{"id":"https://openalex.org/W1539669305","doi":"https://doi.org/10.1007/0-387-34805-0_35","title":"Modular Exponentiation Using Recursive Sums of Residues","display_name":"Modular Exponentiation Using Recursive Sums of Residues","publication_year":1990,"publication_date":"1990-01-01","ids":{"openalex":"https://openalex.org/W1539669305","doi":"https://doi.org/10.1007/0-387-34805-0_35","mag":"1539669305"},"language":"en","primary_location":{"id":"doi:10.1007/0-387-34805-0_35","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-34805-0_35","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F0-387-34805-0_35.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F0-387-34805-0_35.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075289482","display_name":"Patricia Findlay","orcid":"https://orcid.org/0000-0003-1874-916X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"P. A. Findlay","raw_affiliation_strings":["Hatfield Polytechnic, UK"],"affiliations":[{"raw_affiliation_string":"Hatfield Polytechnic, UK","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006480389","display_name":"B. A. Johnson","orcid":"https://orcid.org/0000-0003-3922-2826"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. A. Johnson","raw_affiliation_strings":["Hatfield Polytechnic, UK"],"affiliations":[{"raw_affiliation_string":"Hatfield Polytechnic, UK","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5075289482"],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.0782,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.78947368,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"371","last_page":"386"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modular-exponentiation","display_name":"Modular exponentiation","score":0.8547743558883667},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.8162454962730408},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.8062065839767456},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7691705226898193},{"id":"https://openalex.org/keywords/modular-arithmetic","display_name":"Modular arithmetic","score":0.6690679788589478},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.641205370426178},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5882046222686768},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5152947902679443},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.47759413719177246},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4483335614204407},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.44248875975608826},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.42946910858154297},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.3296393156051636},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1515336036682129},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1468384563922882},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.12525570392608643}],"concepts":[{"id":"https://openalex.org/C152763109","wikidata":"https://www.wikidata.org/wiki/Q1228841","display_name":"Modular exponentiation","level":4,"score":0.8547743558883667},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.8162454962730408},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.8062065839767456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7691705226898193},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.6690679788589478},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.641205370426178},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5882046222686768},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5152947902679443},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.47759413719177246},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4483335614204407},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.44248875975608826},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.42946910858154297},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.3296393156051636},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1515336036682129},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1468384563922882},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.12525570392608643},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/0-387-34805-0_35","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-34805-0_35","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F0-387-34805-0_35.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/0-387-34805-0_35","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-34805-0_35","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F0-387-34805-0_35.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1539669305.pdf","grobid_xml":"https://content.openalex.org/works/W1539669305.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1540582803","https://openalex.org/W1549182183","https://openalex.org/W1974711321","https://openalex.org/W1978473201","https://openalex.org/W1996360405","https://openalex.org/W2023649376","https://openalex.org/W2050652156","https://openalex.org/W2063884927","https://openalex.org/W2169512391","https://openalex.org/W4232836212","https://openalex.org/W6644923360"],"related_works":["https://openalex.org/W2292159208","https://openalex.org/W2137988767","https://openalex.org/W2076621334","https://openalex.org/W2543318645","https://openalex.org/W2107014706","https://openalex.org/W1977356083","https://openalex.org/W2351661629","https://openalex.org/W2365969810","https://openalex.org/W2097880062","https://openalex.org/W2004447057"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
