{"id":18406490,"url":"https://github.com/georgiifirsov/galois-lib","last_synced_at":"2025-04-12T20:29:05.809Z","repository":{"id":178151075,"uuid":"661392585","full_name":"GeorgiiFirsov/galois-lib","owner":"GeorgiiFirsov","description":"Finite field arithmetic library written for my research in cryptography","archived":false,"fork":false,"pushed_at":"2023-10-12T21:07:40.000Z","size":288,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-02-16T04:29:07.173Z","etag":null,"topics":["arithmetic","cryptography","finite-field-arithmetic","finite-field-arithmetics","finite-fields","galois-field","mathematics","symmetric-cryptography"],"latest_commit_sha":null,"homepage":"https://georgyfirsov.github.io/galois-lib/","language":"C","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"gpl-3.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/GeorgiiFirsov.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2023-07-02T17:44:34.000Z","updated_at":"2025-01-04T17:19:44.000Z","dependencies_parsed_at":null,"dependency_job_id":"93caf83a-2256-4531-90b6-79ced8876529","html_url":"https://github.com/GeorgiiFirsov/galois-lib","commit_stats":null,"previous_names":["georgyfirsov/galois-lib","georgiifirsov/galois-lib"],"tags_count":7,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/GeorgiiFirsov%2Fgalois-lib","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/GeorgiiFirsov%2Fgalois-lib/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/GeorgiiFirsov%2Fgalois-lib/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/GeorgiiFirsov%2Fgalois-lib/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/GeorgiiFirsov","download_url":"https://codeload.github.com/GeorgiiFirsov/galois-lib/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":248628481,"owners_count":21136088,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["arithmetic","cryptography","finite-field-arithmetic","finite-field-arithmetics","finite-fields","galois-field","mathematics","symmetric-cryptography"],"created_at":"2024-11-06T03:09:19.295Z","updated_at":"2025-04-12T20:29:05.744Z","avatar_url":"https://github.com/GeorgiiFirsov.png","language":"C","funding_links":[],"categories":[],"sub_categories":[],"readme":"# galois-lib\n\nThis library implements some arithmetic operations in finite fields.\n\n## Implemented operations\n\n`galois-lib` implements not so many algorithms, because it is designed to be a helper library \nfor cryptographic libraries. Hence it contains only few necessary operations.\n\n### Multiplication in $GF(2 ^ {8})$\n\nMultiplication in finite field of size $2 ^ {8}$ is implemented using precomputed\nlogarithm and exponents tables. It works according to the following obvious formula:\n\n$$\na \\cdot b = \\exp \\left( \\log a + \\log b \\right),\n$$\n\nwhere all operations are assumed to be in the finite field.\n\n### multiplication in $GF(2 ^ {128})$\n\nMultiplication in $GF(2 ^ {128})$ is implemented using some kind of Karatsuba algorithm\nwith help of `pclmulqdq` instruction. More information here: [Intel® Carry-Less Multiplication \nInstruction and its Usage for Computing the GCM Mode][1].\n\n[1]: https://www.intel.com/content/dam/develop/external/us/en/documents/clmul-wp-rev-2-02-2014-04-20.pdf\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fgeorgiifirsov%2Fgalois-lib","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fgeorgiifirsov%2Fgalois-lib","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fgeorgiifirsov%2Fgalois-lib/lists"}