{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IS4SY7GKLHZRO47QEEEIIWDYEH","short_pith_number":"pith:IS4SY7GK","canonical_record":{"source":{"id":"1407.4884","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2014-07-18T04:58:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6c6b23f451e9fcf31d7c64f794c0622b7b24fa4ca57465a9937874593bcb39e1","abstract_canon_sha256":"e0fb2ee8fe423febd9766001b1d43336955b1872b63e93e35d5e48d5546a9bb9"},"schema_version":"1.0"},"canonical_sha256":"44b92c7cca59f31773f0210884587821c25d514afc27cac618d5ac3510308167","source":{"kind":"arxiv","id":"1407.4884","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4884","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4884v1","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4884","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"IS4SY7GKLHZR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IS4SY7GKLHZRO47Q","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IS4SY7GK","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IS4SY7GKLHZRO47QEEEIIWDYEH","target":"record","payload":{"canonical_record":{"source":{"id":"1407.4884","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2014-07-18T04:58:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6c6b23f451e9fcf31d7c64f794c0622b7b24fa4ca57465a9937874593bcb39e1","abstract_canon_sha256":"e0fb2ee8fe423febd9766001b1d43336955b1872b63e93e35d5e48d5546a9bb9"},"schema_version":"1.0"},"canonical_sha256":"44b92c7cca59f31773f0210884587821c25d514afc27cac618d5ac3510308167","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:22.459015Z","signature_b64":"QZgAOi6+ayNla3fnIeTgUl5k51fJ9okL9E8wwdBDJfAWSVB18vH/8nFGEqMmmPHFGzmPsH3fBZmpTh3Vi68uCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44b92c7cca59f31773f0210884587821c25d514afc27cac618d5ac3510308167","last_reissued_at":"2026-05-18T02:47:22.458392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:22.458392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.4884","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uNMDQFlhQn8zQ05oswPqtGucGM82AcJI5gICT78utWrrDSGy+isTWQB9L5CFI03vcVQ9didz+zs8Ap5LQWSjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:20:05.978902Z"},"content_sha256":"599db33d51f31bf58b5e421579a963229eed17cd24635aeb3fc26d89e566958a","schema_version":"1.0","event_id":"sha256:599db33d51f31bf58b5e421579a963229eed17cd24635aeb3fc26d89e566958a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IS4SY7GKLHZRO47QEEEIIWDYEH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new construction of differentially 4-uniform permutations over $F_{2^{2k}}$","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chik How Tan, Jie Peng, Qichun Wang","submitted_at":"2014-07-18T04:58:49Z","abstract_excerpt":"Permutations over $F_{2^{2k}}$ with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well known example is that the Advanced Encryption Standard (AES) chooses a differentially 4-uniform permutation, the multiplicative inverse function, as its S-box. In this paper, we present a new construction of differentially 4-uniformity permutations over even characteristic finite fields and obtain many new CCZ-inequivalent functions. All the functions are swit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4884","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OYGBIARIyYvMlkPAN2aRhwBhrPWcjlFoBRk7phH7n6JNcxPoSnOmxIhboGO74aznoyGxpmPIRPGW+zi4ZFlcDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:20:05.979579Z"},"content_sha256":"09e9ab891df3e2c610e6132b16046a9a52c4669f98e04c9c9f2d6b6aad578dd1","schema_version":"1.0","event_id":"sha256:09e9ab891df3e2c610e6132b16046a9a52c4669f98e04c9c9f2d6b6aad578dd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IS4SY7GKLHZRO47QEEEIIWDYEH/bundle.json","state_url":"https://pith.science/pith/IS4SY7GKLHZRO47QEEEIIWDYEH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IS4SY7GKLHZRO47QEEEIIWDYEH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T15:20:05Z","links":{"resolver":"https://pith.science/pith/IS4SY7GKLHZRO47QEEEIIWDYEH","bundle":"https://pith.science/pith/IS4SY7GKLHZRO47QEEEIIWDYEH/bundle.json","state":"https://pith.science/pith/IS4SY7GKLHZRO47QEEEIIWDYEH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IS4SY7GKLHZRO47QEEEIIWDYEH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IS4SY7GKLHZRO47QEEEIIWDYEH","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":"e0fb2ee8fe423febd9766001b1d43336955b1872b63e93e35d5e48d5546a9bb9","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2014-07-18T04:58:49Z","title_canon_sha256":"6c6b23f451e9fcf31d7c64f794c0622b7b24fa4ca57465a9937874593bcb39e1"},"schema_version":"1.0","source":{"id":"1407.4884","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4884","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4884v1","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4884","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"IS4SY7GKLHZR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IS4SY7GKLHZRO47Q","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IS4SY7GK","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:09e9ab891df3e2c610e6132b16046a9a52c4669f98e04c9c9f2d6b6aad578dd1","target":"graph","created_at":"2026-05-18T02:47:22Z","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":"Permutations over $F_{2^{2k}}$ with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well known example is that the Advanced Encryption Standard (AES) chooses a differentially 4-uniform permutation, the multiplicative inverse function, as its S-box. In this paper, we present a new construction of differentially 4-uniformity permutations over even characteristic finite fields and obtain many new CCZ-inequivalent functions. All the functions are swit","authors_text":"Chik How Tan, Jie Peng, Qichun Wang","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2014-07-18T04:58:49Z","title":"A new construction of differentially 4-uniform permutations over $F_{2^{2k}}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4884","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":"sha256:599db33d51f31bf58b5e421579a963229eed17cd24635aeb3fc26d89e566958a","target":"record","created_at":"2026-05-18T02:47:22Z","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":"e0fb2ee8fe423febd9766001b1d43336955b1872b63e93e35d5e48d5546a9bb9","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2014-07-18T04:58:49Z","title_canon_sha256":"6c6b23f451e9fcf31d7c64f794c0622b7b24fa4ca57465a9937874593bcb39e1"},"schema_version":"1.0","source":{"id":"1407.4884","kind":"arxiv","version":1}},"canonical_sha256":"44b92c7cca59f31773f0210884587821c25d514afc27cac618d5ac3510308167","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44b92c7cca59f31773f0210884587821c25d514afc27cac618d5ac3510308167","first_computed_at":"2026-05-18T02:47:22.458392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:22.458392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QZgAOi6+ayNla3fnIeTgUl5k51fJ9okL9E8wwdBDJfAWSVB18vH/8nFGEqMmmPHFGzmPsH3fBZmpTh3Vi68uCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:22.459015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4884","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:599db33d51f31bf58b5e421579a963229eed17cd24635aeb3fc26d89e566958a","sha256:09e9ab891df3e2c610e6132b16046a9a52c4669f98e04c9c9f2d6b6aad578dd1"],"state_sha256":"38a2de871e75d3de802065759e552491b820f75d0b263e32d5ca8e9c2225e790"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XXuoeY70ZKRbkSd9B2dXGxOTLWMnBjGLEK5t8Gg4+BZwxvBCP7LPHyLCe+6WrjVEaTOA5oSoM89E+l4b8ot3AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:20:05.982536Z","bundle_sha256":"4fd3258e2ff902bcf8f02e5a75faeb4a3b414d6a04c3297b8119b320ca2d3eaf"}}