Further Discussion. During the term of this agreement, enterprise bargaining will continue by all parties to further progress the benefits the parties can achieve from improved operational efficiency and should further efficiency improvements be identified and agreed by the parties, then the Agreement will be amended during its term.
Further Discussion. If the employee wishes to discuss the grievance further, he shall, within ten (10) working days of receipt of the department head's reply, appeal the department head's decision in accordance with Section 6.4. or Section 6.5.
Further Discussion. Sublicensor shall, in the event it wishes to be supplied with the Compound and/or the Product from Sublicensee and/or its Third Party Manufacturers, enter into discussion with Sublicensee thereon. In case Sublicensee agrees to supply to Sublicensor said Compound and/or Product, then the Sections 10.1 and 10.2 hereinabove shall apply mutatis mutandis.
Further Discussion. S S Z S Z q
4.4.1 Adaptive Corruptions Adaptive security of our protocol is not achiev- able without relying on additional assumptions. To see this, consider the fol- lowing attack: starts the protocol with two equal pass-strings and, without corrupting anyone, silently observes the transcript produced by using random pass-strings. Afterwards, corrupts both players to learn their internal state. may now choose a value K. This also fixes L′ = K since the pass-strings were equal. Now note that is committed to E, F since signatures are not equivoca- ble. Since perfect shares are sparse in Fn, the probability that there exists a K 8 Instead of labels and one-time signature, one could just sign all the messages, as would be done using the split-functionality [BCL+05], but this would be less efficient. This trade-off, with labels, is especially useful when we use a PAKE that admits adding labels basically for free, as it is the case with the special PAKE protocol we use. such that E K and F K are both perfect shares is negligible. Thus, there do not exist plausible values U, V ′ that explain the transcript9.
4.4.2 Removing Modeling Assumptions All modeling assumptions of our protocol come from the realization of the ideal A-iPAKE functionality. E.g., the l-iPAKE protocol from section 4.1.3 requires a random oracle, an ideal cipher and a CRS. We note that we can remove everything up to the CRS by, e.g., taking the PAKE protocol introduced in [KV11]. This protocol also securely realizes our A-iPAKE functionality10. However, it is more costly than our l-iPAKE protocol since both messages each contain one non-interactive zero knowledge proof. Since fPAKE implies a regular PAKE (simply set δ = 0), [CHK+05] gives strong evidence that we cannot hope to realize 7fPAKE without a CRS.
Further Discussion. During the term of this Agreement, the employer and the employees bound by this Agreement will further progress improved operational efficiency.
Further Discussion. It is understood that there will be further discussion of items 3, 4 and 6 to achieve mutual agreement with both parties.
Further Discussion. Without impairment to, or delay of the completion of, the Project, the parties agree to continue discussions about, and work collaboratively to identify solutions regarding future annexation of the Westucky area, including negotiation of a property tax sharing agreement between the City and County and abatement of all health and safety code violations.
Further Discussion. In this subsection, we describe the two further impacts on performance in constant-time and higher parameter sets in more detail: Radical isogenies scale badly to larger primes, as their cost scales with log(p), and dummy-free isoge- xxxx are more expensive, as we need to switch direction often for a dummy-free evaluation. Radical isogenies do not scale well. Using the results in Tables 1 and 2, the cost of a single radical isogeny is approximately 600 finite field operations, with an overhead of about 2500 finite field operations for a prime of 512 bits. Thus, a CSURF-512 implementation (which uses 2/4- radical isogenies) or a CRADS-512 implementation (which uses 2/4- and 3/9- radical isogenies) could be competitive with a state-of-the-art CSIDH-512 implementation. However, implementations using radical isogenies scale worse than CSIDH implementations, due to the high cost of exponentiation in larger prime fields. For example, for a prime of 2048 bits, just the overhead of switching curve models is already over 8500 finite field operations, which is close to 1% of total cost for a ‘traditional’ CSIDH implementation. Therefore, CSIDH is expected to outperform radical isogenies for larger primes. In Sect. 6, we demonstrate this using a benchmark we have performed on CSIDH, CSURF, CRADS, and an implementation using the hybrid strategy we introduce in Sect. 5, for six different prime sizes, from 512 bits up to 4096 bits. These prime sizes are realistic: several analyses, such as [6, 11, 22], call the claimed quantum security of the originally suggested prime sizes for CSIDH (512, 1024 and 1792 bits) into question. We do not take a stance on this discussion, and therefore provide an analysis that fits both sides of the discussion. Dummy-free radical isogenies are costly. Recall that radical isogenies require an initial point P of order N to switch to the right Xxxx normal form, depending on the direction of the isogeny. So, two kinds of curves in Xxxx normal form arise: P belongs either to E[π 1] or to E[π + 1]. Now, a dummy-free chain of radical isogenies requires (at some steps of the group action) to switch the direction of the isogenies, and therefore to switch to a Xxxx normal form where P belongs to either E[π 1] or E[π + 1]. As we switch direction mi ei times, this requires mi ei torsion points. That is, a dummy-free implementation of a chain of radical isogenies will require at least (mi ei ) torsion points, which leaks information on ei. We can make...
