CN109274503B - Distributed collaborative signature method, distributed collaborative signature device and soft shield system - Google Patents

Distributed collaborative signature method, distributed collaborative signature device and soft shield system Download PDF

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Publication number
CN109274503B
CN109274503B CN201811308545.3A CN201811308545A CN109274503B CN 109274503 B CN109274503 B CN 109274503B CN 201811308545 A CN201811308545 A CN 201811308545A CN 109274503 B CN109274503 B CN 109274503B
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signature
random number
elliptic curve
key
calculating
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CN109274503A (en
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罗燕京
刘鹏
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Beijing Xinchangcheng Technology Development Co ltd
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Beijing Renxinzheng Technology Co ltd
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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
    • H04L9/3252—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 DSA or related signature schemes, e.g. elliptic based signatures, ElGamal or Schnorr schemes
    • 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
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • 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
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0894—Escrow, recovery or storing of secret information, e.g. secret key escrow or cryptographic key storage

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Abstract

The invention relates to a distributed collaborative signature method, a distributed collaborative signature device and a soft shield system, wherein the distributed collaborative signature method comprises the following steps: generating a first random number and a second random number according to the stored elliptic curve parameters, calculating a plurality of segmentation keys and calculating a public key; the method comprises the steps of performing distributed storage on a plurality of split keys, and dividing the split keys into a first split key and a second split key according to a storage area; generating abstract hash according to the sending message, generating a first elliptic point according to the elliptic curve parameters, and calculating a first signature according to the abstract hash and the first elliptic point; encrypting the first signature according to the first segmentation key and the second segmentation key respectively, and calculating a second signature; and combining the first signature and the second signature to obtain a complete signature. The signature method, the signature device and the soft shield system generate the segmentation key and perform distributed storage on the two communication parties, so that the cooperative signature is realized, the two communication parties cannot acquire any information of the private key of the other party, and the security of the key is improved.

Description

Distributed collaborative signature method, distributed collaborative signature device and soft shield system
Technical Field
The invention relates to the field of digital signatures, in particular to a distributed collaborative signature method, a distributed collaborative signature device and a soft shield system.
Background
The security of the traditional financial service is generally realized by adopting a USB Key to store a digital certificate to solve the security problem, the USB Key is a hardware device with a USB interface, a single chip microcomputer or an intelligent card chip is arranged in the USB Key, a certain storage space is provided, a private Key and the digital certificate of a user can be stored, the authentication of the user identity is realized by utilizing a public Key algorithm arranged in the USB Key, and the USB Key is a generally-recognized and relatively-safe identity authentication technology.
The digital certificate is stored by relying on the USB Key hardware equipment, the terminal environment is complex and the resources are limited in the use scenes such as mobile interconnection, and the certificate and the algorithm provided by relying on the hardware equipment cannot be used or are limited. Therefore, virtual key devices are an industry trend.
At present, in the CPK system, the key is issued over the internet and stored in the memory, which is not secure.
Therefore, a distributed collaborative signature method, a distributed collaborative signature device and a soft shield system are provided.
Disclosure of Invention
In view of the above problems, the present invention is provided to provide a distributed collaborative signing method, a distributed collaborative signing apparatus, and a soft shield system, which overcome or at least partially solve the above problems, and generate a split key and perform distributed storage on both communication parties, and both parties jointly perform a signing operation on a message to implement collaborative signing, and both communication parties cannot acquire any information of the private key of the other party, so that an attacker cannot forge a signature when invading either party, thereby improving the security of the key.
According to an aspect of the present invention, there is provided a distributed collaborative signature method, including the steps of:
generating a first random number and a second random number according to the stored elliptic curve parameters, calculating a plurality of segmentation keys according to the first random number and the second random number, and calculating a public key according to the first random number and the elliptic curve parameters;
the method comprises the steps of performing distributed storage on a plurality of split keys, and dividing the split keys into a first split key and a second split key according to a storage area;
generating abstract hash according to the sending message, generating a first elliptic point according to the elliptic curve parameters, and calculating a first signature according to the abstract hash and the first elliptic point;
encrypting the first signature according to the first segmentation key, calculating a first intermediate value, encrypting the first intermediate value according to the second segmentation key, and calculating a second signature;
and combining the first signature and the second signature to obtain a complete signature so that the public key can verify the complete signature.
Further, the elliptic curve parameters include an elliptic curve over a finite field, a base point on the elliptic curve, and an order of the base point on the elliptic curve.
Further, the first random number and the second random number are generated according to the stored elliptic curve parameters, which are as follows:
D∈[1，n-1]
K∈[1，n-1]
wherein D is a first random number, K is a second random number, and n is the order of a base point on the elliptic curve;
calculating a public key according to the first random number and the elliptic curve parameter, which specifically comprises the following steps:
P＝D[*]G
wherein, D is a first random number, G is a base point on the elliptic curve, P is a public key, and [ ] represents the elliptic curve point multiplication operation.
Further, the digest hash is generated according to the sending message, which specifically includes:
e＝HASH(M′)
wherein e is the digest hash, M' is Z | | | M, Z is the identity, M is the message content, and | represents the concatenation.
Further, a first elliptic point is generated according to the elliptic curve parameters, which is as follows:
k1∈[1，n-1]
Q1＝k1[*]G
wherein Q is1Is the first ellipsoid point, k1Is a third random number, n is the order of the base point on the elliptic curve, G is the base point on the elliptic curve [. sup. ]]Representing an elliptic curve point multiplication operation.
Further, a first signature is calculated according to the digest hash and the first ellipsoid, which is as follows:
Q1＝(x1，y1)
r＝(e+x1)mod n
where r is the first signature, Q1Is the first ellipsoid point, x1Is the abscissa, y, of the first ellipsoid point1Is the ordinate of the first ellipsoid point and e is the digest hash.
According to another aspect of the present invention, there is provided a distributed collaborative signing apparatus for implementing the above method, including:
the public and private key generation module is used for generating a first random number and a second random number according to the stored elliptic curve parameters, calculating a plurality of segmentation keys according to the first random number and the second random number, and calculating a public key according to the first random number and the elliptic curve parameters;
the key distribution storage module is used for carrying out distribution storage on the plurality of partition keys and dividing the partition keys into a first partition key and a second partition key according to a storage area;
the first signature calculation module is used for generating abstract hash according to the sending message, generating a first elliptic point according to the elliptic curve parameters and calculating a first signature according to the abstract hash and the first elliptic point;
the second signature calculation module is used for encrypting the first signature according to the first segmentation key, calculating a first intermediate value, encrypting the first intermediate value according to the second segmentation key and calculating a second signature;
and the complete signature generation module is used for combining the first signature and the second signature to obtain a complete signature so that the public key can verify the complete signature.
Further, the elliptic curve parameters in the public-private key generation module and the first signature calculation module include an elliptic curve over a finite field, a base point on the elliptic curve, and an order of the base point on the elliptic curve.
Further, the public and private key generating module comprises:
a split key calculation unit for generating a first random number and a second random number based on the stored elliptic curve parameters, and calculating a plurality of split keys based on the first random number and the second random number;
and the public key calculation unit is used for calculating a public key according to the first random number and the elliptic curve parameters.
According to another aspect of the invention, a soft shield system is provided, which includes the distributed collaborative signature apparatus.
Compared with the prior art, the invention has the following advantages:
the distributed collaborative signature method, the distributed collaborative signature device and the soft shield system generate the segmentation key and perform distributed storage on the two communication parties, the two parties jointly perform signature operation on the message to realize collaborative signature, and the two communication parties cannot acquire any information of the private key of the other party, so that an attacker cannot forge the signature under the condition that the attacker invades any one party, and the security of the key is improved.
Drawings
The invention is further illustrated by the following figures and examples.
FIG. 1 is a diagram of the distributed collaborative signing method steps of the present invention;
FIG. 2 is a flow diagram of an example key split of the present invention;
FIG. 3 is a flow diagram of an example distributed collaborative signature of the present invention;
fig. 4 is a block diagram of a distributed collaborative signing apparatus of the present invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
Fig. 1 is a diagram of steps of a distributed collaborative signature method according to the present invention, and as shown in fig. 1, the distributed collaborative signature method according to the present invention includes the following steps:
generating a first random number and a second random number according to the stored elliptic curve parameters, calculating a plurality of segmentation keys according to the first random number and the second random number, and calculating a public key according to the first random number and the elliptic curve parameters;
the method comprises the steps of performing distributed storage on a plurality of split keys, and dividing the split keys into a first split key and a second split key according to a storage area;
generating abstract hash according to the sending message, generating a first elliptic point according to the elliptic curve parameters, and calculating a first signature according to the abstract hash and the first elliptic point;
encrypting the first signature according to the first segmentation key, calculating a first intermediate value, encrypting the first intermediate value according to the second segmentation key, and calculating a second signature;
and combining the first signature and the second signature to obtain a complete signature so that the public key can verify the complete signature.
The elliptic curve parameters comprise an elliptic curve in a finite field, an upper base point of the elliptic curve and the order of the upper base point of the elliptic curve.
Further, the first random number and the second random number are generated according to the stored elliptic curve parameters, which are as follows:
D∈[1，n-1]
K∈[1，n-1]
wherein D is a first random number, K is a second random number, and n is the order of a base point on the elliptic curve;
calculating a public key according to the first random number and the elliptic curve parameter, which specifically comprises the following steps:
P＝D[*]G
wherein, D is a first random number, G is a base point on the elliptic curve, P is a public key, and [ ] represents the elliptic curve point multiplication operation.
Further, the digest hash is generated according to the sending message, which specifically includes:
e＝HASH(M′)
wherein e is the digest hash, M' is Z | | | M, Z is the identity, M is the message content, and | represents the concatenation.
Further, a first elliptic point is generated according to the elliptic curve parameters, which is as follows:
k1∈[1，n-1]
Q1＝k1[*]G
wherein Q is1Is the first ellipsoid point, k1Is a third random number, n is the order of the base point on the elliptic curve, G is the base point on the elliptic curve [. sup. ]]Representing an elliptic curve point multiplication operation.
Further, a first signature is calculated according to the digest hash and the first ellipsoid, which is as follows:
Q1＝(x1，y1)
r＝(e+x1)mod n
where r is the first signature, Q1Is the first ellipsoid point, x1Is the abscissa, y, of the first ellipsoid point1Is the ordinate of the first ellipsoid point and e is the digest hash.
The distributed collaborative signing method generates the segmentation key and performs distributed storage on the two communication parties, the two parties jointly perform signing operation on the message to realize collaborative signing, and the two communication parties can not acquire any information of the private key of the other party, so that an attacker can not forge the signature under the condition of invading any one party, thereby improving the security of the key.
For simplicity of explanation, the method embodiments are described as a series of acts or combinations, but those skilled in the art will appreciate that the embodiments are not limited by the order of acts described, as some steps may occur in other orders or concurrently with other steps in accordance with the embodiments of the invention. Further, those skilled in the art will appreciate that the embodiments described in the specification are presently preferred and that no particular act is required to implement the invention.
The distributed cooperative signature method can be applied to a soft shield system, the soft shield comprises a soft shield client and a soft shield background, wherein the soft shield background is designed in a layered mode and mainly comprises the following steps:
interface layer: providing an interface which is compatible with various operating systems and used for data encryption, digital signature, signature verification, key management, identity authentication and the like;
the safety technology comprises the following steps: providing security services for the soft shield through key protection such as key encryption and key dispersion, device fingerprinting and security reinforcement;
a file system: mainly for storing various sensitive data such as keys and digital certificates.
Fig. 2 is a flowchart of an example of key splitting according to the present invention, and as shown in fig. 2, fig. 2 is a flowchart illustrating a process of generating a split private key for both communication parties and calculating a public key.
Here, the transmitting side and the receiving side share the elliptic curve parameters E (Fq), G, and n of the SM2 algorithm, the elliptic curve E is an elliptic curve defined on the finite field Fq, G represents a base point of the order n on the elliptic curve E, and specific values and the like of each parameter are set in advance according to the secret SM2 algorithm.
The key segmentation comprises the following specific steps:
first, the sender generates a first random number as D. Namely:
D∈[1，n-1]
second, the sender generates two second random numbers as K, C. Namely:
K∈[1，n-1]
C∈[1，n-1]
thirdly, calculating and dividing the key, and respectively storing the key in different security areas, wherein the private key D is not separately stored, namely:
D1＝[K*(1+D)]-1*C
D2＝K*C
D3＝G-1
D4＝K*D
wherein, is the modular multiplication operation.
Fourth, computing public key
P＝D[*]G
Wherein [ ] represents elliptic curve point multiplication operation.
In particular, the algorithm of the secret SM2 may be replaced by an ECC algorithm, a secret SM3 algorithm, and a secret SM4 algorithm.
Fig. 3 is a flowchart of the distributed collaborative signature of the present invention, and as shown in fig. 3, the distributed collaborative signature is specifically as follows:
firstly, the soft shield client splices Z and M to form M ', calculates HASH (M'), and takes the calculation result as e, wherein Z represents the common identity of the soft shield client and the soft shield background, M represents the message content, and HASH () represents the predetermined cryptographic HASH function. Namely, the method comprises the following steps:
M′＝Z||M
wherein, | | represents concatenation; e ═ HASH (M').
Second, the soft shield client generates a third random number k1And calculate k1[*]G, using the calculation result as Q1And Q is1And e sending the background. Namely, the method comprises the following steps:
k1∈[1，n-1]
Q1＝k1[*]G
thirdly, the soft shield client side is according to e and Q1The first part r of the signature is calculated.
Q1＝(x1，y1)
r＝(e+x1)mod n
Fourthly, the distributed storage of the split keys and the storage of the soft shield client terminal D1、D2Soft shield background storage D3、D4Then use D first1、D2Is calculated to obtain S1、S2：
S1＝D1*D2*k1
S2＝D1*r
Fifthly, soft shield background reuse D3、D4And continuously calculating to obtain s:
s＝S1*D3+S2*D4
sixthly, the signature value sign ═ r | | | s is finally obtained.
Seventhly, the signature verification party, namely the receiving party, uses the public key P to perform signature verification, and the specific algorithm is referred to part 2 of GM/T003.2-2012SM2 elliptic authority public key cryptographic algorithm: chapter 7 "verification algorithm and flow of digital signature" in digital signature algorithm ".
For example, the public key P is used for signature verification, which is as follows:
(1) checking whether r belongs to [1, n-1] or not, and if yes, verifying not to pass;
(2) checking whether s belongs to [1, n-1] or not, and if yes, verifying not to pass;
(3) device for placing
Figure BDA0001854350650000101
(4) Computing
Figure BDA0001854350650000102
(5) Calculating t ═ r + s; if t is 0, the verification is not passed;
(6) calculating the point (x) of the elliptic curve1，y1)＝[s]G+[t]PA；
(7) Calculating R ═ e + x1) mod n checks whether R is true, and if so, the verification is passed; otherwise, the verification is not passed.
Fig. 4 is a block diagram of a distributed collaborative signing apparatus according to the present invention, and as shown in fig. 4, the distributed collaborative signing apparatus according to the present invention includes:
the public and private key generation module is used for generating a first random number and a second random number according to the stored elliptic curve parameters, calculating a plurality of segmentation keys according to the first random number and the second random number, and calculating a public key according to the first random number and the elliptic curve parameters;
the key distribution storage module is used for carrying out distribution storage on the plurality of partition keys and dividing the partition keys into a first partition key and a second partition key according to a storage area;
the first signature calculation module is used for generating abstract hash according to the sending message, generating a first elliptic point according to the elliptic curve parameters and calculating a first signature according to the abstract hash and the first elliptic point;
the second signature calculation module is used for encrypting the first signature according to the first segmentation key, calculating a first intermediate value, encrypting the first intermediate value according to the second segmentation key and calculating a second signature;
and the complete signature generation module is used for combining the first signature and the second signature to obtain a complete signature so that the public key can verify the complete signature.
Further, the elliptic curve parameters in the public-private key generation module and the first signature calculation module include an elliptic curve over a finite field, a base point on the elliptic curve, and an order of the base point on the elliptic curve.
As shown in fig. 4, the public-private key generating module includes:
a split key calculation unit for generating a first random number and a second random number based on the stored elliptic curve parameters, and calculating a plurality of split keys based on the first random number and the second random number;
and the public key calculation unit is used for calculating a public key according to the first random number and the elliptic curve parameters.
As shown in fig. 4, the first signature calculation module includes:
a digest hash generation unit for generating a digest hash from the transmission message;
the first elliptic point generating unit is used for generating a first elliptic point according to the elliptic curve parameters;
and the first signature calculation unit is used for calculating a first signature according to the digest hash and the first elliptic point.
The distributed collaborative signing device generates the segmentation key and performs distributed storage on the two communication parties, the two parties jointly perform signing operation on the message to realize collaborative signing, and the two communication parties can not acquire any information of the private key of the other party, so that an attacker can not forge the signature under the condition of invading any one party, thereby improving the security of the key.
For the device embodiment, since it is basically similar to the method embodiment, the description is simple, and for the relevant points, refer to the partial description of the method embodiment.
The soft shield system provided by the invention comprises the distributed cooperative signature device, specifically, the soft shield of the invention comprises a soft shield client and a soft shield background, one part of the distributed cooperative signature device is installed at the soft shield client, and the other part of the distributed cooperative signature device is installed at the soft shield background, wherein the soft shield background is designed in a layered manner and mainly comprises:
interface layer: providing an interface which is compatible with various operating systems and used for data encryption, digital signature, signature verification, key management, identity authentication and the like;
the safety technology comprises the following steps: providing security services for the soft shield through key protection such as key encryption and key dispersion, device fingerprinting and security reinforcement;
a file system: mainly for storing various sensitive data such as keys and digital certificates.
The soft shield provides security services such as trusted digital signature, identity authentication, encryption and decryption and the like of a terminal without a hardware medium, and provides cross-platform, reliable and uniform security services for mobile internet, internet of things and traditional internet.
The soft shield system generates the segmentation key and performs distributed storage on the two communication parties, the two parties jointly perform signature operation on the message to realize cooperative signature, and the two communication parties cannot acquire any information of the private key of the other party, so that an attacker cannot forge the signature under the condition that the attacker invades any one of the two parties, thereby improving the security of the key.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (5)

1. A distributed collaborative signature method is characterized by comprising the following steps:
generating a first random number and a second random number according to the stored elliptic curve parameters, calculating a plurality of segmentation keys according to the first random number and the second random number, and calculating a public key according to the first random number and the elliptic curve parameters;
the method comprises the steps of performing distributed storage on a plurality of split keys, and dividing the split keys into a first split key and a second split key according to a storage area;
generating abstract hash according to the sending message, generating a first elliptic point according to the elliptic curve parameters, and calculating a first signature according to the abstract hash and the first elliptic point;
encrypting the first signature according to the first segmentation key, calculating a first intermediate value, encrypting the first intermediate value according to the second segmentation key, and calculating a second signature;
combining the first signature and the second signature to obtain a complete signature for the public key to verify the complete signature;
the elliptic curve parameters comprise an elliptic curve in a finite field, a base point on the elliptic curve and the order of the base point on the elliptic curve;
generating a first random number and a second random number according to the stored elliptic curve parameters, which are as follows:
D∈[1，n-1]
K∈[1，n-1]
wherein D is a first random number, K is a second random number, and n is the order of a base point on the elliptic curve;
calculating a public key according to the first random number and the elliptic curve parameter, which specifically comprises the following steps:
P＝D[*]G
wherein G is the base point on the elliptic curve, P is the public key, and [. sup. ] represents the point multiplication operation of the elliptic curve;
generating a digest hash according to the transmission message, specifically as follows:
e＝HASH(M′)
wherein e is digest hash, M' is Z | | | M, Z is an identity, M is message content, and | represents concatenation;
generating a first elliptic point according to the elliptic curve parameters, which is as follows:
k1∈[1，n-1]
Q1＝k1[*]G
wherein Q is1Is the first ellipsoid point, k1Is a third random number, G is a base point on the elliptic curve;
calculating a first signature according to the digest hash and the first ellipsoid, which comprises the following steps:
Q1＝(x1，y1)
r＝(e+X1)mod n
where r is the first signature, x1Is the abscissa, y, of the first ellipsoid point1Is the ordinate of the first ellipsoid point and e is the digest hash.
2. A distributed collaborative signing apparatus that implements the method of claim 1, comprising:
the public and private key generation module is used for generating a first random number and a second random number according to the stored elliptic curve parameters, calculating a plurality of segmentation keys according to the first random number and the second random number, and calculating a public key according to the first random number and the elliptic curve parameters;
the key distribution storage module is used for carrying out distribution storage on the plurality of partition keys and dividing the partition keys into a first partition key and a second partition key according to a storage area;
the first signature calculation module is used for generating abstract hash according to the sending message, generating a first elliptic point according to the elliptic curve parameters and calculating a first signature according to the abstract hash and the first elliptic point;
the second signature calculation module is used for encrypting the first signature according to the first segmentation key, calculating a first intermediate value, encrypting the first intermediate value according to the second segmentation key and calculating a second signature;
and the complete signature generation module is used for combining the first signature and the second signature to obtain a complete signature so that the public key can verify the complete signature.
3. The distributed cooperative signature device as claimed in claim 2, wherein the elliptic curve parameters in the public-private key generation module and the first signature calculation module include an elliptic curve over a finite field, a base point on the elliptic curve, and an order of the base point on the elliptic curve.
4. The distributed collaborative signing apparatus of claim 3, wherein the public-private key generation module comprises:
a split key calculation unit for generating a first random number and a second random number based on the stored elliptic curve parameters, and calculating a plurality of split keys based on the first random number and the second random number;
and the public key calculation unit is used for calculating a public key according to the first random number and the elliptic curve parameters.
5. A soft shield system comprising the distributed collaborative signing apparatus of claim 2.
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