Correctness. If a process with identifier i performs Broadcast(m) in superround r ≥ T , then every cor- rect process performs Accept(m, i) during superround r.
Correctness. If Eve is passive, then Pr[kA = kB] = 1.
Correctness. For all ID, if the leader L is honest and all honest parties are activated on ID, all honest parties would output for ID.
Correctness. If the dealer is honest and inputs secret m in AVSS-Sh, then: • If all honest parties are activated to run AVSS-Sh on ID, all honest parties would output in the AVSS-Sh instance; • The value m∗ reconstructed by any honest party in the corresponding AVSS-Rec instance must be equal to m, for all ID.
Correctness. All the honest parties who have terminated the protocol hold identical bit as the output. Moreover, if all the honest parties had the same input, say ρ, then all honest parties upon termination output ρ. The above definition can be extended in a straight forward way for agreement on l bits, where l > 1 and we call such a protocol as multi-bit ABA protocol.
Correctness. If each Ui computes ski correctly, it implies that all members have security communications in the cloud meeting. Therefore, we trace the process of generating ski, and the resuls are correct: sk = (T (x) mod p)n ×( Taibiai+1 (x) mod p )n−1 × ( Tai+1 bi+1 ai+2 (x) mod p )n−2 i ai−1 bi−1 ai Ta b a (x) mod p Ta b a (x) mod p i−1 i−1 i × . . . × ( Tai+n−1 bi+n−1 ai+n (x) mod p i i i+1 ) Tai+n−2 bi+n−2 ai+n−1 (x) mod p = (Tai−1 bi−1 ai (x) mod p) ×(Taibiai+1 (x) mod p) × (Tai+1 bi+1 ai+2 (x) mod p) × . . . × (Tai+n−1 bi+n−1 ai+n (x) mod p) = (Ta1 b1 a2 (x) mod p) ×(Ta2 b2 a3 (x) mod p) × (Ta3 b3 a4 (x) mod p) × . . . × (Tanbnan+1 (x) mod p).
Correctness. With the formal validation tool Xxxxxxx-Xxxxx-Xxxxxxx Logic (BAN-logic) [27], we provide the proof of correctness of the proposed scheme in this section. Let U be the user, S represent the sensor node and GWN denote the gateway node. We demonstrate that a session key can be created successfully after the process of mutual authentication among S and U. Now, the basic notations of BAN-logic are given below: • P |≡ X: P believes X.
Correctness. For proving the first part, it is clear that (i) the honest dealer must collect at least n f valid digital signature for (C ) from distinct parties to form valid Π and (ii) every honest party can eventually wait the shares of A(x) and B(x) as well as the same C . This implies that all honest parties can eventually broadcast the same Cipher messages, so they would broadcast the same Echo messages and the same Ready messages, thus finally outputting in the AVSS-Sh instance. ⊕ ⊕ For proving the second party, it is easy to see that (i) any honest party must output a ciphertext c same to the ciphertext computed by the honest sender and (ii) all honest parties must receive the same hash h of the commitment C to A(x), where A(x) is a polynomial chosen by the honest deader. Recall that we have proven that all honest parties can reconstruct a message c A(0), which exactly is m because c computed by the honest sender is m A(0).
Correctness. If both players are honest, then the protocol is correct with probability at least −
