a Then verifying sAP＝PAe1+YAIf yes, the authorization is established;
s3: a generation process of the proxy signature; b pair of signature information mBThe following operations were carried out:
s31: computing
Figure BDA0003273404980000041
S32: randomly selecting a positive integer k2，0＜k2< n, calculate YB＝k2PB＝(xB，yB)；
S33: calculating rB≡xBmod n、e2＝h(mB,rB)、s≡xe2+k2(mod n)；
S34: will (m)A,mB,YA,YBS) to C;
s4: a verification process of the proxy signature; c, verification:
s41: calculating rA≡xA mod n，rB≡xB mod n，e1＝h(mA,rA),e2＝h(mB,rB)；
S42: validation of sPB＝YB+e2(YA+e1PA) (ii) a If the equation is true, then the proxy signature generated by B is valid, and if the equation is false, then it is invalid.
The verification method comprises the following steps: a digital signature method based on elliptic curve proxy can prove the correctness thereof, and comprises the following steps:
it is known that: sA≡e1kA+k1(mod n)，
Figure BDA0003273404980000051
PB＝kBP，YB＝k2PB，s≡xe2+k2(mod n)；
Figure BDA0003273404980000052
The above process logically demonstrates the feasibility of the signature scheme, as well as non-repudiation, etc.
Unforgeability of the original signature. In the above proxy authorization process, (m)A,mB,YA，YBS) is actually the original signerAnd proxy signatureA，mBAnd is not forgeable. From sPB＝YB+e2(YA+e1PA) It can be shown that this signature is a valid proxy signature for B that has seen a grant. From the proxy signature, C utilizes the public keys of A and B and the authentication equation sPB＝YB+e2(YA+e1PA) To determine if the signature is a proxy signature generated by B-proxy a; on the other hand, in the document mACan specify the authorization range, the expiration date, etc., and is based on (m)A,YA,sA) The private key of A cannot be calculated, so secret transmission is not needed, and the use cost is reduced.
The impossibility of a proxy signature; in the proxy signature scheme of the invention, the proxy signature private key
Figure BDA0003273404980000053
Private key k containing BBAnyone else does not know the private key kBSo neither can masquerade as B, nor can B repudiate his signature; authorization parameter sA≡e1kA+k1(mod n) includes the original signer's private key kAOnly B authorized by a can generate a valid proxy signature.
In the method described in the background art, the generation process and the verification process of the proxy signature have an inversion operation once respectively, and are respectively s ≡ k-1(m + r σ) mod n and c ≡ s-1modn, the inverse operation in the improved signature method only occurs once in the generation process of the proxy signature
Figure BDA0003273404980000054
The inversion operation is the most complex operation in cryptography, and the operation process is very inefficient. The improved scheme reduces one inversion operation and improves the operation efficiency of the method; in the original method such as Q0＝k0P has 7 times of power operation, such as Y in the improved methodA＝k1The power of P is calculated 8 times. In the original method such as r0≡x0modulo multiplication of modn 9 times, improved methods such as rA≡xAmod n has 6 modular multiplication operations; in general, the improved scheme has greatly improved operation efficiency. The specific cases are as follows:
TABLE 1 comparison of original and modified protocols
Figure BDA0003273404980000061
The above examples only show some embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.

Claims (2)

1. A proxy digital signature method based on elliptic curve is characterized in that: the method comprises the following specific steps:
s1: initializing the process;
s11: let E be set up in a finite field FqThe above elliptic curve, P belongs to E and the order of the point P is n;
s12: a randomly selects a positive integer kA，0＜kAN as private key; public key is PA＝kAP；
S13: b randomly selecting positive integer kB，0＜kBN as private key; public key is PB＝kBP；
S14: disclosing coefficient parameters { E, n, PA，PB}；
S2: a delegation process; a pair of request information mAThe following operations were carried out:
s21: a randomly selects k1，0＜k1< n, calculate YA＝k1P＝(xA，yA)；
S22: calculating rA≡xAmod n、e1＝h(mA，rA)、sA≡e1kA+k1(mod n)；
S23: will (m)A，YA，sA) To B, (Y)A，sA) Is A pair of authorization information mAThe signature of (2); b accept (m)A，YA，sA) Then, first calculate rA≡xA mod n、e1＝h(mA，rA) (ii) a Then verifying sAP＝PAe1+YAIf yes, the authorization is established;
s3: a generation process of the proxy signature; b pair of signature information mBThe following operations were carried out:
s31: computing
Figure FDA0003273404970000011
S32: randomly selecting a positive integer k2，0＜k2< n, calculate YB＝k2PB＝(xB，yB)；
S33: calculating rB≡xB mod n、e2＝h(mB，rB)、s≡xe2+k2(mod n)；
S34: will (m)A，mB，YA，YBS) to C;
s4: a verification process of the proxy signature; c, verification:
s41: calculating rA≡xA mod n，rB≡xB mod n，e1＝h(mA，rA)，e2＝h(mB，rB)；
S42: validation of sPB＝YB+e2(YA+e1PA) (ii) a If the equation is true, then the proxy signature generated by B is valid, and if the equation is false, then it is invalid.
2. The elliptic curve-based proxy digital signature method as claimed in claim 1, wherein: the A represents an original signer; the B represents a proxy signer; the C represents a proxy signature verifier.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114726552A (en) * 2022-06-07 2022-07-08 杭州天谷信息科技有限公司 Digital signature right transfer method and system

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114726552A (en) * 2022-06-07 2022-07-08 杭州天谷信息科技有限公司 Digital signature right transfer method and system
CN114726552B (en) * 2022-06-07 2022-10-11 杭州天谷信息科技有限公司 Digital signature right transfer method and system

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Application publication date: 20211228