Definition 3. If is ϵ-ASU2 with ϵ = 1/ , then is called strongly universal2 (or strongly universal, SU2 for short). We denote strongly universal2 by SU2 and universal2 by U2 for convenience. The value 1/|B| is the minimal value of ϵ for any ϵ-AU2 and ϵ-ASU2.
Definition 3. An MKEM is a public-key primitive with two algorithms MKEM = (kgc, decaps) that have the following syntax: – kgc. Take an (implicit) security parameter and a public key pk0 and xxxxxx (xx0, xx0, xx0, xx0). Here, (sk1, pk1) is a newly generated key pair. If pk0 =⊥ then ct1 = ss1 =⊥ (i. e., xxxxxx (xx0, xx0, ⊥, ⊥) ← kgc(⊥)). Otherwise, use pk0 to generate a ciphertext ct1, in a way that pk1 and a shared secret ss1 can be retrieved from ct1 by invoking decaps. – decaps: receive a secret key sk0 and a ciphertext ct1 and retrieve the shared secret ss1 and pk1, i. e., (ss1, pk1) = decaps(sk0, ct1).
Definition 3. 1Definice
Definition 3. For all sections of the DID and CDRL significant means: events that impact contractual requirements a. Technical (Impact on technical contractual requirements, such as TPM) b. Schedule (impact to schedules milestones identified in IMP, achievability of contractual schedule baseline and latest forecast, significant margin reductions, etc. If there is impact quantify duration)
Definition 3. (Variables) An occurrence of a variable in a λ-term is said to be free if it is not in the scope of an abstraction, and bound otherwise. For example:
Definition 3. 2 (pre-RCGS). A pre-RCGS structure is a tuple A, R, ρ, Q, Π, π, A , where: • A is a finite, non-empty set of players. • Q is the non-empty set of states. • R is a finite, non-empty set of roles. • ρ : Q × A → R assigning a role to an agent depending on the state. • Π is a non-empty set of propositional symbols. • π : Q → 2Π maps states to the propositions true at that state. • × → A : Q R N+ is the number of available actions for the agents in a given role at a given state. ⊆ A subset A A of agents is called a coalition. Given a pre-RCGS, we will need to be able to discuss certain specific coalitions. We introduce the following terminology.
A : = A ⊆ A coalition Aq,r := {a ∈ A | ρ(q, a)= r} agents from A in role r at q Notice particularly, that Aq,r is the set of all agents in role r at state q.
Definition 3. An RA is a tuple (L, R, Q, q0, δ, λ, τ, π). Therein, L, Q, q0 and λ are a set of labels, a set of locations, the start location, and a location output function respectively. R is a finite set of registers. δ : Q × L × (R ∪ {r⊥}) → Q is a register transition function. τ : Q × R → B is a register use predicate, and π : Q × L → (R ∪ {r⊥}) is a register update function. We call a label-value pair an action and denote it l(v) for input label l and parameter v. We assume w.l.o.g. that parameter values are integers (Z). A sequence of actions is called an action string, and is denoted by σ. A set of observations S for an RA comprises a set of action strings that should be accepted S+, and a set of action strings that should be rejected S−. An RA is consistent with S = {S+, S−} if it accepts all action strings in S+, and rejects all action strings in S−. Roughly speaking, an RA can be described as a DFA (Definition 1) enriched with a finite set of registers R and two additional functions. The first function, τ , specifies which registers are in use in a location. In a location q there can be two types of transitions for a label l and parameter value v. If v is equal to some used register r, then the transition δ(q, l, r) is taken. Else (v is different to all used registers), the fresh transition δ(q, l, r⊥) is taken. The second function, π, specifies if and where to store a value v when a fresh transition (δ(q, l, r⊥)) is taken. If π(q, l) = r⊥ then the value v on transition δ(q, l, r⊥) is not stored. Else (if π(q, l) = r for some register r ∈ R), the value v on transition δ(q, l, r⊥) is stored in register r. For the RA to behave as intended we introduce the following axioms. First, we require that no registers are used in the initial location: ∀r ∈ R τ (q0, r) = false (5) Second, if a register is used after a transition, it was used before or updated: ∀q ∈ Q ∀l ∈ L ∀r ∈ R ∀rj ∈ (R ∪ {r⊥}) τ (δ(q, l, rj), r) = true =⇒ ( τ (q, r) = true ∨ (rj = r⊥ ∧ π(q, l) = r) ) (6) Third, if a register is updated, then it is used afterwards: ∀q ∈ Q ∀l ∈ L ∀r ∈ R π(q, l) = r =⇒ τ (δ(q, l, r⊥), r) = true (7) Our goal is to learn an RA that is consistent with a set of action strings S = S+, S− . For this, we need to define a function that keeps track of the valuation of registers during runs over these action strings. Let A = (L, RA, QA, q0, δA, λA,τ A, πA) be an RA, and let T = (L Z, QT , λT ) be an OT for S. In addition to the map function (map : QT QA), we define a valu- ation function v...
Definition 3. An IB-AAGKA protocol is said to be secure against semantically indistinguish- able chosen identity and plaintext attacks (Ind-ID-CPA), if no randomized polynomial-time adversary has a non-negligible advantage in the above game. In other words, any randomized polynomial-time Ind-ID-CPA adversary A has an advantage Adv(A) = |2 Pr[b = bj] − 1| In this paper, we only consider security against chosen-plaintext attacks (CPA) for our IB- ASGKA protocol. To achieve security against chosen-ciphertext attacks (CCA), there are some generic approaches that convert a CPA secure encryption scheme into a CCA secure one, such as the Fujisaki-Okamoto conversion [16,6].
Definition 3. For every variable x defined in the described algorithms, we define xi to be node i’s x variable. For example, termination_timeεi is node i’s termination_timeε set. Xxxxxxxxx 0 XxxxxXxxXxxxxxXxxxx(x0, x) Input: A value v0 ∈ Rm , precision n. Output: A value v ∈ Rm in the convex hull of the valid inputs. 1: global r ← 0 2: global termination_timeε ← ∅ ⊲ all of the initializations are of multisets 3: global waiting_valueε ← ∅ ⊲ value messages waiting to be processed
Definition 3. A B3-set S ⊂ [n] is r-bounded if RS < r. The following corollary of Lemma 3.3.4 provides a conclusion that is stronger than Corollary 3.3.6 at the cost of requiring a better bound on RS.
