{"id":"https://openalex.org/W2022789141","doi":"https://doi.org/10.1007/s10623-006-9014-9","title":"On binary signed digit representations of integers","display_name":"On binary signed digit representations of integers","publication_year":2006,"publication_date":"2006-11-07","ids":{"openalex":"https://openalex.org/W2022789141","doi":"https://doi.org/10.1007/s10623-006-9014-9","mag":"2022789141"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-006-9014-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-006-9014-9","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091219827","display_name":"Nevine Ebeid","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Nevine Ebeid","raw_affiliation_strings":["Department of Electrical and Computer Engineering and Centre for Applied Cryptographic Research, University of Waterloo, Waterloo Ontario, Canada","Department of Electrical and Computer Engineering and Centre for Applied Cryptographic Research, University of Waterloo, Waterloo Ontario, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and Centre for Applied Cryptographic Research, University of Waterloo, Waterloo Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering and Centre for Applied Cryptographic Research, University of Waterloo, Waterloo Ontario, Canada#TAB#","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024426963","display_name":"M.A. Hasan","orcid":"https://orcid.org/0000-0003-4103-7945"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"M. Anwar Hasan","raw_affiliation_strings":["Department of Electrical and Computer Engineering and Centre for Applied Cryptographic Research, University of Waterloo, Waterloo Ontario, Canada","Department of Electrical and Computer Engineering and Centre for Applied Cryptographic Research, University of Waterloo, Waterloo Ontario, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and Centre for Applied Cryptographic Research, University of Waterloo, Waterloo Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering and Centre for Applied Cryptographic Research, University of Waterloo, Waterloo Ontario, Canada#TAB#","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091219827"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.6323,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.69112872,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"42","issue":"1","first_page":"43","last_page":"65"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9957000017166138,"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/T11130","display_name":"Coding theory and cryptography","score":0.9919999837875366,"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/integer","display_name":"Integer (computer science)","score":0.8123033046722412},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7697135806083679},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.7524523138999939},{"id":"https://openalex.org/keywords/numerical-digit","display_name":"Numerical digit","score":0.5424251556396484},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5422008037567139},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5215715765953064},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5158050060272217},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5073935389518738},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.45982101559638977},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4597165584564209},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3457215428352356},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13357186317443848}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.8123033046722412},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7697135806083679},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.7524523138999939},{"id":"https://openalex.org/C94957134","wikidata":"https://www.wikidata.org/wiki/Q82990","display_name":"Numerical digit","level":2,"score":0.5424251556396484},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5422008037567139},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5215715765953064},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5158050060272217},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5073935389518738},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.45982101559638977},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4597165584564209},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3457215428352356},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13357186317443848},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10623-006-9014-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-006-9014-9","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.5323","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.5323","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.vlsi.uwaterloo.ca/~ahasan/web_papers/technical_reports/web_BSD_rand_rev.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1515945839","https://openalex.org/W1532287828","https://openalex.org/W1539482743","https://openalex.org/W1566391339","https://openalex.org/W1584722274","https://openalex.org/W1634503271","https://openalex.org/W2105374413","https://openalex.org/W2115190247","https://openalex.org/W2141469508","https://openalex.org/W3144805728","https://openalex.org/W4230265636","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2033860701","https://openalex.org/W1963930613","https://openalex.org/W1569173638","https://openalex.org/W4290792871","https://openalex.org/W1489205002","https://openalex.org/W3138640319","https://openalex.org/W2090853787","https://openalex.org/W4249399111","https://openalex.org/W2131256658","https://openalex.org/W4245042232"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}