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A Recovery Method for Expired Shares Based on (k,n) Threshold Secret Sharing

A recovery method and threshold secret technology, which is applied in the field of key management, can solve the problems of original secret exposure, etc., and achieve the effects of easy operation, enhanced practicability, and simple steps

Active Publication Date: 2018-10-19
CHENGDU UNIV OF INFORMATION TECH
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, if the original secret is restored and the share is recalculated according to the method of secret sharing, the original secret will be completely exposed

Method used

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  • A Recovery Method for Expired Shares Based on (k,n) Threshold Secret Sharing

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0019] Assumptions: 1. The secret to be shared is 1; 2. The threshold of the secret sharing system is (3,n), where n is an integer greater than 3; 3. All operations are performed on the modulo 7 integer finite field; 4. Confirmation The polynomial of the secret sharing system is f(x)=2x 2 +3x+1.

[0020] According to the assumption, the share holder P is obtained 1 ~P 4 The shares of f(1)=6, f(2)=1, f(3)=0, f(4)=3 respectively. When share holder P 4 After the share f(4) is lost or damaged, it can be recovered according to the following steps:

[0021] S1. Select k effective share holders, that is, 3 effective share holders, denoted as p 1 ,p 2 ,p 3 , its holding shares are denoted as F(1), F(2), F(3), that is, F(1)=f(1)=6, F(2)=f(2)=1, F(3 ) = f(3) = 0

[0022] S2. For share holders p 1 Arbitrarily choose to satisfy the condition g 1 (r)=g 1 (4) = 0 and g 1 (0)≠0 polynomial: g 1 (x)=x 2 +6x+2;

[0023] To share holders p 2 Arbitrarily choose to satisfy the con...

Embodiment 2

[0034] Assumptions: 1. The secret that needs to be shared is 1; 2. The threshold of the secret sharing system is (4,6); 2. The secret that needs to be shared is 1; 3. All operations are performed on the modulo 11 integer finite field; 4 , The polynomial to determine the secret sharing system is f(x)=x 3 +2x 2 +3x+1.

[0035] According to the assumption, the share holder P is obtained 1 ~P 6 The shares of f(1)=7, f(2)=1, f(3)=0, f(4)=10, f(5)=4, f(6)=10 respectively. When share holder P 3 and P 4 After the shares f(3) and f(4) are lost or damaged, they can be recovered according to the following steps:

[0036] Recover holder P first 3 share f(3), the steps are as follows:

[0037] S1. Select holders of k valid shares, that is, 4 valid share holders, denoted as p 1 ,p 2 ,p 3 ,p 4 , its holding shares are denoted as F(1), F(2), F(3), F(4), that is, F(1)=f(1)=7, F(2)=f(2)= 1, F(3)=f(5)=4, F(4)=f(6)=10;

[0038] S2. For share holders p 1 Arbitrarily choose to satisf...

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Abstract

The invention relates to a recovery method for invalid shares based on (k, n) threshold secret sharing. When the share f(r) of the r-th share holder Pr becomes invalid, select k effective share holders p1, p2,...,pk, whose effective shares are F(1), F(2), ...,F(k); for each effective share holder pi, determine a polynomial gi(x) of order k‑1, and calculate gi(1), gi(2),..., gi(k), And distributed to the corresponding effective share holders p1, p2,...,pk; calculate g1(i)+g2(i)+...+gk(i)+F(i)=h(i); the data to be obtained The set {h(i), 1≤i≤k} performs Lagrangian interpolation polynomial algorithm to obtain a k-1 order polynomial h(x); the calculated value of h(r) is the lost share. The method of the present invention can be recovered without revealing the secret after no more than n-k shares fail, which enhances the practicability of the secret sharing system.

Description

technical field [0001] The invention belongs to the technical field of key management, and relates to a share recovery method for secret sharing, in particular to an invalid share recovery method based on (k, n) threshold secret sharing. Background technique [0002] Secret sharing is a cryptographic technology that divides and stores secrets. The purpose is to prevent secrets from being too concentrated, so as to achieve the purpose of dispersing risks and tolerating intrusions. It is an important means in information security and data confidentiality. In many real-world situations, people hope that the access rights to objects with important value cannot be controlled by only one person. For example: There are 3 tellers in a bank, and they have to open the vault every day. For safety reasons, the bank requires that at least two tellers be present to open the vault. This prevents the accidental loss or damage of the vault key, or possible self-theft by each cashier. [0...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H04L9/08
Inventor 唐聃舒红平杨洋王亚强赵卓宁刘魁曹亮罗飞
Owner CHENGDU UNIV OF INFORMATION TECH