New Results. In this paper we solve Byzantine Agreement in the full-information, asynchronous model against an adaptive adversary, by adopting the same forensic accounting paradigm of Xxxx and Saia [KS16]. We design a coin- flipping protocol and two simple statistical tests such that if the Byzantine players continually foil attempts to flip a fair coin, they will be detected in a polynomial number of rounds by at least one of the tests, so long ≥ as f < n/4. (The tests measure individual deviation in l2 norm and pair-wise correlation.) Our analysis is tight inasmuch as these two particular tests may not detect anything when f n/4. One factor contributing to the low resiliency of King and Saia’s protocols [KS16, KS18] is that two good players may blacklist different sets of players, making it easier for the adversary to induce disagreements on the outcome of the shared coin flip. A technical innovation in our protocol is a method to drastically reduce the level of disagreement between the views of good players. First, we use a fractional blacklisting scheme. Second, to ensure better consistency across good players, we extend King and Saia’s [KS16] Blackboard to an Iterated Blackboard primitive that drastically reduces good players’ disagreements of the historical transaction record by allowing retroactive corrections to the record.
New Results. Following all these improvements the measurement of dose in 90Y solution was repeated and after uncertainty analysis was found to have improved with expanded uncertainty 1.98 % (k=2). The uncertainty on volume of solution was now <1 % (k=1) compared to 1.24 % previously. Preliminary analysis also showed an agreement, with the previous 90Y measurement of 0.1 %. Agreement with analytic data from MIRD, RADAR and the Decay Data Evaluation Project (DDEP) evaluation are in the order of 98 % (see Figure 20). The same technique was then used to determine the chamber response with solutions of 177Lu and 131I. A depth range of 0.25 mm to 2.5 mm was covered with 0.25 mm steps. The current at each depth was corrected for, temperature, pressure, humidity, leak current, ion recombination and source decay using LabVIEW software remotely controlling the measurements. New measurements with a 177Lu solution gave results that again showed agreement with MIRD and RADAR data with a measurement uncertainty of 1.92 % (k=2) (see Figure 20). However, for 131I solution the measurements show a significant disagreement when compared to the MIRD and RADAR data of +7%. This inconsistency has been identified as most likely to be a problem with simulation of the photons in the laboratory environment, and due to backscatter not being accounted for during the simulation. Figure 20: Comparison of measured absorbed dose to water for 90Y, 177Lu and 131I to reference values. Datasets from this work (2018 - cross) and previous measurement (2015 - square) are shown for 90Y. Red dashed line indicate line of unity Film measurements of absorbed dose The preceding HLT11 MetroMRT project established the use of radiochromic film measurements as a way of verifying the MC codes used for simulation of beta radiation transport. This was achieved with the measurement of dose in 90Y solution in a cylindrical phantom geometry at NPL. Therefore, this project aimed to expand on this and further verify the technique for both 177Lu and 131I solution in the same geometry where a film is suspended between mylar layers within the radionuclide solution. MC calculations were performed in EGSnrc software to determine the absorbed dose profiles from all emitted particles at the edge of the film and into the surrounding phantom wall. Measurements were made for all three isotopes (i.e. 90Y, 177Lu and 131I). Profiles across the dose map of the three radionuclide solutions were used to compare with MC simulations. Unfortun...
New Results. − One feature of the asynchronous model is that every player must perpetually entertain the possibility that f players have crashed and will never be heard from again. Thus, when n = 3f + 1, the number of fully participating players at any stage is n f = 2f + 1 and up to f of these players may be corrupt! Among the set of participating players, the good players hold the thinnest possible majority: f + 1 vs. f. We develop a special coin-flipping protocol to be used in Bracha’s framework [Bra87, Ben83] when the − corrupt and non-corrupt players have roughly equal influence. Initially all players have weight 1. The coin- flipping protocol has the property that if the corrupt players repeatedly foil its attempts to flip a global coin, then we can fractionally blacklist players (reduce their weights) in such a way that the blacklisting rate for good players is only infinitesimally larger than the blacklisting rate for corrupt players. Specifically, we guarantee that among any n f = 2f + 1 participating players, the total weight of the good players minus the total weight of the corrupt players is bounded away from zero. Eventually all corrupt players have their weights reduced to zero (meaning they have no influence over the global coin protocol) and at this point, the scheduling power of the adversary is insufficient to fix the behavior of the global coin. Agreement is reached in a few more iterations of Xxxxxx’s algorithm, with high probability. ≥ The final result is a randomized f-resilient Byzantine Agreement protocol with latency (expected and with high probability) O˜(n4ǫ−8), where n = (3 + ǫ)f, ǫ 1/f. In other words, the latency ranges between n4 and n12, depending on ǫ. This latency-resiliency tradeoff is always at least as good as [HPZ22], but is slower than [KS16, KS18] when f < n/400 or f < n/(0.87 × 109) is sufficiently small; see Table 1. Citation Resilience Latency Local Computation per Message Ben-Or [Ben83] f < n/5 2Θ(n) poly(n) f = O(√tn) exp(t2) poly(n) Bracha [Bra87] f < n/3 2Θ(n) poly(n) King & Saia [KS16, KS18] f < n/400 O˜(n5/2) exp(n) f < n/(0.87 × 109) O(n3) poly(n) Xxxxx, Xxxxxx & Xxx [HPZ22] f < n/(4 + ǫ) O˜(n4/ǫ4) poly(n) new f < n/(3 + ǫ) O˜(n4/ǫ8) poly(n) Table 1: Randomized Byzantine Agreement protocols in the asynchronous, full information model against an adaptive adversary. Here ǫ = Ω(1/n).
