{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FW62VZWR336Y6G7A2H6SDQHJY6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"86cd66e8b86d756f57a9ab8f617186cbc4e614fe959250babdbb2e5c1355008a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-01-26T01:49:10Z","title_canon_sha256":"b192fcdde6e1501bf76ebf92ab05ecceee42205153d89084b9d439d30c713f79"},"schema_version":"1.0","source":{"id":"1401.6604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6604","created_at":"2026-05-18T03:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6604v1","created_at":"2026-05-18T03:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6604","created_at":"2026-05-18T03:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"FW62VZWR336Y","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FW62VZWR336Y6G7A","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FW62VZWR","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:ea254037119fa009ee3f431bd9035d9d9030da1cdc35d824ade12fca2f1bc6bf","target":"graph","created_at":"2026-05-18T03:01:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We propose a general approach to construct cryptographic significant Boolean functions of $(r+1)m$ variables based on the additive decomposition $\\mathbb{F}_{2^{rm}}\\times\\mathbb{F}_{2^m}$ of the finite field $\\mathbb{F}_{2^{(r+1)m}}$, where $r$ is odd and $m\\geq3$. A class of unbalanced functions are constructed first via this approach, which coincides with a variant of the unbalanced class of generalized Tu-Deng functions in the case $r=1$. This class of functions have high algebraic degree, but their algebraic immunity does not exceeds $m$, which is impossible to be optimal when $r>1$. By m","authors_text":"Baofeng Wu, Dongdai Lin, Qingfang Jin, Zhuojun Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-01-26T01:49:10Z","title":"Constructing Boolean Functions With Potential Optimal Algebraic Immunity Based on Additive Decompositions of Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6604","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:18ca4965d20418b8257b1859c191bc570a83b8b92c0efd96482dedea91a820fa","target":"record","created_at":"2026-05-18T03:01:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"86cd66e8b86d756f57a9ab8f617186cbc4e614fe959250babdbb2e5c1355008a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-01-26T01:49:10Z","title_canon_sha256":"b192fcdde6e1501bf76ebf92ab05ecceee42205153d89084b9d439d30c713f79"},"schema_version":"1.0","source":{"id":"1401.6604","kind":"arxiv","version":1}},"canonical_sha256":"2dbdaae6d1defd8f1be0d1fd21c0e9c7ae37ad84972c7746664234d1f5e76dfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2dbdaae6d1defd8f1be0d1fd21c0e9c7ae37ad84972c7746664234d1f5e76dfa","first_computed_at":"2026-05-18T03:01:01.198128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:01.198128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uf0mRstbYOao95vV7OY3JIZFSL0MchKfI9kAGnZlhCrVRhsrUCLM+Z0wtm/5AcUl2P6LYZEIY+VKmTmgWZKsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:01.198849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18ca4965d20418b8257b1859c191bc570a83b8b92c0efd96482dedea91a820fa","sha256:ea254037119fa009ee3f431bd9035d9d9030da1cdc35d824ade12fca2f1bc6bf"],"state_sha256":"5b3d611923a01cdd6915dba9a8f96647a5aa583a04f5c47db66e259118e4497f"}