Computability Clause Samples
The Computability clause defines the requirement that certain calculations, processes, or obligations within the agreement must be capable of being performed using a clear, systematic, and executable method. In practice, this means that any formulas, algorithms, or procedures referenced in the contract must be sufficiently detailed and unambiguous so that they can be carried out by a person or a computer without subjective interpretation. This clause ensures that all parties can reliably determine outcomes or fulfill obligations, thereby reducing disputes and ambiguity over how contractual terms are to be implemented.
Computability. P, Q G1 there is an efficient algo- rithm to compute e(P, Q).
Computability. There exists an efficient algorithm to compute eˆ(u, v) for any u, v ∈ G1. The security of our protocol is based on the hardness of the computational ▇▇▇▇▇▇-▇▇▇▇▇▇▇ (CDH) problem and the k-Bilinear ▇▇▇▇▇▇-▇▇▇▇▇▇▇ Exponent (BDHE) problem [5], which are as follows: CDH Problem: Given g, gα, gβ for unknown α, β ∈ Zq, compute gαβ. CDH Assumption: Let B be an algorithm which has advantage Adv(B) = Pr ΣB(g, gα, gβ) = gαβΣ in solving the CDH problem. The CDH assumption is that Adv(B) is negligible for any polynomial- time algorithm B. k-BDHE Problem: Given g, h, and yi = gα in G for i = 1, 2, ..., ▇, ▇ + 2, ..., 2k as input, compute eˆ(g, h)αk . Since the input vector is missing the term gαk+1 , the bilinear map does not seem to help computing e(g, h)αk+1 .
Computability. There exists a polynomial time algorithm to compute e(P, Q), ∀P, Q ∈ G1. A bilinear map is defined as a probabilistic polyno- mial time algorithm (E) that takes a security pa- rameter k and returns a uniformly random tuple (G1, GT , e, g, q) of bilinear parameters, where g is the generator of G1 and e is the bilinear map. Consequences of Pairings. Pairings have important consequences on the hardness of certain variants of the ▇▇▇▇▇▇-▇▇▇▇▇▇▇ problem. For instance, symmet- ric pairings lead to a strict separation between the intractability of the Computational ▇▇▇▇▇▇-▇▇▇▇▇▇▇ problem and the hardness of the corresponding de- cision problem. The security of our proposal is based on the hardness of the computational ▇▇▇▇▇▇- ▇▇▇▇▇▇▇ (CDH) problem, Divisible computational ▇▇▇▇▇▇-▇▇▇▇▇▇▇ and K-Bilinear ▇▇▇▇▇▇-▇▇▇▇▇▇▇ expo- nent, which are described below: • Computational ▇▇▇▇▇▇-▇▇▇▇▇▇▇ (CDH): Given g, gα, gβ for unknown α, β ∈ Zq, compute gαβ.
Computability. There exists a polynomial time algorithm which can compute the value of e(P, Q) efficiently for all P, Q ∈ G1. For the details of the construction of such bilinear maps in a secure and efficient manner, please refer to [2, 3, 9, 12].
1. The Discrete Logarithm Problem (DLP): given P, Q ∈ G1, the DLP in G1 is to find an integer n, such that Q = n ╳ P, whenever such an integer exists.
Computability. There is an efficient algorithm to compute ê(P, Q) for all P, Q ∈ G1. Note that the bilinearity of pairings also implies that ê : G1 × G1 G2 is symmetric. Thus, for any Q, R ∈ G1, the equality ê(Q, R) = ê(R, Q) holds. Both Q, R ∈ G1 can be represented by some generator P such that Q = aP and R = bP where a, b ∈ Z. Then it’s followed that ê(Q, R) = ê(aP, bP) = ê(P, P)ab = ê(bP, aP) = ê(R, Q). The map ê may be computed using a Weil pairing [41] or a ▇▇▇▇ pairing [25] on an elliptic curve over Fq. In principle, the antisymmetry of the Weil pairing forces the two subgroups to be distinct. However, given a supersingular curve1 one may define a modified Weil pairing on a single subgroup of order q using distortion maps introduced by Verheul [59]. Distortion maps (also called endomorphisms) makes it possible to send points from one subgroup of the l-torsion to another. Of the two, the Weil pairing has simpler mathematic properties. However, it does not always reach the optimal value for ▇. ▇▇▇▇ on the other hand, always reaches its optimal value.
Computability. There is an efficient algorithm to compute for all ∈ .
Computability. There is an efficient algorithm to compute e(P, Q) for all P, Q ∈ G1 . In this section, we generate the pair-wise key first which is used to compute the group session key afterward, then present our ID-based one round authenticated group key agreement protocol enlightened by the modified ID-based public key infrastructure described in section 3. Let U1 ,U 2 ,⋯,Un be the users who are going We note that the Weil [13] and ▇▇▇▇ [23] pairings associated with supersingular elliptic curves or abelian varieties can be modified to create such bilinear maps.
Computability this means that there exists an efficient algorithm to compute e (P, P) ∀ P ∈ G. by ▇.