Security Model. We now briefly describe the formal security model of Bel- xxxx et al. [6] as standardized by Xxxxxxx et al. [12, 13] and refer the reader to [6, 12, 13] for more details. A protocol P for password-based group key agreement assumes that there is a set P = {U1, U2, . . . , Un} of n users (n is fixed), who share a low entropy secret password pw drawn uniformly from a small dictionary of size N . The adversary is given control over all communication in the external network. We assume that users do not deviate from the protocol and adversary never participates as a user in the proto- col. This adversarial model allows concurrent execution of the protocol among n users. The interaction between the adversary A and the protocol participants occur only via oracle queries, which model the adversary’s capabil- ities in a real attack. These queries are as follows (Πi denotes the i-th instance of user U and ski denotes the session key after execution of the protocol by Πi ): – Send(U, i, m): The adversary can carry out an ac- tive attack by this query. The adversary may in- tercept a message and then either modify it, create a new one or simply forward it to the intended par- ticipant. The output of the query is the reply (if any) generated by the instance Πi upon receipt of message m. The adversary is allowed to prompt the unused instance Πi to initiate the protocol by invok- 2 Preliminaries In this section, we define the Computation Xxxxxx-Xxxxxxx (CDH) problem and describe the security notion that a password-based group key agreement protocol should achieve. We use the notation a∈RS to denote that a is chosen uniformly from the set S.
2.1 Computation Xxxxxx-Xxxxxxx (CDH) ing Send(U, i, “Start”). U1 U – Execute({(U1, i1), . . . , (Un, in)}): This query reflects the adversary’s ability to passively eavesdrop on hon- est execution of password-based group key agreement protocol among unused instances Πi1 , . . . , Πin and outputs the transcript of the execution. A transcript consists of the messages that were exchanged during the honest execution of the protocol. – Reveal(U, i): If a group key ski has previously been ac- Problem i U Let G = ⟨g⟩ be a multiplicative group of some large prime order q. Then Computation Xxxxxx-Xxxxxxx (CDH) problem in G is defined as follows: Instance: (g, ga, gb) for some a, b ∈ Z∗.
Security Model. This section defines the components of the system, the adversary and its capabilities and the meaning of system breakdown.
4.1.1. System The system comprises nodes belonging to one administrative unit under the same TA. It is assumed that TA has access to a cryptographically secure random number generator. The master keys are assumed secure and cannot be stolen. If need be, they can be deleted after generating all of the possible public and private key sets. The nodes have access to secure cryptographic algorithms, such as AESencryption and hash algorithms.
Security Model. The model is defined by the following game which is run between a challenger C H and an adversary A . A controls all communications from and to the protocol participants via accessing to a set of oracles as described below. Every participant involved in a session is treated as an oracle. We denote an instance i of the participant U as k = sr (R + PK − X ) = sr (r + s − x )P = ∏i , where U ∈ {C , · · · ,C } S S. Each client C has an 3 S C C C S C C C U 1 n (rC + sC − xC)rSsP = (rC + sC − xC)RS = k4. Thus the client C and the server S establish a common session key sk = H4(IDC, RS, RC,WC, Ppub, k3) = H4(IDC, RS, RC,WC, Ppub, k4).
Security Model.
3.1. We settle the basic notation of distinguishers in Sect.
3.2. For reference, the black-box duplex security model of Daemen et al. [15] is treated in Sect.
3.3. We lift the model to leakage resilience in Sect. 3.4.
3.1 Sampling of Keys D ←−− { } The duplex construction of Sect. 2 is based on an array of u k-bit keys. These keys may be generated uniformly at random, as K DK ( 0, 1 k)u. In our analysis of leakage resilience, however, we will require the scheme to be still secure if the keys are not uniformly random but as long as they have sufficient min-entropy. Xxxxxxxxxx, we will adopt the approach of Daemen et al. [15] to consider keys sampled using a distribution K , that distributes the key independently1 and with sufficient min-entropy, i.e., for which D∞ δ H ( K ) = min ∈[1,u] H∞(K[δ]) is sufficiently high. Note that if DK is the random distribution, H∞(DK ) = k.
Security Model. We prove our protocols secure in the Universal Composability framework intro- duced in [Can01]. This model is explained in Appendix A.
Security Model. Before going to prove that the session key security is preserved by the proposed scheme, we discuss describe the ROR model [46]. • Participants. Let V , Dj , and CC denote the αth Lemma 1 (Difference Lemma): Let A, B, F denote the events defined in some probability distribution, and assume instance of vehicle Vi, the βth instance of drone Dj and that A ∧ ¬F ⇐⇒ B ∧ ¬F . Then | Pr[A] − Pr[B] ≤ Pr[F ]. the γth instance of CC, respectively. These instances are named the oracles. • Accepted state. If an instance V α jumps to the accepted state after the last expected protocol message is received, it will be in the accepted state. The session identification (sid) of V α for the current session that is constructed
Security Model. Λ Based on the works of He et al. [32] and Xxxx et al. [34], we adopt a security model for the PCAKA scheme. The security of our proposed authentication and key negotiation (PCAKA) scheme on a peer-to-peer cloud can be defined as a game between adversary A and challenger C. We indicate the kth instance of Λ by Πk , where Λ ∈ {C1, C2, ...}. A can perform some queries on C, and C will responds as follows.
Security Model. We formulated a series of games between challenger X and adversary 𝐴 to define our security model. Assume that participant ∏𝑖 ∈ {𝑈, 𝐸𝐷, 𝐶𝑆} represents the i-th instance and 𝛬 represents the entire protocol. The 𝐴 can ask the 𝐶 oracle queries, and the C can respond. ⚫ 𝑆𝑒𝑛𝑑(∏𝑖, 𝑚): If A asks the query for the message 𝑚, the 𝐶 executes the specific steps of the protocol and returns the result. ⚫ 𝐸𝑥𝑒𝑐𝑢𝑡𝑒(∏𝑈 , ∏𝐸𝐷 , ∏𝐶𝑆): This oracle query models a
Security Model. U { } { } ∈U ∈U ← ← ID { } A ∈ ID ID A ID A
Security Model. The security of ring signature schemes is defined via the following notions.