A Threshold Cryptosystem without a Trusted Party
0 likes83 views
The document discusses a threshold cryptosystem developed without a trusted party, as presented at Eurocrypt '91. It details the steps for key computation and sharing among players using polynomials and secret verification. The method allows participants to collectively reconstruct a secret while ensuring the integrity of individual shares.
A Threshold Cryptosystem without a Trusted Party
- 1. A Threshold Cryptosystem without a Trusted Party Advances in Cryptology — EUROCRYPT ’91. EUROCRYPT 1991 Torben Pryds Pedersen Aarhus University, Computer Science Department 林彥賓 2021/1/23
- 2. 1. chooses at random and computes and brocast 2. each player opnen , the public key is 3. choose random polynomial of degree such that . f (z) = i f + i,0 f z + i,1 ... + f z i,k−1 k−1 where 4. compute for and brocast 5. send secretely to for 6. verifies share received by by checking Pi xi h = i gxi C = i Com(h ) i Ci h = h ∏i=1 n i Pi f (z) i k − 1 f (0) = i xi f = i,0 xi Pi F = i,j gfi,j j = 0, ..., k − 1 Fi,j Pi s = i,j f (j) i Pj j = 0, ..., k − 1 Pi Pj g = si,j F ∏ℓ=0 k−1 j,ℓ iℓ 2
- 3. Set Let be polynomid over we know that for , thus is a share of f (0), f (1), f (2), ..., f (k − 1 1 1 1 1) + ... + f (0), f (1), f (2), ..., f (k − k−1 k−1 k−1 k−1 1) x = f(0), s = 1 f(1), ..., s = k−1 f(k − 1) s = i s ∑j=1 n j,i f Z : q f(z) = f (z) + 1 ... + f (z) n s = i f(i) i = 1, ..., n si f(0) = x 3
- 4. For share of , can compute public key σ = i g = j=1 ∏ n sj,i (h F ) j=1 ∏ n j ℓ=1 ∏ k−1 j,ℓ iℓ si Pi 4