Kỹ thuật chia sẻ khóa bí mật Tiếng Anh

SECRET KEY SHARING

1. Notation

N : number of authorities

A1, A2, … , An: N authorities

t: maximum number of malicious and dishonest authorities

A: any set of t+1 authorities

M: number of eligible voters

m: number of voters participating in the voting; m<=M

V1, V2, …, Vm: M voters

v1, v2, …, vm: intentions (voters) of the voters

Zp: field of positive integers modulo p, where p is prime number

Zn: set of integers modulo, i.e. {0, 1, …, n-1}

Zn*: set of integers from Zn relatively prime to n

a|b: an integer a is a divisor of an integer b

gcd(a,b): greatest comon divisor of the integer a,b

a||b: concatenation of the string a, b

a⊕ b: bitwise exclusive or

x∈RX: x is a random element of the set X (uniformly distributed)

X∈RY: X is a random subset of the set Y (uniformly distributed)

x ?= y: check whether x=y

2. Secret Sharing Scheme

Purpose of secret sharing scheme is to share a secret among N authorities. In such away

that only some predefined coalitions of authorities can later reconstruct the secret. Other

coalitions of authorities should get no knowledge about the secret. We introdure Shamir’s

(t+1, N) secret sharing scheme from [Sha 79] that alows any coalition of t+1 from N

authorities to get the secret. Any set of at most t authorities knows noting about the secret.

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