{"id":"https://openalex.org/W4210722209","doi":"https://doi.org/10.1109/tetc.2022.3144101","title":"Ultra High-Speed Polynomial Multiplications for Lattice-Based Cryptography on FPGAs","display_name":"Ultra High-Speed Polynomial Multiplications for Lattice-Based Cryptography on FPGAs","publication_year":2022,"publication_date":"2022-01-25","ids":{"openalex":"https://openalex.org/W4210722209","doi":"https://doi.org/10.1109/tetc.2022.3144101"},"language":"en","primary_location":{"id":"doi:10.1109/tetc.2022.3144101","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tetc.2022.3144101","pdf_url":null,"source":{"id":"https://openalex.org/S2496326734","display_name":"IEEE Transactions on Emerging Topics in Computing","issn_l":"2168-6750","issn":["2168-6750","2376-4562"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Emerging Topics in Computing","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/A5032044511","display_name":"Dur\u2010e\u2010Shahwar Kundi","orcid":"https://orcid.org/0000-0001-5120-0887"},"institutions":[{"id":"https://openalex.org/I126231945","display_name":"Queen's University Belfast","ror":"https://ror.org/00hswnk62","country_code":"GB","type":"education","lineage":["https://openalex.org/I126231945"]},{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN","GB"],"is_corresponding":true,"raw_author_name":"Dur-e-Shahwar Kundi","raw_affiliation_strings":["College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China","Queen's University Belfast, Belfast, U.K"],"affiliations":[{"raw_affiliation_string":"College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"Queen's University Belfast, Belfast, U.K","institution_ids":["https://openalex.org/I126231945"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100401884","display_name":"Yuqing Zhang","orcid":"https://orcid.org/0000-0001-8306-7195"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuqing Zhang","raw_affiliation_strings":["College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055800000","display_name":"Chenghua Wang","orcid":"https://orcid.org/0000-0001-8415-0548"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenghua Wang","raw_affiliation_strings":["College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045204653","display_name":"Ayesha Khalid","orcid":"https://orcid.org/0000-0002-4815-6966"},"institutions":[{"id":"https://openalex.org/I126231945","display_name":"Queen's University Belfast","ror":"https://ror.org/00hswnk62","country_code":"GB","type":"education","lineage":["https://openalex.org/I126231945"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ayesha Khalid","raw_affiliation_strings":["Centre for Secure Information Technologies (CSIT), Queen&#x0027;s University Belfast, Belfast, U.K"],"affiliations":[{"raw_affiliation_string":"Centre for Secure Information Technologies (CSIT), Queen&#x0027;s University Belfast, Belfast, U.K","institution_ids":["https://openalex.org/I126231945"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079438004","display_name":"M\u00e1ire O\u05f3Neill","orcid":"https://orcid.org/0000-0002-6865-6212"},"institutions":[{"id":"https://openalex.org/I126231945","display_name":"Queen's University Belfast","ror":"https://ror.org/00hswnk62","country_code":"GB","type":"education","lineage":["https://openalex.org/I126231945"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Maire ONeill","raw_affiliation_strings":["Centre for Secure Information Technologies (CSIT), Queen&#x0027;s University Belfast, Belfast, U.K"],"affiliations":[{"raw_affiliation_string":"Centre for Secure Information Technologies (CSIT), Queen&#x0027;s University Belfast, Belfast, U.K","institution_ids":["https://openalex.org/I126231945"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023734605","display_name":"Weiqiang Liu","orcid":"https://orcid.org/0000-0001-8398-8648"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiqiang Liu","raw_affiliation_strings":["College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5032044511"],"corresponding_institution_ids":["https://openalex.org/I126231945","https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":8.3322,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.97944219,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"10","issue":"4","first_page":"1993","last_page":"2005"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9998999834060669,"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":0.9998000264167786,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9998000264167786,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lattice-based-cryptography","display_name":"Lattice-based cryptography","score":0.6781558394432068},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6613335609436035},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.6145021915435791},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5926173329353333},{"id":"https://openalex.org/keywords/throughput","display_name":"Throughput","score":0.5003085136413574},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.4976251423358917},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4868156611919403},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.46486788988113403},{"id":"https://openalex.org/keywords/virtex","display_name":"Virtex","score":0.4459649622440338},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.4440637230873108},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.41144269704818726},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2945416569709778},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2668488323688507},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.226748526096344},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.19476443529129028},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.1413780152797699},{"id":"https://openalex.org/keywords/quantum-cryptography","display_name":"Quantum cryptography","score":0.12320801615715027}],"concepts":[{"id":"https://openalex.org/C137660015","wikidata":"https://www.wikidata.org/wiki/Q6497083","display_name":"Lattice-based cryptography","level":5,"score":0.6781558394432068},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6613335609436035},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.6145021915435791},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5926173329353333},{"id":"https://openalex.org/C157764524","wikidata":"https://www.wikidata.org/wiki/Q1383412","display_name":"Throughput","level":3,"score":0.5003085136413574},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.4976251423358917},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4868156611919403},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.46486788988113403},{"id":"https://openalex.org/C2777674469","wikidata":"https://www.wikidata.org/wiki/Q20741011","display_name":"Virtex","level":3,"score":0.4459649622440338},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.4440637230873108},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.41144269704818726},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2945416569709778},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2668488323688507},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.226748526096344},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.19476443529129028},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.1413780152797699},{"id":"https://openalex.org/C144901912","wikidata":"https://www.wikidata.org/wiki/Q471906","display_name":"Quantum cryptography","level":4,"score":0.12320801615715027},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tetc.2022.3144101","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tetc.2022.3144101","pdf_url":null,"source":{"id":"https://openalex.org/S2496326734","display_name":"IEEE Transactions on Emerging Topics in Computing","issn_l":"2168-6750","issn":["2168-6750","2376-4562"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Emerging Topics in Computing","raw_type":"journal-article"},{"id":"pmh:oai:pure.qub.ac.uk/portal:publications/3d180815-a04b-4afd-b0ce-0163528e2b52","is_oa":false,"landing_page_url":"https://pure.qub.ac.uk/en/publications/3d180815-a04b-4afd-b0ce-0163528e2b52","pdf_url":null,"source":{"id":"https://openalex.org/S4306402319","display_name":"Research Portal (Queen's University Belfast)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126231945","host_organization_name":"Queen's University Belfast","host_organization_lineage":["https://openalex.org/I126231945"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kundi , D-S , Zhang , Y , Wang , C , Khalid , A , O'Neill , M &amp; Liu , W 2022 , ' Ultra High-Speed Polynomial Multiplications for Lattice-based Cryptography on FPGAs ' , IEEE Transactions on Emerging Topics in Computing . https://doi.org/10.1109/TETC.2022.3144101","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4070429046","display_name":null,"funder_award_id":"62022041","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4164594981","display_name":"The EPSRC Quantum Communications Hub","funder_award_id":"EP/T001011/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7118155122","display_name":null,"funder_award_id":"62134002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7824805094","display_name":null,"funder_award_id":"EP/X022323/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G87932940","display_name":null,"funder_award_id":"EP/T001011/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W159145550","https://openalex.org/W179223734","https://openalex.org/W1498685334","https://openalex.org/W1579862686","https://openalex.org/W1649758727","https://openalex.org/W2040236464","https://openalex.org/W2061171222","https://openalex.org/W2061949491","https://openalex.org/W2093721992","https://openalex.org/W2098290658","https://openalex.org/W2113992957","https://openalex.org/W2168676717","https://openalex.org/W2246684855","https://openalex.org/W2355377132","https://openalex.org/W2467320551","https://openalex.org/W2534948908","https://openalex.org/W2610487593","https://openalex.org/W2616692762","https://openalex.org/W2798942644","https://openalex.org/W2889344598","https://openalex.org/W2913851998","https://openalex.org/W2945132152","https://openalex.org/W2953289753","https://openalex.org/W3003308444","https://openalex.org/W3011360178","https://openalex.org/W3013501169","https://openalex.org/W3023641472","https://openalex.org/W3049114471","https://openalex.org/W3091012253","https://openalex.org/W4212923121","https://openalex.org/W4235199656","https://openalex.org/W4237773356","https://openalex.org/W4250640407","https://openalex.org/W4254706618","https://openalex.org/W6629789561","https://openalex.org/W6634566335","https://openalex.org/W6636949950","https://openalex.org/W6650607579","https://openalex.org/W6668387570","https://openalex.org/W6728192890","https://openalex.org/W6762596054","https://openalex.org/W6777067054"],"related_works":["https://openalex.org/W4318464993","https://openalex.org/W2047588290","https://openalex.org/W1543798151","https://openalex.org/W2366466109","https://openalex.org/W1994641651","https://openalex.org/W2047360623","https://openalex.org/W2104779926","https://openalex.org/W2017469192","https://openalex.org/W4312354936","https://openalex.org/W2001175489"],"abstract_inverted_index":{"Lattice-based":[0],"cryptography":[1,30],"(LBC)":[2],"has":[3],"emerged":[4],"as":[5,15],"the":[6,11,23,27,46,118,123,141,145,154],"most":[7],"viable":[8],"substitutes":[9],"to":[10,168],"classical":[12],"cryptographic":[13],"schemes":[14,21],"5":[16],"out":[17],"of":[18,26,50,81,148,153],"7":[19],"finalist":[20],"in":[22,37,45,57,166],"3rd":[24],"round":[25],"NIST":[28],"post-quantum":[29],"(PQC)":[31],"standardization":[32],"process":[33],"are":[34,75,101],"lattice":[35],"based":[36,98],"construction.":[38,60],"This":[39],"work":[40],"explores":[41],"novel":[42],"architectural":[43],"optimizations":[44],"FPGA-based":[47],"hardware":[48],"implementation":[49],"polynomial":[51,67],"multiplication,":[52],"which":[53],"is":[54,84,114],"a":[55,77],"bottleneck":[56],"every":[58],"LBC":[59,120,170],"To":[61],"target":[62],"ultra-high":[63],"throughput,":[64],"both":[65],"schoolbook":[66],"multiplication":[68],"(SPM)":[69],"and":[70,90],"number":[71],"theoretic":[72],"transform":[73],"(NTT)":[74],"explored:":[76],"completely":[78],"parallel":[79],"architecture":[80],"an":[82],"SPM":[83,106],"undertaken":[85],"while":[86],"for":[87,140],"NTT,":[88],"radix-2":[89],"radix-":[91],"<inline-formula><tex-math":[92,131,137],"notation=\"LaTeX\">$2^2$</tex-math></inline-formula>":[93,132],"multi-path":[94],"delay":[95],"commutator":[96],"(MDC)":[97],"pipelined":[99],"architectures":[100],"adopted.":[102],"Our":[103],"proposed":[104,124,155],"high-speed":[105,125],"(HSPM)":[107],"structure":[108,128],"on":[109],"latest":[110],"Xilinx":[111],"UltraScale+":[112],"FPGA":[113],"5\u00d7":[115],"faster":[116],"than":[117],"state-of-the-art":[119],"designs.":[121,171],"Whereas,":[122],"NTT":[126],"(HNTT)":[127],"(i.e.,":[129,161],"R":[130],"MDC)":[133],"takes":[134],"only":[135],"0.63":[136],"notation=\"LaTeX\">$\\mu$</tex-math></inline-formula>":[138],"s":[139],"encryption,":[142],"hence":[143],"achieving":[144],"highest":[146,158],"throughput":[147,162],"408":[149],"Mbps.":[150],"Moreover,":[151],"all":[152],"designs":[156],"achieve":[157],"design":[159],"efficiencies":[160],"per":[163],"slice":[164],"(TPS))":[165],"comparison":[167],"available":[169]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":19},{"year":2023,"cited_by_count":17},{"year":2022,"cited_by_count":7}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}