Zot-Mk
| dc.contributor.author | Jahani, Shahram | |
| dc.date.accessioned | 2014-11-03T02:12:28Z | |
| dc.date.available | 2014-11-03T02:12:28Z | |
| dc.date.issued | 2009 | |
| dc.description | Master | en_US |
| dc.description.abstract | Multiplication of big numbers is being used heavily in scientific computation. However, there are only a few existing algorithms today that gain their efficiency through the multiplication of the big integer characteristic. Since the multiplication on integers is not native to the computer architecture numbering structure of bits and bytes, such algorithms are bound to be a bit slower on the implementation. This research focuses on big number multiplication algorithm that is based on the symbols extracted from the binary numbering system. We named the new numbering structure as “ZOT”. The new algorithm for big numbers multiplication, ZOT-MK, is constructed from the combination of Karatsuba algorithm and the ZOT structure. For evaluation purposes, we simulate an environment capable of handling big numbers to compare the performance of the propose algorithm against the well known Karatsuba algorithm. Over the range of 25 to 5000 bits numbers, results show that the compression rate of those numbers represented by the ZOT structure against the normal binary representation is 41 percent. Therefore, theoretically, in average the execution speed of ZOT-MK should be about double of the Karatsuba algorithm. However because of efficient memory utilization of ZOT-MK that eliminates extensive memory paging, the experimental result shows the average execution time of ZOT-MK in lower range numbers (25 bits to 1Kbits) is about 35 percent of the Karatsuba algorithm. This average value will decrease for higher range numbers (1Kbits to 5Kbits) to 25 percent. In conclusion, the available results validate the efficiency of the ZOT-MK multiplication algorithm against Karatsuba algorithm, which is currently the defacto standard for big number multiplication algorithm. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/233 | |
| dc.language.iso | en | en_US |
| dc.subject | Computer Science | en_US |
| dc.subject | Zot-Mk | en_US |
| dc.subject | Algorithm | en_US |
| dc.subject | Integer multiplication | en_US |
| dc.title | Zot-Mk | en_US |
| dc.title.alternative | A new algorithm for big integer multiplication | en_US |
| dc.type | Thesis | en_US |
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