{"component": "clause", "props": {"groups": [{"snippet_links": [{"key": "the-system", "type": "definition", "offset": [100, 110]}, {"key": "specific-conditions", "type": "definition", "offset": [177, 196]}], "snippet": "Before discussing the simulation-based results, it is crucial to perform the complexity analysis of the system. Therefore, we can better understand how the system behaves under specific conditions.", "samples": [{"hash": "kYePoDhHJrQ", "uri": "/contracts/kYePoDhHJrQ#complexity-analysis", "label": "Thesis Submission Agreement", "score": 30.8583374023, "published": true}, {"hash": "5l7tDVl4Vq8", "uri": "/contracts/5l7tDVl4Vq8#complexity-analysis", "label": "Master's Thesis", "score": 29.5142288208, "published": true}], "size": 2, "hash": "a767d890eb8e08ff35bab8cd32e56cdf", "id": 1}, {"snippet_links": [{"key": "the-proposed-protocol", "type": "clause", "offset": [51, 72]}, {"key": "table-of", "type": "clause", "offset": [198, 206]}, {"key": "registered-users", "type": "definition", "offset": [211, 227]}, {"key": "after-receiving", "type": "clause", "offset": [310, 325]}, {"key": "registration-phase", "type": "clause", "offset": [352, 370]}, {"key": "smart-card", "type": "definition", "offset": [453, 463]}, {"key": "the-user", "type": "definition", "offset": [501, 509]}, {"key": "registration-process", "type": "definition", "offset": [545, 565]}, {"key": "in-addition", "type": "clause", "offset": [619, 630]}, {"key": "for-users", "type": "clause", "offset": [696, 705]}, {"key": "as-shown", "type": "definition", "offset": [780, 788]}, {"key": "table-1", "type": "clause", "offset": [792, 799]}, {"key": "new-features", "type": "definition", "offset": [982, 994]}, {"key": "very-important", "type": "clause", "offset": [999, 1013]}, {"key": "agreement-for", "type": "clause", "offset": [1074, 1087]}, {"key": "session-initiation-protocol", "type": "definition", "offset": [1088, 1115]}, {"key": "the-protocol", "type": "clause", "offset": [1120, 1132]}, {"key": "terms-of", "type": "clause", "offset": [1276, 1284]}], "snippet": "In this section, we summarize the functionality of the proposed protocol and compare the proposed protocol with \u2587\u2587\u2587 et al.\u2019s protocol. In Xie et al.\u2019s protocol, the server needs to store a password table of all registered users for verification. In the proposed protocol, the password is embedded in h(PW a) . After receiving {h(PW\na) username} in the registration phase, the server computes R = h(h(PW\na) username)s\u22121P and stores it in the memory of a smart card, and then delivers the smart card to the user U via a secure channel. During the registration process, the server does not need to store a password table. In addition, the proposed protocol provides a securely update password phase for users to change their password freely and can resist stolen smart card attacks. As shown in Table 1, the proposed protocol can provide more unique properties such as no password or verifier table and password update freely, which were not considered in Xie et al.\u2019s protocol. These new features are very important in implementing a practical and universal authenticated key agreement for session initiation protocol. As the protocol of Xie et al. is currently the most secure and efficient one in the literatures, we compare the proposed protocol and Xie et al.\u2019s protocol in terms of computational costs. First, we define some notations as follows.", "samples": [{"hash": "7X4cv2RMCX7", "uri": "/contracts/7X4cv2RMCX7#complexity-analysis", "label": "Password Authenticated Key Agreement Protocol", "score": 26.7392223655, "published": true}], "size": 2, "hash": "62106de5118d1e9e7460f7150a36a3c8", "id": 2}, {"snippet_links": [{"key": "security-properties", "type": "clause", "offset": [32, 51]}, {"key": "group-key-agreement", "type": "clause", "offset": [55, 74]}, {"key": "and-security", "type": "clause", "offset": [185, 197]}, {"key": "most-important", "type": "clause", "offset": [283, 297]}, {"key": "computation-costs", "type": "clause", "offset": [311, 328]}, {"key": "communication-costs", "type": "definition", "offset": [333, 352]}], "snippet": "Above section has discussed the security properties of group key agreement schemes. Important is also their complexity, namely performance costs. Sometimes trade-off between complexity and security is required, so that the schemes are suitable to particular environments. Two of the most important criteria are computation costs and communication costs.", "samples": [{"hash": "lwqibfPc9IB", "uri": "/contracts/lwqibfPc9IB#complexity-analysis", "label": "Dissertation", "score": 20.4042701721, "published": true}], "size": 2, "hash": "b33e7b3d9cf71f8196ef9582e972d7ce", "id": 3}, {"snippet_links": [{"key": "and-communication", "type": "clause", "offset": [357, 374]}], "snippet": "This section provides various comparisons among M2MAKA-FS and well-known related protocols including Shuai et al.\u2019s protocol, \u2587\u2587\u2587\u2587\u2587 et al.\u2019s protocol, Kapito et al.\u2019s protocol, Yang et al.\u2019s protocol and Li et al.\u2019s protocol. First of all, we will focus on feature comparisons to know the distinctive feature differences among them. After that, computation and communication analysis follows, to show IoT environmental fitness of them.", "samples": [{"hash": "ead1wMyaY1J", "uri": "/contracts/ead1wMyaY1J#complexity-analysis", "label": "Machine to Machine Authenticated Key Agreement With Forward Secrecy for Internet of Things", "score": 34.9277267456, "published": true}], "size": 1, "hash": "ad5e4335dd4dd3f6d596e80ddd946d76", "id": 4}, {"snippet_links": [{"key": "costs-of", "type": "definition", "offset": [76, 84]}, {"key": "group-members", "type": "definition", "offset": [130, 143]}, {"key": "the-current", "type": "clause", "offset": [274, 285]}, {"key": "the-sponsor", "type": "clause", "offset": [343, 354]}, {"key": "sum-of", "type": "clause", "offset": [422, 428]}, {"key": "merge-protocol", "type": "clause", "offset": [474, 488]}, {"key": "total-number-of", "type": "definition", "offset": [593, 608]}, {"key": "the-cumulative", "type": "clause", "offset": [629, 643]}, {"key": "number-of-members", "type": "clause", "offset": [796, 813]}, {"key": "according-to", "type": "definition", "offset": [1133, 1145]}], "snippet": "\u200c ^ In this section we analyze the memory, communica- tion, and computation costs of \u00b5STR, \u00b5TGDH, and TFAN. The number of current group members, merging mem- bers, merging groups, and leaving members are denoted by: n, m, k, and p, respectively. Additionally, the height of the current and updated tree are denoted by h and h, respec- tively. The sponsor is denoted by ls, vs (or lsi , vsi if several sponsors exist). The sum of the heights of all non- highest trees in the merge protocol is denoted by \u03b1. We fo- cus on the number of stored secret and public keys, the num- ber of rounds, the total number of broadcast messages, the cumulative broadcast message size 4, and the serial num- ber of multiplications 5. We consider here random \u00b5TGDH trees and half fully filled TFAN trees, i.e., the number of members in each cs-tree is [ q+1 | for art = S and 2q\u20141 and public keys outside the cs-tree is decreased. It is obvi- ous that the required memory space for TFAN (art = S) is lower than for \u00b5STR, and of TFAN (art = T ) is higher than for \u00b5TGDH. Hence as a whole, all protocol suites can be sorted from the least to the highest according to their memory consumption as follows: \u00b5TGDH < TFAN (art = T ) < TFAN (art = S) < \u00b5STR.", "samples": [{"hash": "3H6UrvqnhzP", "uri": "/contracts/3H6UrvqnhzP#complexity-analysis", "label": "Tree Based Group Key Agreement Framework", "score": 19.0, "published": true}], "size": 1, "hash": "c4b1f4b1b872d9d90231019c581f1d57", "id": 5}, {"snippet_links": [{"key": "communication-of", "type": "clause", "offset": [42, 58]}, {"key": "group-key-agreement", "type": "clause", "offset": [90, 109]}, {"key": "based-on", "type": "clause", "offset": [276, 284]}, {"key": "communication-delay", "type": "clause", "offset": [483, 502]}, {"key": "total-number-of", "type": "definition", "offset": [504, 519]}, {"key": "communication-system", "type": "definition", "offset": [798, 818]}, {"key": "lack-of", "type": "clause", "offset": [922, 929]}, {"key": "measures-to", "type": "clause", "offset": [961, 972]}, {"key": "table-1", "type": "clause", "offset": [1079, 1086]}, {"key": "the-current", "type": "clause", "offset": [1109, 1120]}, {"key": "the-protocol", "type": "clause", "offset": [1221, 1233]}, {"key": "new-members", "type": "definition", "offset": [1326, 1337]}, {"key": "the-cost", "type": "clause", "offset": [1410, 1418]}, {"key": "average-value", "type": "definition", "offset": [1435, 1448]}, {"key": "security-reasons", "type": "definition", "offset": [1624, 1640]}, {"key": "in-communication", "type": "definition", "offset": [1748, 1764]}, {"key": "section-5", "type": "definition", "offset": [1807, 1816]}, {"key": "wide-area-network", "type": "definition", "offset": [2017, 2034]}, {"key": "to-provide", "type": "clause", "offset": [2075, 2085]}, {"key": "cascaded-events", "type": "clause", "offset": [2105, 2120]}, {"key": "communication-cost", "type": "clause", "offset": [2139, 2157]}, {"key": "partition-protocol", "type": "clause", "offset": [2237, 2255]}, {"key": "cost-of", "type": "clause", "offset": [2363, 2370]}], "snippet": "This section compares the computation and communication of STR proto- col to other recent group key agreement methods, Cliques GDH.2 [STW00], Tree-Based \u2587\u2587\u2587\u2587\u2587\u2587-\u2587\u2587\u2587\u2587\u2587\u2587\u2587 (TGDH) [KPT00], and \u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587/\u2587\u2587\u2587\u2587\u2587\u2587\u2587 (BD) [BD94]. These protocols provide contributory group key agreement based on different extensions of the two-party \u2587\u2587\u2587\u2587\u2587\u2587-\u2587\u2587\u2587\u2587\u2587\u2587\u2587 key exchange. Moreover, they all support dynamic membership operations. We consider the following costs: \u25a0 Number of rounds: this affects serial communication delay. Total number of messages: as the number of messages grows, the probability of message loss or corruption is increased, and so is the delay. \u25a0 Number of unicasts and broadcasts: a broadcast is much more expensive operation than a unicast, since it requires many acknowledgments within the group communication system. \u25a0 Number of serial exponentiation: this is the main factor in the computation overhead. \u25a0 Robustness: Lack of robustness requires additional measures to make the secure group communication system robust against cascaded (nested) faults and membership events. Table 1 shows a comparison of the current approaches for group key manage- ment. The bold text refers to a parameter that severely slows down the protocol in a WAN deployment, for which STR is best suited. In Cliques GDH.2 protocol, the number of new members k is considered, since the merge cost depends on number of new members. The cost for TGDH is the average value when the key tree is fully balanced. The partition or leave cost for STR is computed on average, since it depends on the depth of the lowest-numbered leaving member node. For security reasons [STW00], BD always has to restart anew upon every membership event. As seen from the table, STR is minimal in communication on every mem- bership event. We showed in Section 5 that robustness in the STR protocol is not only easier to implement than in other protocols, but it also achieves higher robustness to network partitions. Cliques GDH.2 is quite expensive protocol in wide area network, since: 1) it is hard or very expensive to provide robustness against cascaded events [AKNR+ 01] and 2) communication cost for merge in- creases linearly as the number of new members does. In TGDH, the partition protocol is expensive (relatively slow) which may cause more cascaded faults and long delays to agree on a key. The cost of BD is mostly acceptable but large number of simultaneous broadcast messages can be problematic over a wide area network. [AAH + 00] Y. \u2587\u2587\u2587\u2587, \u2587. \u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587, \u2587. \u2587\u2587\u2587\u2587\u2587, \u2587. \u2587\u2587\u2587, \u2587. \u2587\u2587\u2587\u2587-\u2587\u2587\u2587\u2587\u2587\u2587, \u2587. \u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587, \u2587. \u2587\u2587\u2587\u2587\u2587\u2587\u2587, \u2587. \u2587\u2587\u2587\u2587\u2587\u2587\u2587, and \u2587. \u2587\u2587\u2587\u2587\u2587\u2587. Secure group communication in asyn- chronous networks with failures: Integration and experiments. In ICDCS 2000, April 2000. [AKNR + 01] Y. \u2587\u2587\u2587\u2587, \u2587. \u2587\u2587\u2587, \u2587. \u2587\u2587\u2587\u2587-\u2587\u2587\u2587\u2587\u2587\u2587, \u2587. \u2587\u2587\u2587\u2587\u2587\u2587\u2587, \u2587. \u2587\u2587\u2587\u2587\u2587\u2587\u2587, and \u2587. \u2587\u2587\u2587\u2587\u2587\u2587. Exploring robustness in group key agreement. In ICDCS 2001, 2001.", "samples": [{"hash": "9XZvjitADp8", "uri": "/contracts/9XZvjitADp8#complexity-analysis", "label": "Communication Efficient Group Key Agreement", "score": 19.0, "published": true}], "size": 1, "hash": "60c8198596c9b71ecdedded2fc485ea6", "id": 6}, {"snippet_links": [{"key": "table-1", "type": "clause", "offset": [0, 7]}, {"key": "costs-of", "type": "definition", "offset": [57, 65]}, {"key": "missing-data", "type": "definition", "offset": [160, 172]}, {"key": "the-group", "type": "clause", "offset": [209, 218]}, {"key": "total-number-of", "type": "definition", "offset": [254, 269]}, {"key": "in-practice", "type": "clause", "offset": [443, 454]}, {"key": "computation-costs", "type": "clause", "offset": [470, 487]}, {"key": "based-on", "type": "clause", "offset": [556, 564]}, {"key": "to-handle", "type": "definition", "offset": [807, 816]}, {"key": "group-size", "type": "clause", "offset": [881, 891]}, {"key": "the-sponsor", "type": "clause", "offset": [963, 974]}, {"key": "ing-group", "type": "definition", "offset": [998, 1007]}, {"key": "note-h", "type": "clause", "offset": [1083, 1089]}, {"key": "concerning-the", "type": "clause", "offset": [1431, 1445]}, {"key": "in-case-of", "type": "clause", "offset": [1512, 1522]}, {"key": "in-other-cases", "type": "clause", "offset": [1604, 1618]}, {"key": "all-members", "type": "definition", "offset": [2256, 2267]}, {"key": "group-members", "type": "definition", "offset": [2398, 2411]}, {"key": "performed-by", "type": "clause", "offset": [2452, 2464]}, {"key": "the-function", "type": "clause", "offset": [2480, 2492]}, {"key": "note-f", "type": "definition", "offset": [2496, 2502]}, {"key": "distribution-of-costs", "type": "clause", "offset": [2720, 2741]}, {"key": "as-required", "type": "clause", "offset": [2742, 2753]}, {"key": "the-protocol", "type": "clause", "offset": [2886, 2898]}, {"key": "a-member", "type": "definition", "offset": [3536, 3544]}], "snippet": "Table 1 provides communication, computation and mem- ory costs of the optimized protocols. We consider one pro- tocol round as over if members have to wait for missing data to continue with the computation of the group key. Columns U and B represent the total number of unicast and broadcast messages, respectively. The message size column gives the total size of sent messages in log q-bits where q is the pa- rameter of the finite field Fq (in practice q \u2248 160 bits). Computation costs specify the total number of scalar-point multiplications per member based on member\u2019s index (po- sition) in the group. This creates a basis for the suitabil- ity analysis of the protocols for homogeneous and hetero- geneous groups. The memory costs column specifies the size of data that a device has to store in order to handle dynamic events. The following notations are used: n - ini- tial group size, i - updated index (position) of Mi, s - up- dated index (position) of the sponsor, m - size of the merg- ing group, p - number of leaving (partitioned) members, h - height of the TGDH tree (note h = \u2308log n\u2309), li (ls) - up- dated level of member\u2019s Mi (sponsor\u2019s Ms) node in TGDH initial merging group with sponsor Msj , Msr - the right- most sponsor in \u00b5TGDH partition, s\u2217 - index of sponsor Msj whose level lsj is maximal compared to other spon- sors in \u00b5TGDH merge. Communication Obviously, \u00b5STR provides best commu- nication efficiency concerning the total number of rounds and sent messages. The total messages size in case of join is constant, in case of merge depends on the number of merging members, and in other cases scales linearly with the sponsor\u2019s position, varying between 1 and n. Compared to \u00b5STR the size of \u00b5TGDH messages scales linearly with the level of sponsor\u2019s node ls, which varies between 0 and h = \u2308log n\u2309. Thus, in some cases \u00b5TGDH may require less communication bandwidth than \u00b5STR. Computation \u00b5BD protocol requires only 3 scalar-point multiplications (we do not count additional n \u2212 1 multi- plications with a small integer whose costs may become non-negligible for large n). From all protocols that were de- signed to handle dynamic events we point out \u00b5CLIQUES and \u00b5TGDH. \u00b5CLIQUES requires a constant number of multiplications for all members except for the sponsor. Sig- nificant drawback is that the number of sponsor\u2019s multipli- cations scales linearly in the number of group members. In \u00b5TGDH the number of multiplications performed by Mi is given by the function f (note f (i, s) \u2264 min(li, ls)), and can be approximated by O(log n). Notable is also that in \u00b5STR and \u00b5STR-H the number of multiplications per member is proportional to its node\u2019s position in the tree. This allows non-uniform distribution of costs as required in heteroge- neous groups. Memory \u00b5BD is stateless and requires, therefore, from group members to save only the group key. However, the protocol has to be restarted to update the group key af- ter occuring dynamic events. The handling of dynamic events by other CGKA protocols requires from mem- bers to save some auxiliary information. In \u00b5CLIQUES all members have to save equal amount of informa- tion (i.e, (n + 1) log q bits), regardless of their position in the group. In \u00b5TGDH required memory space de- pends on the level of member\u2019s node li, which varies between 0 and h = \u2308log n\u2309. Since the tree manage- ment policy of \u00b5TGDH tries to keep the tree balanced most members have to save \u2308log n\u2309 keys (i.e, \u2308log n\u2309 log q bits), whereas in \u00b5STR and \u00b5STR-H the number of keys that a member has to save scales linearly with his posi- tion in the tree and may, therefore, vary between 4 and 2n keys (i.e, between 4 log q and 2n log q bits). This is essen- tial for heterogeneous groups where less-powerful devices are assigned to the lower nodes and have to save, there- (l sj tree (note, li, ls \u2208 {0, . . . , h}), lsj \u2032 ) - updated (initial) fore, less data. CGKA Protocol Com munication Computation Memory M m + 1 m 1 m2+5m+4n+2 2 i < n: 1 n \u2264 i \u2264 n + m: i + 2 P min(\u2308log p\u2309 + 1, h) 0 min(2p, \u2308 n \u2309)2 h \u00b7 min(2p, \u2308 n \u2309)2 Msj : 2lsj \u2212 1, Msr : 2lsr Mi : max({f (i, sj )|\u2200sj }) Remarks: S - (setup, J - join, L - leave, M - merge, P - partition, Message size and size of saved data are given in log q bits, l\u03b1 \u2212 \u230alog |v\u03b1 \u2212 \u230av\u03b2 /2l\u03b2 \u2212l\u03b1 \u230b|\u230b, if l\u03b1 \u2264 l\u03b2 f (\u03b1, \u03b2) = l\u03b2 \u2212 \u230alog |v\u03b2 \u2212 \u230av\u03b1/2l\u03b1\u2212l\u03b2 \u230b|\u230b, if l\u03b1 > l\u03b2 k \u2208 {1, . . . , h \u2212 1} is the smallest integer such that \u230avi/2k \u230b is even.", "samples": [{"hash": "jIy61HIM9e3", "uri": "/contracts/jIy61HIM9e3#complexity-analysis", "label": "Contributory Group Key Agreement Protocols", "score": 19.0, "published": true}], "size": 1, "hash": "c80405c2bda4019fa01263dcfb6946ca", "id": 7}, {"snippet_links": [{"key": "operations-only", "type": "clause", "offset": [73, 88]}, {"key": "the-state", "type": "clause", "offset": [198, 207]}, {"key": "group-key-agreement", "type": "clause", "offset": [234, 253]}, {"key": "scheme-a", "type": "definition", "offset": [254, 262]}, {"key": "based-on", "type": "clause", "offset": [328, 336]}, {"key": "the-assumption", "type": "clause", "offset": [337, 351]}, {"key": "maximum-number", "type": "definition", "offset": [361, 375]}, {"key": "group-members", "type": "definition", "offset": [379, 392]}, {"key": "maximum-height", "type": "definition", "offset": [422, 436]}, {"key": "the-cost", "type": "clause", "offset": [459, 467]}, {"key": "the-case", "type": "definition", "offset": [494, 502]}, {"key": "a-member", "type": "definition", "offset": [532, 540]}, {"key": "the-current", "type": "clause", "offset": [555, 566]}, {"key": "the-group", "type": "clause", "offset": [637, 646]}, {"key": "table-1", "type": "clause", "offset": [773, 780]}, {"key": "in-practice", "type": "clause", "offset": [888, 899]}, {"key": "communication-overhead", "type": "clause", "offset": [921, 943]}, {"key": "total-number-of", "type": "definition", "offset": [1579, 1594]}, {"key": "all-members", "type": "definition", "offset": [1669, 1680]}, {"key": "leave-protocol", "type": "clause", "offset": [1748, 1762]}], "snippet": "We discuss the communication and computation overhead for join and leave operations only, because these operations are more frequent than merge or partition operations6. We compare the protocols to the state-of- the-art authenticated group key agreement scheme A-GDH.2 described in [4]. Our worst-case computation complexity is based on the assumption that the maximum number of group members is N = 2d, in which case the maximum height of the key tree is d. The cost for join is computed from the case when we have N 1 members and a member is joining to the current group. The leave cost is when we have N members and one member leaves the group. We do not include the number of exponentiations for the long-term key computation (A-GDH) and signature/verification (TGDH). Table 1 shows the comparison. We would like to emphasize that these numbers represent worst-case numbers for TGDH. In practice, we can optimize the communication overhead of TGDH to O(log N ), because only the keys on the key path of the joining or leaving member change, hence only these blinded keys need to be broadcasted, and not the entire key tree. For the computation overhead, TGDH offers a substantial saving for consecutive (serial or non-parallelizable) exponentiations, because every member only needs to perform at most log N exponentiations, which is much faster than the A-GDH.2 protocol. Note that since the joining point in the join and merge operation is located at a shallower node than the deepest node, the average join and leave cost is lower than the worst case. The savings for the total number of exponentiations, however, is smaller, so TGDH offers less of a benefit if all members run on the same workstation, which is a rare case. Operations Join Leave Protocol A-GDH TGDH A-GDH TGDH Broadcasts 1 2 1 1 Total messages 2 2 1 1 Maximum bandwidth N 2N N 1 2N 2 Serial exponentiation Total exponentiation 2N +1 3N +2 2(d 1) 2(N 2) N 1 2N 3 2(d 1) 2(N d 2)", "samples": [{"hash": "kYi8pySbyyS", "uri": "/contracts/kYi8pySbyyS#complexity-analysis", "label": "Key Agreement Protocol", "score": 19.0, "published": true}], "size": 1, "hash": "d0f25f248abe74afaf0c9b57961257ea", "id": 8}, {"snippet_links": [{"key": "communication-of", "type": "clause", "offset": [42, 58]}, {"key": "group-key-agreement", "type": "clause", "offset": [88, 107]}, {"key": "based-on", "type": "clause", "offset": [276, 284]}, {"key": "communication-delay", "type": "clause", "offset": [483, 502]}, {"key": "total-number-of", "type": "definition", "offset": [504, 519]}, {"key": "communication-system", "type": "definition", "offset": [798, 818]}], "snippet": "This section compares the computation and communication of STR protocol to other recent group key agreement methods, Cliques GDH.2 [STW00], Tree-Based \u2587\u2587\u2587\u2587\u2587\u2587-\u2587\u2587\u2587\u2587\u2587\u2587\u2587 (TGDH) [KPT00], and \u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587\u2587/Desmedt (BD) [BD94]. These protocols provide contribu- tory group key agreement based on different extensions of the two-party \u2587\u2587\u2587\u2587\u2587\u2587-\u2587\u2587\u2587\u2587\u2587\u2587\u2587 key exchange. Moreover, they all support dynamic mem- bership operations. We consider the following costs: Number of rounds: this affects serial communication delay. Total number of messages: as the number of messages grows, the probability of message loss or corruption is increased, and so is the delay. Number of unicasts and broadcasts: a broadcast is much more expen- sive operation than a unicast, since it requires many acknowledgments within the group communication system. Number of serial exponentiation: this is the main factor in the com- putation overhead.", "samples": [{"hash": "kqMRiBlnMjO", "uri": "/contracts/kqMRiBlnMjO#complexity-analysis", "label": "Communication Efficient Group Key Agreement", "score": 19.0, "published": true}], "size": 1, "hash": "ffcbbcf6f23e4dba6f7c6924e108ea04", "id": 9}, {"snippet_links": [], "snippet": "As \u2587\u2587\u2587\u2587\u2587\u2587\u2587 is guaranteed to terminate in the first good 4t+1 iteration and the probability that each iteration is good is 2t+1 \u2265 1 , Reducer terminates in O(1) expected time. As correct processes send O(n\u2113 + n2\u03bb log n) bits during the dissemination phase and during each iteration, with Reducer terminating in constantly many iterations, the expected bit complexity is O(n\u2113+ n2\u03bb log n).", "samples": [{"hash": "jjM9AUND1HL", "uri": "/contracts/jjM9AUND1HL#complexity-analysis", "label": "Multi Valued Validated Byzantine Agreement (Mvba) Protocol", "score": 35.4896888733, "published": true}], "size": 1, "hash": "fda188aa987008eb3d97423a6405f5ee", "id": 10}], "next_curs": "ClwSVmoVc35sYXdpbnNpZGVyY29udHJhY3RzcjgLEhZDbGF1c2VTbmlwcGV0R3JvdXBfdjU2Ihxjb21wbGV4aXR5LWFuYWx5c2lzIzAwMDAwMDBhDKIBAmVuGAAgAA==", "clause": {"parents": [["performance-analysis", "PERFORMANCE ANALYSIS"], ["cascaded-events", "CASCADED EVENTS"], ["participant-mobility-modeling-and-prediction", "Participant Mobility Modeling and Prediction"], ["robustness", "Robustness"], ["conclusion", "Conclusion"]], "size": 14, "children": [["", ""], ["tecsm", "Tecsm"], ["b-gkap-join", "B-GKAP Join"], ["b-gkap-leave-operation", "B-GKAP Leave Operation"], ["b-gkap1-key-computation", "B-GKAP1 Key Computation"]], "title": "Complexity Analysis", "id": "complexity-analysis", "related": [["risk-analysis", "Risk Analysis", "Risk Analysis"], ["quantitative-analysis", "Quantitative Analysis", "Quantitative Analysis"], ["independent-analysis", "Independent Analysis", "Independent Analysis"], ["investment-analysis-and-implementation", "Investment Analysis and Implementation", "Investment Analysis and Implementation"], ["sampling-and-analysis", "Sampling and Analysis", "Sampling and Analysis"]], "related_snippets": [], "updated": "2025-07-17T06:09:22+00:00"}, "json": true, "cursor": ""}}