Definition 2 Sample Clauses

Definition 2. Let E be a tweakable blockcipher that internally uses a dedicated blockcipher E. We say that it is optimally standard/ideal-model secure if for any distinguisher making q queries to its construction oracle and r evaluations of the primitive (where in the standard model, r = τ /τE): Advs/i-s˜prp(Ð) ≤ const · max{q, r} , ˜ min{|K|, |ł|} ˜|K|

Definition 2. In (G1, G2, eˆ), the BDH problem is defined as follows. Given G ∈ G1 and (G, aG, bG, cG) for some a, b, c ∈ Zq∗, compute W = eˆ(G, G)abc ∈ G2 [10]. An algorithm is said to have advantage ε in solving the BDH problem in (G1, G2, eˆ) if Pr[A(G, aG, bG, cG) = eˆ(G, G)abc] ≥ ε, Group Storage Auditing Info exchange where ε > 0 and the probability is based on the random choice of a, b, c Zq∗, the random choice of G∗1 and the random bits of . The BDH assumption states that no polynomial time al- gorithm has an advantage of at least ε in solving the BDH problem in (G1, G2, eˆ), which means that this advantage is negligible.

Definition 2. By a valuation on a field K we mean a map val: K → R ∪ {∞} that satifies the following

Definition 2. Suppose Γ(t) is evolving with normal velocity vν . Define the material velocity field v := vν + vτ where vτ is the tangential velocity field. The material derivative of a scalar function f = f (x, t) defined on GT := ∪t∈[0,T ]Γ(t)×{t} is given as ∂•f := ∂f + v · ∇f. We now give a generalisation of integration by parts for a hypersurface Γ, the proof of which is found in Xxxxxxx and Xxxxxxxxx [2001].

Definition 2. Trust in wireless mesh networks is determined by a trust tuple (α, θ). α N + represents the authentication and θ R+ the grade of autho- rization. The first part is the recognition or authentication part which is necessary to dis- tinguish nodes from each other. Recognition means that every node has a distinct cryptographic attribute (e.g. a self signed certificate) that proves his binding to a self chosen identity. Authentication extends this by creating a cryptographic binding to an approved identity. Actually, authentication and recognition are binary decisions, because there are always only two possibilites: you have iden- tified a user or you have not. After all, the authentication value α is determined by the addition of all binary authentication results. However, the value of α (if greater than one) is not the determining part of the trust level, it just represents the number of nodes who authenticated a certain node. The second part of trust is a valuing component, namely how trusted a user is. We call this part authorization value, since it will be used to authorize users to become part of the network. Later on, the authorization value can also be used for choosing the best (most trustful) route for a packet through the network, if our scheme is combined with a source routing algorithm. Authorization is expressed by the real value θ.

Definition 2. A key agreement scheme k is a subscheme of key agree- ment scheme K if every session [a, b, c, d, e, f ] of k is a session of K. The prototypical example is a subscheme of Diffie–Xxxxxxx key agreement in which b is fixed to be an element of multiplicative order q modulo p (where q is prime). Also, a and c are often taken to be integers strictly between 1 and q.

Definition 2. 1. A probability measure Pµ on DΩ[0, ∞) satisfying (2.3) is said to be cone-mixing if, for all θ ∈ (0, 1 π), t→∞ A∈F0, B∈Fθ P (A)>0 sup Pµ(B | A) − Pµ(B) = 0, (2.11)

Definition 2. A hash function is a function h : D R where the domain D = {0, 1}∗ and the range R = {0, 1}n for some n ≥ 1. is said to be one-way if it’s computationally infeasable to recover the message x from a hash value H(x). A collision resistant hash function implies that no two messages should generate the same output.

Definition 2. (Agreement Clause). Let G be a predicate, n an integer denoting a time unit, and a = p, an, d be an action. The syntax of agreement clauses is defined as follows: C :: = IF G THEN P(a) | IF G THEN F (a) | IF G THEN O(a) | IF G THEN On(a) In the following, we provide an intuitive explanation of the clause syntax. A more precise meaning will be given later when representing agreement clauses in the Event-B language. A permission clause is denoted as IF G THEN (a), which indicates that provided the condition G holds, the system may perform action a. A prohibition clause is denoted as IF G THEN (a), which indicates that the system must not perform ac- tion a when condition G holds. An obligation clause is denoted as IF G THEN (a), which indicates that provided the condition G holds, the system eventually must per- form action a. Finally, a bounded-obligation clause is denoted as IF G THEN n(a), which indicates that provided the condition G holds, the system must perform action a within n time units. A data sharing agreement can be defined as follows. Definition 3. (Data Sharing Agreement). A DSA is a tuple (Principals, Data, ActionNames, fromTime, endTime, P(C)). Principals is the set of principals signing the agreement and abiding by its clauses. Data is the data elements to be shared. ActionNames is a set containing the name of the actions that a party can perform on a data. fromTime and endTime denotes the starting and finishing time of the agreement respectively; this is an abstraction rep- resenting the starting and finishing date of the agreement. Finally, P( ) is the set of clauses of the agreement.

Definition 2. A canonically twisted module over V is a super vector space over V , M = M0¯ M1¯ equipped with a linear map: X V → End(M )[[z±1/2]] (50) a → Ytw(a, z1/2) = a(n) n2 1 Z z—n—1 (51) equipped with twisted vertex operator Ytw(a, z1/2) such that satisfying the fol- lowing axioms for a, b, c ∈ V :