{"id":"https://openalex.org/W2038828464","doi":"https://doi.org/10.1007/s10623-007-9101-6","title":"On \u03c4-adic representations of integers","display_name":"On \u03c4-adic representations of integers","publication_year":2007,"publication_date":"2007-10-08","ids":{"openalex":"https://openalex.org/W2038828464","doi":"https://doi.org/10.1007/s10623-007-9101-6","mag":"2038828464"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-007-9101-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-007-9101-6","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 Maurice Ebeid","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Centre for Applied Cryptographic Research, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada, N2L 3G1","Department of Electrical and Computer Engineering, Centre for Applied Cryptographic Research, University of Waterloo, Waterloo, Canada N2L 3G1"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Centre for Applied Cryptographic Research, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada, N2L 3G1","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Centre for Applied Cryptographic Research, University of Waterloo, Waterloo, Canada N2L 3G1","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, Centre for Applied Cryptographic Research, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada, N2L 3G1","Department of Electrical and Computer Engineering, Centre for Applied Cryptographic Research, University of Waterloo, Waterloo, Canada N2L 3G1"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Centre for Applied Cryptographic Research, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada, N2L 3G1","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Centre for Applied Cryptographic Research, University of Waterloo, Waterloo, Canada N2L 3G1","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":4.1488,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.94201958,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"3","first_page":"271","last_page":"296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9994000196456909,"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":0.9994000196456909,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9980999827384949,"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/T11130","display_name":"Coding theory and cryptography","score":0.9922999739646912,"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/cryptosystem","display_name":"Cryptosystem","score":0.7339372634887695},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.6182558536529541},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5950884222984314},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.585990309715271},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5677177906036377},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.544442355632782},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.4518054723739624},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4279429614543915},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.4264904856681824},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.42179742455482483},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.42145904898643494},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41391921043395996},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.41263532638549805},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30621251463890076},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2712818384170532},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24327093362808228},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08555373549461365}],"concepts":[{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.7339372634887695},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.6182558536529541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5950884222984314},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.585990309715271},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5677177906036377},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.544442355632782},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.4518054723739624},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4279429614543915},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.4264904856681824},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.42179742455482483},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.42145904898643494},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41391921043395996},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.41263532638549805},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30621251463890076},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2712818384170532},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24327093362808228},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08555373549461365},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"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/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10623-007-9101-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-007-9101-6","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:10.1.1.216.6992","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.216.6992","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-22.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.700.7307","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.700.7307","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://ece.uwaterloo.ca/%7Eahasan/web_papers/journal_articles/web_tau_adic_rep_DCC.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W182470270","https://openalex.org/W1515707356","https://openalex.org/W1515945839","https://openalex.org/W1532287828","https://openalex.org/W1566391339","https://openalex.org/W1981663184","https://openalex.org/W1994584977","https://openalex.org/W2002089154","https://openalex.org/W2003250112","https://openalex.org/W2022789141","https://openalex.org/W2099317248","https://openalex.org/W2109801498","https://openalex.org/W2113956435","https://openalex.org/W2115190247","https://openalex.org/W2131722136","https://openalex.org/W2141469508","https://openalex.org/W2161531038","https://openalex.org/W2505714894","https://openalex.org/W2752853835","https://openalex.org/W3144805728","https://openalex.org/W4241418880","https://openalex.org/W4253103663","https://openalex.org/W6649090136"],"related_works":["https://openalex.org/W2008960744","https://openalex.org/W2105471374","https://openalex.org/W2963549154","https://openalex.org/W2158117886","https://openalex.org/W1987803429","https://openalex.org/W1582340598","https://openalex.org/W1519122282","https://openalex.org/W2182731056","https://openalex.org/W3013281356","https://openalex.org/W2740543340"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}