February 19, 2002
Practical Aspects of Modern Cryptography
21
Shamir’s Threshold Scheme
nTo distribute a secret value s Î Zp amongst a set of n Trustees {T1,T2,…,Tn} such that any k can determine the secret
n
npick random coefficients a1,a2,…,ak-1 Î Zp
nlet P(x) = ak-1xk-1 + … + a2x2 + a1x + s
ngive P(i) to trustee Ti.
nThe secret value is s = P(0).
n