From 68adf301303cee6d084e52ad2a3a6ec25856814d Mon Sep 17 00:00:00 2001 From: derekpierre Date: Thu, 20 Jul 2023 15:49:46 -0400 Subject: [PATCH] Clarify tpke default. --- book/src/tpke.md | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/book/src/tpke.md b/book/src/tpke.md index 519838d4..fae4a0c0 100644 --- a/book/src/tpke.md +++ b/book/src/tpke.md @@ -25,7 +25,7 @@ Check that \\(e(U, H_{\mathbb{G}_2} (U))= e(G, W)\\) for ciphertext validity. 1. Check ciphertext validity. 2. Let \\(s = e(U, Z)\\) -### Threshold Decryption (simple method) +### Threshold Decryption (simple method - default) 1. Check ciphertext validity. 2. Each decryption share is \\(C_i = e(U, Z_i)\\). @@ -65,4 +65,3 @@ Suppose there is an adversary that wins the IND-CCA2 game. Then on input \\((G, The shared secret \\(s\\) can be rekeyed with respect to the secret key \\(Z_1\\) to a new secret key \\(\hat{Z} = [\alpha] Z_1 + Z_2\\), as the new shared secret \\(\hat{s} = s^{\alpha} e(U, Z_2) = e(U, [\alpha] Z_2)e(U, Z_2) = e(U, [\alpha]Z_1 + Z_2)\\). The shared secret \\(s\\) can be rekeyed with respect to the public key \\(Y_1\\) to a new public key \\(\hat{Y} = [\alpha] Y_1 + Y_2\\) as the new shared secret \\(\hat{s} = s^{\alpha} e([r] Y_2, H) = e([r\alpha] Y_1, H)e([r]Y_2, H) = e([r]([\alpha]Y_1 + Y_2), H)\\). - \ No newline at end of file