On the Construction of Short Addition-Subtraction Chains and their Applications
The problem of computing effciently, such that and are known to be very interesting, specially when is very large. In order to find effcient methods to solve this problem, addition chains have been much studied, and generalized to addition-subtraction chains. These various chains have been useful in...
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| Veröffentlicht in: | Tatra Mountains Mathematical Publications 2023-02, Vol.83 (1), p.131-144 |
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| container_title | Tatra Mountains Mathematical Publications |
| container_volume | 83 |
| creator | Ngom, Moussa Tall, Amadou |
| description | The problem of computing
effciently, such that
and
are known to be very interesting, specially when
is very large. In order to find effcient methods to solve this problem, addition chains have been much studied, and generalized to addition-subtraction chains. These various chains have been useful in finding effcient exponentiation algorithms. In this paper, we present a new method to recover all existing exponentiation algorithms. It will be applied to design a new fast exponentiation method. |
| doi_str_mv | 10.2478/tmmp-2023-0010 |
| format | Article |
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and
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is very large. In order to find effcient methods to solve this problem, addition chains have been much studied, and generalized to addition-subtraction chains. These various chains have been useful in finding effcient exponentiation algorithms. In this paper, we present a new method to recover all existing exponentiation algorithms. It will be applied to design a new fast exponentiation method.</description><identifier>ISSN: 1338-9750</identifier><identifier>EISSN: 1338-9750</identifier><identifier>DOI: 10.2478/tmmp-2023-0010</identifier><language>eng</language><publisher>Sciendo</publisher><subject>addition-subtraction chains ; Euclidean algorithm ; generalized continued fractions ; minimal length of chain ; non-adjacent form ; strategy</subject><ispartof>Tatra Mountains Mathematical Publications, 2023-02, Vol.83 (1), p.131-144</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2021-94b01f2576b2c613b7c0af280aad8586fe84ad410bbd7590a75a5701489143843</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://sciendo.com/pdf/10.2478/tmmp-2023-0010$$EPDF$$P50$$Gwalterdegruyter$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://sciendo.com/article/10.2478/tmmp-2023-0010$$EHTML$$P50$$Gwalterdegruyter$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27922,27923,75934,75935</link.rule.ids></links><search><creatorcontrib>Ngom, Moussa</creatorcontrib><creatorcontrib>Tall, Amadou</creatorcontrib><title>On the Construction of Short Addition-Subtraction Chains and their Applications</title><title>Tatra Mountains Mathematical Publications</title><description>The problem of computing
effciently, such that
and
are known to be very interesting, specially when
is very large. In order to find effcient methods to solve this problem, addition chains have been much studied, and generalized to addition-subtraction chains. These various chains have been useful in finding effcient exponentiation algorithms. In this paper, we present a new method to recover all existing exponentiation algorithms. It will be applied to design a new fast exponentiation method.</description><subject>addition-subtraction chains</subject><subject>Euclidean algorithm</subject><subject>generalized continued fractions</subject><subject>minimal length of chain</subject><subject>non-adjacent form</subject><subject>strategy</subject><issn>1338-9750</issn><issn>1338-9750</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kD1rwzAQhkVpoSHN2ll_QKlOki0ZugTTLwh4SDsL2bJrlcQ2kkzJv69FOnTpdMe9PMfLg9A90C0TUj3E02kijDJOKAV6hVbAuSKFzOj1n_0WbUJwNQUmuGRQrFBVDTj2LS7HIUQ_N9GNAx47fOhHH_HOWpcu5DDX0ZtLWvbGDQGbwSbSebybpqNrTArDHbrpzDG0m9-5Rh_PT-_lK9lXL2_lbk-apSSQQiwlOpbJvGZNDryWDTUdU9QYqzKVd60SxgqgdW1lVlAjM5NJCkIVILgSfI22l7-NH0Pwbacn707GnzVQnYzoZEQnIzoZWYDHC_BtjrH1tv3083lZ9Nc4-2Gp-g-oOAAH_gMNO2f_</recordid><startdate>20230201</startdate><enddate>20230201</enddate><creator>Ngom, Moussa</creator><creator>Tall, Amadou</creator><general>Sciendo</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230201</creationdate><title>On the Construction of Short Addition-Subtraction Chains and their Applications</title><author>Ngom, Moussa ; Tall, Amadou</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2021-94b01f2576b2c613b7c0af280aad8586fe84ad410bbd7590a75a5701489143843</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>addition-subtraction chains</topic><topic>Euclidean algorithm</topic><topic>generalized continued fractions</topic><topic>minimal length of chain</topic><topic>non-adjacent form</topic><topic>strategy</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ngom, Moussa</creatorcontrib><creatorcontrib>Tall, Amadou</creatorcontrib><collection>CrossRef</collection><jtitle>Tatra Mountains Mathematical Publications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ngom, Moussa</au><au>Tall, Amadou</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Construction of Short Addition-Subtraction Chains and their Applications</atitle><jtitle>Tatra Mountains Mathematical Publications</jtitle><date>2023-02-01</date><risdate>2023</risdate><volume>83</volume><issue>1</issue><spage>131</spage><epage>144</epage><pages>131-144</pages><issn>1338-9750</issn><eissn>1338-9750</eissn><abstract>The problem of computing
effciently, such that
and
are known to be very interesting, specially when
is very large. In order to find effcient methods to solve this problem, addition chains have been much studied, and generalized to addition-subtraction chains. These various chains have been useful in finding effcient exponentiation algorithms. In this paper, we present a new method to recover all existing exponentiation algorithms. It will be applied to design a new fast exponentiation method.</abstract><pub>Sciendo</pub><doi>10.2478/tmmp-2023-0010</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1338-9750 |
| ispartof | Tatra Mountains Mathematical Publications, 2023-02, Vol.83 (1), p.131-144 |
| issn | 1338-9750 1338-9750 |
| language | eng |
| recordid | cdi_crossref_primary_10_2478_tmmp_2023_0010 |
| source | De Gruyter Open Access Journals |
| subjects | addition-subtraction chains Euclidean algorithm generalized continued fractions minimal length of chain non-adjacent form strategy |
| title | On the Construction of Short Addition-Subtraction Chains and their Applications |
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