Complexity Analysis and Comparison Sample Clauses

Complexity Analysis and Comparison. We analyze the communication and computation costs for join, leave, merge and partition protocols. We focus on the number of rounds, the total number of messages, the serial number of exponentiations, the serial number of signature generations, and the serial number of signature verifications. Note that we use RSA signature for message authenti- cation since RSA is particularly efficient in verification. The serial cost assumes parallelization within each protocol round and represents the greatest cost incurred by any participant in a given round. The total cost is the sum of all participants’ costs in a given round. We also compare our protocol to other contributory group key agreement schemes including GDH.3 [34], BD (▇▇▇▇▇▇▇▇▇-▇▇▇▇▇▇▇) [14], and STR [22]. Although BD was originally designed to support only group formation, we modify the BD protocol to support dynamic membership operation. This modification is minimal. Table 1 summarizes the communication and computation costs of four protocols. The numbers of current group members, merging members, merging groups, and leaving members are denoted as: and , respectively. The height of the key tree constructed by the TGDH protocol is . The overhead of the TGDH protocol depends on the tree height, the balancedness of the key tree, the location of the joining tree, and the leaving nodes. In our analysis, we assume the worst case configuration and list the worst-case cost for TGDH. Table 1. Communication and Computation Costs Communication Computation Rounds Messages Exponentiations Signatures Verifications GDH Join 4 4 Partition 1 1 1 1 BD Join 2 3 2 The BD protocol has a hidden cost that is not listed in Table 1: BD has modular exponentiations with a small exponent. Unfortunately, such exponentiations can be expensive when is large. For example, BD requires 1024-bit modular multiplications, if modular exponentiation is implemented with the square-and-multiply algorithm. (OpenSSL uses ▇▇▇▇▇▇▇▇▇▇ reduction and the sliding window algorithm to implement the modular exponentiation, which is faster than simple square-and-multiply algorithm. However, the former requires almost the same time as the latter for small exponents.) Because of this hidden cost, it is hard to compare the computational overhead of BD to the other protocols. Below, we compare the four protocols for each membership event.
View SourceView Similar (2)
Complexity Analysis and Comparison. We analyze the communication and computation costs for join, leave, merge and partition protocols. We focus on the number of rounds, the total number of messages, the serial number of exponentiations, the serial number of signature generations, and the serial number of signature verifications. Note that we use RSA signature for message authenti- cation since RSA is particularly efficient in verification. The serial cost assumes parallelization within each protocol round and represents the greatest cost incurred by any participant in a given round. The total cost is the sum of all participants’ costs in a given round. We also compare our protocol to other contributory group key agreement schemes including GDH.3 [32], BD (▇▇▇▇▇▇▇▇▇-▇▇▇▇▇▇▇) [12], and STR [20]. Although BD was originally designed to support only group formation, we modify the BD protocol to support dynamic membership operation. This modification is minimal. Table 1 summarizes the communication and computation costs of four protocols. The numbers of current group members, merging members, merging groups, and leaving members are denoted as: n, m, k and p, respectively. The height of the key tree constructed by the TGDH protocol is h. The overhead of the TGDH protocol depends on the tree height, the balancedness of the key tree, the location of the joining tree, and the leaving nodes. In our analysis, we assume the worst case configuration and list the worst-case cost for TGDH. Table 1. Communication and Computation Costs Communication Computation Rounds Messages Exponentiations Signatures Verifications GDH Join 4 n + 3 n + 3 4 n + 3 Leave 1 1 n − 1 1 1 Merge m + 3 n + 2m + 1 n + 2m + 1 m + 3 n + 2m + 1 Leave 1 1 3h 2 1 1 merge log2k + 1 2k 3h 2 log2 k + 1 log2 k Leave 2 2n − 2 3 2 n + 1 Merge 2 2n + 2m 3 2 n + m + 2 Partition 2 2n − 2p 3 2 n − p + 2 − − The BD protocol has a hidden cost that is not listed in Table 1: BD has n 1 modular exponentiations with a small exponent. Unfortunately, n 1 such exponentiations can be expensive when n is large. For example, BD requires O(n2) 1024-bit modular multiplications, if modular exponentiation is implemented with the square-and-multiply algorithm. (OpenSSL uses ▇▇▇▇▇▇▇▇▇▇ reduction and the sliding window algorithm to implement the modular exponentiation, which is faster than simple square-and-multiply algorithm. However, the former requires almost the same time as the latter for small exponents.) Because of this hidden cost, it is hard to compare the c...
View Source

Related to Complexity Analysis and Comparison

  • Quantitative Analysis Quantitative analysts develop and apply financial models designed to enable equity portfolio managers and fundamental analysts to screen potential and current investments, assess relative risk and enhance performance relative to benchmarks and peers. To the extent that such services are to be provided with respect to any Account which is a registered investment company, Categories 3, 4 and 5 above shall be treated as “investment advisory services” for purposes of Section 5(b) of the Agreement.”

  • Investment Analysis and Implementation In carrying out its obligations under Section 1 hereof, the Advisor shall: (a) supervise all aspects of the operations of the Funds; (b) obtain and evaluate pertinent information about significant developments and economic, statistical and financial data, domestic, foreign or otherwise, whether affecting the economy generally or the Funds, and whether concerning the individual issuers whose securities are included in the assets of the Funds or the activities in which such issuers engage, or with respect to securities which the Advisor considers desirable for inclusion in the Funds' assets; (c) determine which issuers and securities shall be represented in the Funds' investment portfolios and regularly report thereon to the Board of Trustees; (d) formulate and implement continuing programs for the purchases and sales of the securities of such issuers and regularly report thereon to the Board of Trustees; and (e) take, on behalf of the Trust and the Funds, all actions which appear to the Trust and the Funds necessary to carry into effect such purchase and sale programs and supervisory functions as aforesaid, including but not limited to the placing of orders for the purchase and sale of securities for the Funds.

  • Investment Analysis and Commentary The Subadviser will provide quarterly performance analysis and market commentary (the “Investment Report”) during the term of this Agreement. The Investment Reports are due within 10 days after the end of each quarter. In addition, interim Investment Reports shall be issued at such times as may be mutually agreed upon by the Adviser and Subadviser; provided however, that any such interim Investment Report will be due within 10 days of the end of the month in which such agreement is reached between the Adviser and Subadviser. The subject of each Investment Report shall be mutually agreed upon. The Adviser is freely able to publicly distribute the Investment Report.

  • Risk Analysis The Custodian will provide the Fund with a Risk Analysis with respect to Securities Depositories operating in the countries listed in Appendix B. If the Custodian is unable to provide a Risk Analysis with respect to a particular Securities Depository, it will notify the Fund. If a new Securities Depository commences operation in one of the Appendix B countries, the Custodian will provide the Fund with a Risk Analysis in a reasonably practicable time after such Securities Depository becomes operational. If a new country is added to Appendix B, the Custodian will provide the Fund with a Risk Analysis with respect to each Securities Depository in that country within a reasonably practicable time after the addition of the country to Appendix B.

  • Independent Analysis Each Party hereby confirms that its decision to execute this Agreement has been based upon its independent assessment of documents and information available to it, as it has deemed appropriate.