Definition 3. 3.6 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. 1.7.1 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) c. Cost (impact on contract BAC and EACs. If there is impact quantify the cost) 3.1.7.2 Working Days means work days (Monday to Friday) with exception of official federal Government holidays. 3.2.
Definition 3. 3.9. 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.
Definition 3. An APDB protocol with a sender s consists of a provable dispersal subprotocol (PD) and a recast subprotocol (RC) with a pair of validation functions (ValidateLock, ValidateDone): P ∈ { } • PD subprotocol. In the PD subprotocol (with identifier ID) among n parties, a designated sender s inputs a value v 0, 1 A, and aims to split v into n encoded fragments and disperses each fragment to the corresponding party. During the PD subprotocol with identifier ID, each party is allowed to invoke an abandon(ID) function. After PD terminates, each party shall output two strings store and lock, and the sender shall output an additional string done. Note that the lock and done strings are said to be valid for the identifier ID, if and only if ValidateLock(ID, lock) = 1 and ValidateDone(ID, done) = 1, respectively. • RC subprotocol. In the RC subprotocol (with identifier ID), all honest parties take the output of the PD subprotocol (with the same ID) as input, and aim to output the value v that was dispersed in the RC subprotocol. Once RC is completed, the parties output a common value in {0, 1}A ∪ ⊥. An APDB protocol (PD, RC) with identifier ID satisfies the following properties except with negligible probability: P • P
Definition 3. .5.1. Define P0 to be the set of all probability vectors p = (p1, p2, . . .) for which s+3
Definition 3. .9. (Minimum Set Cover Problem [96]) Given a universe W, a col- lection S of subsets of W, and a cost function c : S → R+ find a minimum cost sub-collection of S that covers each element of W.
Definition 3. The probability P (A) is negligible if for any polynomial f (A), where A is the security parameter, there exists an integer Nf such that P (A) ≤ 1 for all A ≥ Nf . − Informally, a secure authenticated key agreement protocol with key confirmation guarantees that only the legitimate oracle can possibly compute the session key. Any oracle that accepts can confirm that it has n 1 partner oracles which compute the same session key. A formal statement is as follows.
Definition 3. Elliptic Curve Factorization Problem (ECFP). Given two points Q and Q1 = s Q + t Q, it is computationally infeasible to discriminate two points s ∗ Q and t ∗ Q, where s, t ∈ Zq∗. Until now, it is commonly believed that there are no efficient algorithms to solve the above problems in a polynomial-time with a non-negligible probability [12, 16].
