CN112118096A - Secret sharing method taking specific numerical value as share - Google Patents

Secret sharing method taking specific numerical value as share Download PDF

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CN112118096A
CN112118096A CN202010920060.0A CN202010920060A CN112118096A CN 112118096 A CN112118096 A CN 112118096A CN 202010920060 A CN202010920060 A CN 202010920060A CN 112118096 A CN112118096 A CN 112118096A
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secret
share
secret sharing
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CN112118096B (en
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荆继武
何俊霖
王平建
寇春静
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University of Chinese Academy of Sciences
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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
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/085—Secret sharing or secret splitting, e.g. threshold 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
    • H04L9/0866—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving user or device identifiers, e.g. serial number, physical or biometrical information, DNA, hand-signature or measurable physical characteristics
    • 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
    • H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds

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  • Computer Networks & Wireless Communication (AREA)
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Abstract

The invention relates to a secret sharing method taking a specific numerical value as a share, and belongs to the technical field of passwords. On the basis of the Shamir secret sharing method, a certain secret share is set to be a specific numerical value in the secret sharing process, and the specific numerical value can be directly set in a self-defining mode or can be converted from the self-defining value. The method and the device realize that a certain specific numerical value is used as the secret share, and on the basis of keeping the original share secret unchanged and not destroying the security strength of the original secret share scheme, a user can associate own identity characteristics, machine characteristics or password information and the like with the secret share in the secret share process through self-defining the numerical value or using a related transformation algorithm and participate in calculation, so that the characteristics of strong correlation between the secret share and a person, strong association with equipment and the like can be realized, the secret share can be easier to remember, and the dependence of the secret share security on the storage device security is reduced.

Description

Secret sharing method taking specific numerical value as share
Technical Field
The invention relates to a secret sharing method taking a specific numerical value as a share, and belongs to the technical field of passwords.
Background
Secret sharing is a method of distributing a secret among a group of participants, by which the secret can be split into shares that are distributed among multiple participants so that the participants holding the shares can jointly recover the original secret under certain conditions. Specifically, in the secret sharing scheme of the (t, n) threshold, the secret d to be shared is dispersed in n participants, each participant holds a share, and the secret d can be recovered when no less than t +1 participants are combined.
The prior art relating to the Shamir Secret Sharing (SS) algorithm and the Joint Shamir random secret sharing (Joint-RSS) algorithm mainly comprises the following steps:
(1) shamir Secret Sharing (SS) algorithm
In a Shamir Secret Sharing (SS) algorithm with a (t, n) threshold, the set of participants C, C ═ C1,c2,…,cnShare a parameter prime p, and the secret to be shared is d, d<p, each participant ciI 1, …, n holds a share d that needs to share a secret diI is 1, …, n. Any participant with t +1 bits or more can recover the secret d together, and any participant with t bits or less cannot recover the secret d together. The specific sharing steps are as follows:
(1-1) the distributor randomly selects t random numbers { a }i},ai<p, i is 1, …, t, let a0Secret construction of a random polynomial of degree t
Figure BDA0002666406690000011
(1-2) distributor as Each participant ciI 1, …, n calculating diF (i), and secretly combining diI 1, …, n to the corresponding participant ci,i＝1,…,n。
(1-3) participant ciD to be receivediStored as secret share shares.
When the secret d needs to be recovered, the arbitrary t +1 bit participant set C' can be calculated by a Lagrange interpolation formula
Figure BDA0002666406690000012
(2) Joint Shamir random secret sharing (Joint-RSS) algorithm
In a Joint Shamir random secret sharing (Joint-RSS) algorithm with a (t, n) threshold, the set of participants C, C ═ C1,c2,…,cnEach participant c iniWhere i is 1, …, n is the distributor executing the Shamir Secret Sharing (SS) algorithm of the (t, n) threshold once(i)The secret shared by the final set of participants C is determined according to the rules of Shamir-based secret and/or differential sharing algorithm
Figure BDA0002666406690000013
The specific sharing steps are as follows:
(2-1) Each participant C in the set of participants CiEach distributor c runs the Shamir Secret Sharing (SS) algorithm with a (t, n) threshold as distributor, i-1, …, niI-1, …, n secret is constructed with d(i)Random polynomial f of degree t being a constant termi(x) And is the remaining participant cjJ-1, …, n calculates and secretly sends a share fi(j)。
(2-2) Each participant C in the set of participants CjJ-1, …, n receives a share d sent to it by the n-1 bit distributorj (i)Calculating
Figure BDA0002666406690000021
As its own secret share.
In the above existing secret sharing method, the share held by each participant is generated by algorithm calculation, so that the self-definition of the secret share cannot be realized, the secret share cannot be linked with the characteristics of user identity, equipment hardware and the like, and the secret share value is not easy to be memorized by people and is seriously dependent on the protection of external safe storage equipment.
Disclosure of Invention
The invention aims to provide a secret sharing method taking a specific secret as a share, which aims to overcome the defects of the prior art and support the setting of a secret share as a specific numerical value in the secret sharing process
Figure BDA0002666406690000028
The specific value can be directly self-defined and can also be transformed by the self-defined value, and the transformation comprises but is not limited to hash function, encryption and signature.
The invention provides a secret sharing method taking a specific numerical value as a share, which comprises the following steps:
(1) in a Shamir secret sharing system with a (t, n) threshold, a secret sharing participant set is set as C, and C is ═ Ci1, …, n, all secret sharing participants share a prime number p, and finally each secret sharing participant c in the threshold secret sharing system is enabled to execute a secret sharing algorithmiSecret shares held are diThe shared secret value is d, d<p；
(2) Specifying a secret sharing participant C from a set of secret sharing participants CmSecret sharing participant cmSelecting a segment of numerical value PIN as password value, and calculating
Figure BDA0002666406690000025
Will be provided with
Figure BDA0002666406690000026
As a special value share, secret sharing participant cmAs a specified numerical value share
Figure BDA0002666406690000027
Wherein H (x) is a hash function, mod (x) is a congruence operation symbol;
(3) secret sharing participant cmAs distributor, randomly selects t random numbers { a }j},j＝1,…,t,aj∈{0,…,p-1},atNot equal to 0, such that
Figure BDA0002666406690000022
Secret sharing participant cmSecret construction of a t-th polynomial
Figure BDA0002666406690000023
Wherein mod (x) is a congruence operation symbol, dmSharing participants for secrets cmA secret share held;
(4) secret sharing participant c using the t-th order polynomial f (x) of step (3)mSharing participants c for each secretiCompute share update parametersi，iF (i) and stores its share update parametermThen, updating the parameters of each share except the own share updating parameteriSecret sending to corresponding secret sharing participant ci；
(5) Each secret sharing participant C in the set of secret sharing participants CiThe updated secret share d is calculated using the formulai，di＝i+dimod (p), share updates and stores.
In step (1) of the secret sharing method, the secret sharing algorithm may be a Shamir secret sharing algorithm, and the Shamir secret sharing algorithm includes the following steps:
(1) any secret sharing participant C in the set of secret sharing participants CkK is equal to {1, …, n } as distributor, t random numbers { b } are randomly selectedj},bj∈{0,…,p-1},btNot equal to 0, a t-th order polynomial f' (x) is constructed secretly,
Figure BDA0002666406690000031
Figure BDA0002666406690000032
(2) secret sharing participant c using the t-th order polynomial f' (x) of step (1)kSharing participants c for each secretiComputing secret shares diF' (i) and stores its own secret share dkThen each secret share d except its own secret share is addediSecret sending to corresponding secret sharing participant ci；
(3) Secret sharing participant ciReceiving and storing secret shares di。
In the step (1) of the secret sharing method, the secret sharing algorithm may also be a joint Shamir random secret sharing algorithm, and the joint Shamir random secret sharing algorithm includes the following steps:
(1) each secret sharing participant C in the set of secret sharing participants CiAs distributor, randomly selects t random numbers el},l＝0,…t,el∈{0,…,p-1},etNot equal to 0, secret constructing a t-degree polynomial fi(x)，
Figure BDA0002666406690000033
Figure BDA0002666406690000034
(2) Using the t-th order polynomial f of step (1)i(x) Each secret sharing participant C in the set of secret sharing participants CiAs distributors, all secret sharing participants C in the secret sharing participant set C are respectivelyzCalculating secret sub-shares fi(z) and stores its own secret sub-share fi(i) Then each secret sub-share f except its secret sub-share is addedi(z) secret sending to a corresponding secret sharing participant czWherein, z is 1, …, n;
(3) secret sharing participant ciReceiving secret sub-shares fz(i) The secret share d is calculated byi，
Figure BDA0002666406690000035
And stores secret shares diAt this time, the secret value shared inside the secret sharing participant set C is d,
Figure BDA0002666406690000036
in step (2) of the secret sharing method, a specific value is specified
Figure BDA0002666406690000039
Is a self-defined value, the self-defined value is PIN code and machineA serial number, password, or identification; or from custom values, including hash functions, encryption, or signatures.
In step (3) of the secret sharing method, a method for constructing a t-th order polynomial f (x) is as follows: randomly selecting t-1 random numbers { aj},ajE.g., {0, …, p-1}, calculating
Figure BDA0002666406690000037
Wherein
Figure BDA0002666406690000038
For secret sharing participant c in step (2)mOf the specific numerical value of.
The secret sharing method taking the specific numerical value as the share has the advantages that:
the secret sharing method using the specific value as the share supports that a certain secret share is set as the specific value in the secret sharing process on the basis of the Shamir secret sharing method, and the specific value can be directly set in a self-defining mode or can be obtained through self-defining value transformation (such as a hash function, encryption and signature). The invention realizes that a certain specific numerical value is used as the secret share, and on the basis of keeping the original share secret unchanged and not destroying the security strength of the original secret share scheme, a user can associate the identity, machine characteristics or password information and the like with the secret share in the secret share process through self-defining the numerical value or using a related transformation algorithm and participate in calculation, so that the characteristics of strong correlation between the secret share and a person, strong association with equipment and the like can be realized, the secret share can be easier to remember, and the dependence of the secret share security on the storage equipment security is reduced
Drawings
Fig. 1 is a schematic flow chart of a secret sharing method using a specific value as a share according to the present invention.
Detailed Description
The invention provides a secret sharing method taking a specific numerical value as a share, which comprises the following steps:
(1) in a Shamir secret sharing system with a (t, n) threshold, a secret sharing participant set is set as C, and C is ═ Ci1, …, n, all secret sharing participants share a prime number p, and finally each secret sharing participant c in the threshold secret sharing system is enabled to execute a secret sharing algorithmiSecret shares held are diThe shared secret value is d, d<p；
(2) Specifying a secret sharing participant C from a set of secret sharing participants CmSecret sharing participant cmSelecting a segment of numerical value PIN as password value, and calculating
Figure BDA0002666406690000046
Will be provided with
Figure BDA0002666406690000045
As a special value share, secret sharing participant cmAs a specified numerical value share
Figure BDA0002666406690000047
Wherein H (x) is a hash function, mod (x) is a congruence operation symbol;
(3) secret sharing participant cmAs distributor, randomly selects t random numbers { a }j},j＝1,…,t,aj∈{0,…,p-1},atNot equal to 0, such that
Figure BDA0002666406690000041
Secret sharing participant cmSecret construction of a t-th polynomial
Figure BDA0002666406690000042
Wherein mod (x) is a congruence operation symbol, dmSharing participants for secrets cmA secret share held;
(4) secret sharing participant c using the t-th order polynomial f (x) of step (3)mSharing participants c for each secretiCompute share update parametersi，i(ii) and (i) togetherStore own share update parametersmThen, updating the parameters of each share except the own share updating parameteriSecret sending to corresponding secret sharing participant ci；
(5) Each secret sharing participant C in the set of secret sharing participants CiThe updated secret share d is calculated using the formulai，di＝i+dimod (p), share updates and stores.
In step (1) of the secret sharing method, the secret sharing algorithm may be a Shamir secret sharing algorithm, and the Shamir secret sharing algorithm includes the following steps:
(1) any secret sharing participant C in the set of secret sharing participants CkK is equal to {1, …, n } as distributor, t random numbers { b } are randomly selectedj},bj∈{0,…,p-1},btNot equal to 0, a t-th order polynomial f' (x) is constructed secretly,
Figure BDA0002666406690000043
Figure BDA0002666406690000044
(2) secret sharing participant c using the t-th order polynomial f' (x) of step (1)kSharing participants c for each secretiComputing secret shares diF' (i) and stores its own secret share dkThen each secret share d except its own secret share is addediSecret sending to corresponding secret sharing participant ci；
(3) Secret sharing participant ciReceiving and storing secret shares di。
In the step (1) of the secret sharing method, the secret sharing algorithm may also be a joint Shamir random secret sharing algorithm, and the joint Shamir random secret sharing algorithm includes the following steps:
(1) each secret sharing participant C in the set of secret sharing participants CiAs distributor, randomly selects t random numbers el},l＝0,…t,el∈{0,…,p-1},etNot equal to 0, secret constructing a t-degree polynomial fi(x)，
Figure BDA0002666406690000051
Figure BDA0002666406690000052
(2) Using the t-th order polynomial f of step (1)i(x) Each secret sharing participant C in the set of secret sharing participants CiAs distributors, all secret sharing participants C in the secret sharing participant set C are respectivelyzCalculating secret sub-shares fi(z) and stores its own secret sub-share fi(i) Then each secret sub-share f except its secret sub-share is addedi(z) secret sending to a corresponding secret sharing participant czWherein, z is 1, …, n;
(3) secret sharing participant ciReceiving secret sub-shares fz(i) The secret share d is calculated byi，
Figure BDA0002666406690000053
And stores secret shares diAt this time, the secret value shared inside the secret sharing participant set C is d,
Figure BDA0002666406690000054
in step (2) of the secret sharing method, a specific value is specified
Figure BDA00026664066900000510
The user-defined value is a PIN code, a machine serial number, a password or an identity; or from custom values, including hash functions, encryption, or signatures.
In step (3) of the secret sharing method, a method for constructing a t-th order polynomial f (x) is as follows: randomly selecting t-1 random numbers { aj},ajE.g., {0, …, p-1}, calculating
Figure BDA0002666406690000055
Wherein
Figure BDA0002666406690000056
For secret sharing participant c in step (2)mOf the specific numerical value of.
Specific values in the method of the invention
Figure BDA0002666406690000057
By self-defining, the identity characteristics (such as biological characteristics of fingerprints, irises and the like) of the user can be associated with the secret share, so that the correlation relation between the secret share and the personal identity is established; meanwhile, machine characteristics (such as hardware serial numbers, MAC addresses and the like) of the equipment can be associated with the secret share, so that the secret share is associated with the equipment characteristics; in addition, the user password can be directly used as the secret share after being transformed, so that the secret share becomes easier to remember, and the dependence of the secret share on the security of the storage device is reduced; finally, to
Figure BDA00026664066900000511
The process of customizing the value also broadens the use of secret share shares.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (5)

1. A secret sharing method using a specific value as a share, the method comprising the steps of:
(1) in a Shamir secret sharing system with a (t, n) threshold, a secret sharing participant set is set as C, and C is ═ CiN, all secret sharing participants share a prime number p, and finally each secret sharing party in the threshold secret sharing system is enabled to share a prime number p by operating a secret sharing algorithmSecret sharing participant ciSecret shares held are diThe shared secret value is d, d is less than p;
(2) specifying a secret sharing participant C from a set of secret sharing participants CmSecret sharing participant cmSelecting a segment of numerical value PIN as password value, and calculating
Figure FDA0002666406680000011
Will be provided with
Figure FDA0002666406680000012
As a special value share, secret sharing participant cmAs a specified numerical value share
Figure FDA0002666406680000016
The owner of (1), wherein the slice (x) is a hash function, mod (x) is a congruence operation symbol;
(3) secret sharing participant cmAs distributor, randomly selects t random numbers { a }j}，j＝1，...，t，aj∈{0，...，p-1}，atNot equal to 0, such that
Figure FDA0002666406680000013
Secret sharing participant cmSecretly constructing a t degree polynomial f (x),
Figure FDA0002666406680000014
wherein mod (x) is a congruence operation symbol, dmSharing participants for secrets cmA secret share held;
(4) secret sharing participant c using the t-th order polynomial f (x) of step (3)mSharing participants c for each secretiCompute share update parametersi，iF (i) and stores its share update parametermThen, updating the parameters of each share except the own share updating parameteriSecret sending to corresponding secret sharing participant ci；
(5) Secret sharing participationEach secret sharing participant C in the set of parties CiThe updated secret share d is calculated using the formulai，di＝i+dimod (p), share updates and stores.
2. The secret sharing method according to claim 1, wherein the secret sharing algorithm in step (1) is a Shamir secret sharing algorithm, and the Shamir secret sharing algorithm includes the steps of:
(1) any secret sharing participant C in the set of secret sharing participants CkK is in the distribution list { 1.,. n }, and t random numbers { b } are randomly selectedj}，bj∈{0，...，p-1}，btNot equal to 0, a t-th order polynomial f' (x) is constructed secretly,
Figure FDA0002666406680000015
(2) secret sharing participant c using the t-th order polynomial f' (x) of step (1)kSharing participants c for each secretiComputing secret shares diF' (i) and stores its own secret share dkThen each secret share d except its own secret share is addediSecret sending to corresponding secret sharing participant ci；
(3) Secret sharing participant ciReceiving and storing secret shares di。
3. The secret sharing method according to claim 1, wherein the secret sharing algorithm in step (1) is a federated Shamir random secret sharing algorithm, and the federated Shamir random secret sharing algorithm comprises the following steps:
(1) each secret sharing participant C in the set of secret sharing participants CiAs distributor, randomly selects t random numbers el}，l＝0，...t，el∈{0，...，p-1}，etNot equal to 0, secret constructing a t-degree polynomial fi(x)，
Figure FDA0002666406680000021
Figure FDA0002666406680000022
(2) Using the t-th order polynomial f of step (1)i(x) Each secret sharing participant C in the set of secret sharing participants CiAs distributors, all secret sharing participants C in the secret sharing participant set C are respectivelyzCalculating secret sub-shares fi(z) and stores its own secret sub-share fi(i) Then each secret sub-share f except its secret sub-share is addedi(z) secret sending to a corresponding secret sharing participant czWherein, z is 1.
(3) Secret sharing participant ciReceiving secret sub-shares fz(i) The secret share d is calculated byi，
Figure FDA0002666406680000023
And stores secret shares diAt this time, the secret value shared inside the secret sharing participant set C is d,
Figure FDA0002666406680000024
4. the secret sharing method according to claim 1, wherein in the step (3), the specific numerical value
Figure FDA0002666406680000025
The user-defined value is a PIN code, a machine serial number, a password or an identity; or from custom values, including hash functions, encryption, or signatures.
5. The secret sharing method according to claim 1, wherein in the step (3), the method for constructing a t-degree polynomial f (x) comprises: randomly selecting t-1 random numbers { aj}，ajE.g., { 0.,. p-1}, calculating
Figure FDA0002666406680000026
Figure FDA0002666406680000027
Wherein
Figure FDA0002666406680000028
For secret sharing participant c in step (2)mOf the specific numerical value of.
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Cited By (10)

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Publication number Priority date Publication date Assignee Title
CN113254410A (en) * 2021-05-29 2021-08-13 陕西师范大学 Provable and safe public verification multi-level multi-secret sharing method and system
CN113254410B (en) * 2021-05-29 2024-02-02 陕西师范大学 Publicly verifiable multi-level multi-secret sharing method and system capable of proving safety
CN113315631A (en) * 2021-06-09 2021-08-27 华控清交信息科技(北京)有限公司 Data processing method and device and data processing device
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CN113765662A (en) * 2021-09-10 2021-12-07 长春吉大正元信息安全技术有限公司 Signature and decryption method and system based on SM2 algorithm
CN113810184A (en) * 2021-09-14 2021-12-17 东莞理工学院 Equipment password escrow method and system based on dynamic threshold multi-secret sharing
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CN113761563B (en) * 2021-11-05 2022-02-08 深圳致星科技有限公司 Data intersection calculation method and device and electronic equipment
CN117114059A (en) * 2023-05-16 2023-11-24 华为云计算技术有限公司 Method and device for calculating activation function in neural network and computing equipment

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