Asymmetric Group Key Agreement Sample Clauses

Asymmetric Group Key Agreement. This scheme was proposed by ▇▇, ▇▇, ▇▇▇▇▇▇, ▇▇▇, and ▇▇▇▇▇▇▇-▇▇▇▇▇▇ (2009). This scheme is an asymmetric group key agreement (ASGKA) protocol. They proposed a generic construction of one-round asymmetric group key agreement protocol based on a new primitive referred to as aggregatable signature based broadcast (ASBB), in which the public key can be simultaneously used to verify signatures and encrypt messages and signature can be used to decrypt ciphertext. A round means that each party sends one message and can broadcast simultaneously. This scheme was also implemented using bilinear pairings. From a generic construction, to realize one-round ASGKA protocol, they need only to implement a secure ASBB scheme. They construct an ASBB scheme secure in the random oracle model using bilinear pairing techniques. 2.4.2.1 An Efficient ASBB Scheme Let PairGen be an algorithm taking on input a security parameter 1λ, and outputs a tuple ϒ = (p, G, Gτ , e) where G and Gτ have the same prime order p, and e: G × G→ Gτ is an efficient non- degenerate bilinear map such that e(g, g) ≠ 1 for any generator g of G, and for all u, v ∈ Z, it holds that e(gu, gv) = e(g, g)uv. 1) Public parameters: Let ϒ = (p,G,Gτ ,e) ← PairGen (1λ), G=〈g〉. Let H:{0,1}* → G be a cryptographic hash function. The system parameters are π = (ϒ,g,H). 2) Public/secret keys: Select at random r∈Zp*. X∈G \ {1}. Compute R = g –r, A = e(X, g). The public key is pk = (R,A) and the secret key is sk = (r,X). 3) Sign: The signature of any string s ∈ {0,1}* under the public key pk is σ = X H(s)r.