P P Clause Samples
P P. 91583 CONTRACTORS - SUB-WORK, 1, 2 FAM DWGS B B ------------------------------------------------------------------------------------------------------------------------------- 91581 CONTRACTORS - SUB-WORK, ▇▇▇ ▇▇▇▇▇ ▇ ▇ ------------------------------------------------------------------------------------------------------------------------------- ▇▇▇▇▇ CONTRACTORS - SUB-WORK, INDUSTRIAL SS SS ------------------------------------------------------------------------------------------------------------------------------- 91585 CONTRACTORS - SUB-WORK, BUILDINGS B B Yes ------------------------------------------------------------------------------------------------------------------------------- 91589 CONTRACTORS STREET HWY CONSTRUCT SS SS ------------------------------------------------------------------------------------------------------------------------------- 91590 CONTRACTORS PERMANENT YARDS B + ------------------------------------------------------------------------------------------------------------------------------- 91629 DEBRIS REMOVAL, CONSTRUCTION SITE B B ------------------------------------------------------------------------------------------------------------------------------- 52134 DOOR OR WINDOW MANUFACTURING P P ------------------------------------------------------------------------------------------------------------------------------- 52315 DOOR OR WINDOW MFG - WOOD P P ------------------------------------------------------------------------------------------------------------------------------- 91746 DOOR OR WINDOW INSTALLATION (METAL) P P ------------------------------------------------------------------------------------------------------------------------------- 92102 DRILLING WATER SS SS ------------------------------------------------------------------------------------------------------------------------------- 92215 DRIVEWAY, PARKING LOT, SIDEWALK PAVING P P ------------------------------------------------------------------------------------------------------------------------------- 92338 DRY WALL OR WALL BOARD INSULATION P P ------------------------------------------------------------------------------------------------------------------------------- 92451 ELECTRICAL APPARATUS INSTALL, SVC. REP. B SS ------------------------------------------------------------------------------------------------------------------------------- 92478 ELECTRICAL WORK WITHIN BUILDING B B Yes --------------------------------------------------------...
P P. Lemma 5. If two parties i and j sends valid Vote(ID, G) and valid Vote(ID, Gj) to all parties, respectively, i.e., there exists ( , A, r, ) matching the majority elements in G and r is the largest VRF evaluation among all elements in G, and there exists ( , Aj, rj, ) matching the majority elements in Gj and rj is the largest VRF evaluation among all elements in Gj, then the (A, r) = (Aj, rj).
P P. Commitment. Assume that Pi is the first party who starts to run the protocol’s revealing phase, it implies that i received a valid ▇▇▇▇▇▇▇▇▇▇▇▇▇(▇▇, ▇, ▇) message from leader L. If another honest j received a valid CommitAggPvss(ID, hj, Σj) message from leader L, where hj = h, since a valid Σ contains 2f + 1 valid signatures for a same hash value from distinct parties, it induces that at least one honest party signed for both h and hj, which is impossible. Hence, when some honest party i starts to run the protocol’s revealing phase, the h from any valid ▇▇▇▇▇▇▇▇▇▇▇▇▇(▇▇, ▇, ▇) message is unique. Following the commitment of the PVSS scheme, there exists a fixed value seed corresponding to the pvss, where h = (pvss). Suppose that some honest party outputs seedj from the Seeding. By the code, it receives 2f + 1 SeedReady messages containing seedj. Then at least one honest party received 2f + 1 valid SeedEcho messages with the same seedj from distinct parties, which means that at least f + 1 honest parties received valid Seed(ID, h, Σ, seedj) message from the leader. From the previous analysis, no honest party will accept a seedj seed from PL or multicast it. Thus, seedj = seed. – Unpredictability. Prior to f +1 honest parties are activated to run the revealing phase of the Seeding protocol, the adversary can only collect at most 2f decryption shares for the committed pvss script. Trivially according to the Unpredictability of PVSS with weight tags, since the aggregated pvss has a weight with 2f +1 non-zero positions, it is infeasible for the adversary to compute a seed∗ = seed at the moment, where seed is the actual secret committed to the aggregated pvss script. The complexities can be easily seen as follows: The message complexity of Seeding is O(n2), which is due to each party sends n SeedEcho and SeedReady messages; considering that the input secret s and pvss both are O(λ) bits, and there are O(n) messages with O(λn) bits and O(n2) messages with O(λ) bits, thus the communication complexity of the protocol is of overall O(λn2) bits.
P P. Fully asynchronous system without private setup. There are n designated parties, each of which has a unique identity (i.e., 1 through n) known by everyone. Moreover, we consider the asynchronous message-passing model with static corruptions and bulletin public key infrastructure (PKI) assumption in the absence of any private setup. In particular, our system and threat models can be detailed as: – Bulletin PKI. There exists a PKI functionality that can be viewed as a bulletin board, such that each party i j j∈[n] can register some public keys (e.g., the verification key of digital signature) bounded to its identity via the PKI before the start of protocol. – Computing model. We let the n parties and the adversary A be probabilistic polynomial-time inter- active Turing machines (ITMs). A party i is an ITM defined by the given protocol: it is activated upon receiving an incoming message to carry out some polynomial steps of computations, update its states, possibly generate some outgoing messages, and wait for the next activation. Moreover, we explicitly require the bits of the messages generated by honest parties to be probabilistic uniformly bounded by a polynomial in the security parameter λ, which naturally rules out infinite protocol executions and thus restrict the running time of the adversary through the entire protocol. – Up to n/3 static Byzantine corruptions. The adversary can choose up to f out of n parties to corrupt and fully control, before the course of a protocol execution. No asynchronous BFT can tolerate more than f = (n 1)/3 such static corruptions. Through the paper, we stick with this optimal resilience. We also consider that the adversary can control the corrupted parties to generate their key materials maliciously, which captures that the compromised parties might exploit advantages whiling registering public keys at the PKI. – Fully asynchronous network. We assume that there exists an established p2p channel between any two parties. The channels are considered as secure, which means the adversary cannot modify or drop the messages sent between honest parties and cannot learn any information of the messages except their lengths. Moreover, the adversary must be consulted to approve the delivery of mes- sages, namely, it can arbitrarily delay and reorder messages. Remark that we assume asynchronous secure channels (instead of merely asynchronous reliable channels) for presentation simplicity, and they are not extra assumptions as can be ...
P P. Proof. The fact that S (PXY Z ) = 0 when either E < B or E < A follows from Theorem 5 because PXY Z is either X-simulatable or Y -simulatable by ▇▇▇. The fact that S (PXY Z ) = S(PXY Z) when E > B and E > A can be proved as follows. A suboptimal protocol based on the authentication method of Theorem 7 can be used to generate a relatively small t-bit secret key K, using O(t) bits of the random string. This key can then be used, similar to a bootstrapping process, for instance based on the protocols of [10], to authenticate the messages exchanged in an optimal passive-adversary protocol achieving S(PXY Z). The size of K must only be logarithmic in the maximal size of a message exchanged in [10] and linear in the number of rounds of . No matter what amount of secret key must be generated by , this can be achieved by using messages of size proportional to the key size in a constant number of rounds. Therefore, the ratio of size of K and the size of the generated key vanishes asymptotically. min[h( AE); h( BE)] h( AB) S(PXY Z) 1 h( AB): It was recently proved that S(PXY Z) > 0 unless E = 0 [17], even when both E < B and E < A, i.e., even when the above lower bound vanishes (or is negative).
P P. As usual in security notions for key exchange, the adversary also sets the session keys for corrupted players. In the definition of ▇▇▇▇▇▇▇ et al. [20], the adversary additionally sets Pi’s key if P1−i is corrupted. However, contrarily to the original definition, we do not allow the adversary to set i’s key if 1−i is corrupted but did not guess i’s pass-string. We make this change in order to protect an honest i from, for instance, revealing sensitive information to an adversary who did not successfully guess her pass-string, but did corrupt her partner. Another minor change we make is considering only two parties — 0 and ▇▇▇ composability takes care of ensuring that a two-party functionality remains secure in a multi-party world. As in the definition of ▇▇▇▇▇▇▇ et al. [20], we consider only static corruptions in the standard corruption model of ▇▇▇▇▇▇▇ [17]. Also as in their definition, we chose not to provide the players with confirmation that key agreement was successful. The players might obtain such confirmation from subsequent use of the key. By default, in the fPAKE functionality the TestPwd interface provides the adversary with one bit of information — whether the pass-string guess was cor- rect or not. This definition can be strengthened by providing the adversary with no information at all, as in implicit-only PAKE ( iPAKE, Figure 7), or weakened by providing the adversary with extra information when the adversary’s guess is close enough. To capture the diversity of possibilities, we introduce a more general TestPwd interface, described in Figure 2. It includes three leakage functions that we will instantiate in different ways below—Lc if the guess is close-enough to succeed, Lf if it is too far. Moreover, a third leakage function—Lm for medium distance— allows the adversary to get some information even if the adversary’s guess is only The functionality fPAKE is parameterized by a security parameter λ and ▇▇▇▇▇-
P P. To model the possibility of dictionary attacks, the functionality allows the adversary to make one pass-string guess against each player ( 0 and 1). In the real world, if the adversary succeeds in guessing (a pass-string similar enough to) party i’s pass-string, it can often choose (or at least bias) the session key computed by i. To model this, the functionality then allows the adversary to set the session key for i.
P P. In other words, F now generates a random session key upon a first NewKey query for an honest party i with fresh record ( i, pwi) where the other party is also honest, if (at least) one of the following events happens:
P P. Σ Suppose that all the x aborted oracles resulting from the password guessing attacks, the attacker’s advantage over the password is x+1 p + 1, where 1 is
j=1 negligible. As a result, in this game A’s advantage AdvA(π) = F (x, x+1 pj +P1) is also negligible and we have proved this claim. H
P P. Case 2 : Suppose A and B are in different pseudospheres S(FA) and S(FB) for distinct faces FA and FB of S. We can assume without loss of generality that every vertex of B A is labeled with S, and we can show that FA <f FB. − − ∩ − ∈ − ∈ P ≺ ∩ ⊆ R Case 2a: Suppose dim(FA) > dim(FB). Since dim(FA) > dim(FB), the set FA FB must be nonempty, so choose any vertex v FA FB. Since A S(FA), the simplex A must be a labeling of FA with simplexes between FA and S. Since v is a vertex of FA, this means that v appears in all simplexes labeling A, and hence in all simplexes labeling A B. Since we have assumed that S is the label of every vertex in B A, and since S certainly contains the vertex v, the vertex v appears in all labels of B A. It follows that v appears in every simplex labeling B. Let BA be the simplex consisting of B together with the vertex v labeled with S, and notice that BA is a simplex in A(S). We have BA r B since dim(BA) = dim(B) + 1 > dim(B). We have A B BA since { − } { − } ≺ ∩ ⊆ ⊆ A B B BA. We have codim(B, BA) = 1 since B and BA differ only in v. Case 2b: Suppose dim(FA) = dim(FB), in which case we have pA p pB where pA = min ids(FA) ids(FB) and pB = min ids(FB) ids(FA) . Let vA and vB be the vertexes for processors pA and pB in the faces FA and FB of S. Let FC be the face of S obtained from FB by replacing vB with vA, and let C be the labeling of FC obtained by labeling vA with S and every other ver- tex with its label in B. Since A is a labeling of FA with simplexes between FA and S, and since vA is a vertex of FA, the vertex vA appears in every simplex labeling A and hence A ∩ B; and since we are assuming that every vertex of B − A is labeled with S which certainly contains vA, it follows that every vertex of B − A is labeled with a simplex containing vA; and hence it follows that every label in B contains FC. It follows that C ∈ RA(S) since C is a labeling of a face FC of S with simplexes between FC and S. We have C ≺r B since min {ids(FC) − ids(FB)} = pA ≺p pB = min {ids(FB) − ids(FC)} . We have A ∩ B ⊆ C and codim(B, C) = 1. Taking BA = C, we are done. H