{"id":"https://openalex.org/W7136346564","doi":"https://doi.org/10.46586/tosc.v2026.i1.506-526","title":"HILL: Efficient Low-Latency Implementations of Linear Layers via Heuristic Search","display_name":"HILL: Efficient Low-Latency Implementations of Linear Layers via Heuristic Search","publication_year":2026,"publication_date":"2026-03-16","ids":{"openalex":"https://openalex.org/W7136346564","doi":"https://doi.org/10.46586/tosc.v2026.i1.506-526"},"language":"en","primary_location":{"id":"doi:10.46586/tosc.v2026.i1.506-526","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2026.i1.506-526","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/12794/12483","source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://tosc.iacr.org/index.php/ToSC/article/download/12794/12483","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129425704","display_name":"Yongchao Li","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I5343935","display_name":"Guilin University of Electronic Technology","ror":"https://ror.org/05arjae42","country_code":"CN","type":"education","lineage":["https://openalex.org/I5343935"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Yongchao Li","raw_affiliation_strings":["Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, China; School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, China; School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005","https://openalex.org/I5343935"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yongzhuang Wei","orcid":null},"institutions":[{"id":"https://openalex.org/I5343935","display_name":"Guilin University of Electronic Technology","ror":"https://ror.org/05arjae42","country_code":"CN","type":"education","lineage":["https://openalex.org/I5343935"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongzhuang Wei","raw_affiliation_strings":["Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, China","institution_ids":["https://openalex.org/I5343935"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129462332","display_name":"Lang Li","orcid":null},"institutions":[{"id":"https://openalex.org/I149735164","display_name":"Hengyang Normal University","ror":"https://ror.org/006bvjm48","country_code":"CN","type":"education","lineage":["https://openalex.org/I149735164"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lang Li","raw_affiliation_strings":["College of Computer Science and Technology, Hengyang Normal University, Hengyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Hengyang Normal University, Hengyang, China","institution_ids":["https://openalex.org/I149735164"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5129433826","display_name":"Jian Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Jian Guo","raw_affiliation_strings":["School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30849582,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2026","issue":"1","first_page":"506","last_page":"526"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9779000282287598,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9779000282287598,"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":0.00800000037997961,"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/T12122","display_name":"Physical Unclonable Functions (PUFs) and Hardware Security","score":0.00430000014603138,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/implementation","display_name":"Implementation","score":0.7245000004768372},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.7096999883651733},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5374000072479248},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.49950000643730164},{"id":"https://openalex.org/keywords/incremental-heuristic-search","display_name":"Incremental heuristic search","score":0.46630001068115234},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.4523000121116638}],"concepts":[{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.7245000004768372},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.7096999883651733},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5576000213623047},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5374000072479248},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.49950000643730164},{"id":"https://openalex.org/C139979381","wikidata":"https://www.wikidata.org/wiki/Q17056021","display_name":"Incremental heuristic search","level":4,"score":0.46630001068115234},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4537999927997589},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.4523000121116638},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4088999927043915},{"id":"https://openalex.org/C125583679","wikidata":"https://www.wikidata.org/wiki/Q755673","display_name":"Search algorithm","level":2,"score":0.382099986076355},{"id":"https://openalex.org/C19889080","wikidata":"https://www.wikidata.org/wiki/Q2835852","display_name":"Beam search","level":3,"score":0.36090001463890076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32749998569488525},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.29030001163482666},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.28119999170303345},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.2721000015735626},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.46586/tosc.v2026.i1.506-526","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2026.i1.506-526","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/12794/12483","source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:77555bebc75949c1bef30dae2021864c","is_oa":true,"landing_page_url":"https://doaj.org/article/77555bebc75949c1bef30dae2021864c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IACR Transactions on Symmetric Cryptology, Vol 2026, Iss 1 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46586/tosc.v2026.i1.506-526","is_oa":true,"landing_page_url":"https://doi.org/10.46586/tosc.v2026.i1.506-526","pdf_url":"https://tosc.iacr.org/index.php/ToSC/article/download/12794/12483","source":{"id":"https://openalex.org/S4210236173","display_name":"IACR Transactions on Symmetric Cryptology","issn_l":"2519-173X","issn":["2519-173X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IACR Transactions on Symmetric Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.4156222939491272}],"awards":[{"id":"https://openalex.org/G5006771462","display_name":null,"funder_award_id":"62402132","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320323266","display_name":"Guilin University of Electronic Technology","ror":"https://ror.org/05arjae42"},{"id":"https://openalex.org/F4320337368","display_name":"Division of Graduate Education","ror":"https://ror.org/00whkrf32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7136346564.pdf","grobid_xml":"https://content.openalex.org/works/W7136346564.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Lightweight":[0],"cryptography":[1],"aims":[2],"to":[3,40,57,104,151],"achieve":[4,105],"security":[5],"with":[6,116],"minimal":[7],"resource":[8],"footprints":[9],"and":[10,69,88,113,180],"low":[11],"computational":[12],"overhead.":[13],"In":[14,62],"particular,":[15],"efficient":[16,168],"implementations":[17,66,170],"of":[18,36,159,165,171,177],"linear":[19,37,173],"layers":[20,38,174],"are":[21,67,101,185],"recognized":[22],"as":[23],"a":[24,70,152],"crucial":[25],"component.":[26],"Boyar":[27],"et":[28,123,198],"al.":[29,124,199],"showed":[30],"that":[31],"finding":[32],"an":[33,106,129],"optimal":[34],"implementation":[35,132,183],"reduces":[39],"the":[41,90,110,117,147,157,166],"Shortest":[42],"Linear":[43,80],"Program":[44],"(SLP)":[45],"problem,":[46],"which":[47,127],"is":[48,82,93,163],"NP-hard.":[49],"Consequently,":[50],"various":[51],"heuristic":[52,71,118],"methods":[53],"have":[54],"been":[55],"developed":[56],"search":[58,72,119],"for":[59,78,187],"near-optimal":[60],"solutions.":[61],"this":[63,162],"work,":[64],"low-latency":[65],"prioritized,":[68],"algorithm":[73],"named":[74],"HILL":[75],"(Heuristic":[76],"Implementation":[77],"Low-Latency":[79],"layers)":[81],"proposed.":[83],"To":[84,156],"further":[85],"balance":[86],"cost":[87],"delay,":[89],"h-XOR":[91],"metric":[92],"integrated":[94],"into":[95],"HILL,":[96],"where":[97],"2/3-input":[98],"XOR":[99],"gates":[100],"dynamically":[102],"weighted":[103],"optimized":[107],"trade-off":[108],"between":[109],"circuit":[111],"area":[112,154,179],"depth.":[114,181],"Compared":[115],"proposed":[120,195],"by":[121,196],"Li":[122,197],"(FSE":[125],"2019),":[126],"yields":[128],"AES":[130,172],"MixColumns":[131],"requiring":[133],"315":[134],"gate":[135],"equivalents":[136],"(GEs)":[137],"at":[138,146],"depth":[139],"3,":[140],"our":[141,160],"approach":[142],"achieves":[143],"270.4":[144],"GEs":[145],"same":[148],"depth,":[149],"corresponding":[150],"14.2%":[153],"reduction.":[155],"best":[158],"knowledge,":[161],"one":[164],"most":[167],"hardware":[169],"in":[175],"terms":[176],"both":[178],"Furthermore,":[182],"costs":[184],"minimized":[186],"all":[188],"4254":[189],"Maximum":[190],"Distance":[191],"Separable":[192],"(MDS)":[193],"matrices":[194]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-03-17T00:00:00"}