{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:D5N6XXSHU5YE4HPLQLL7OV3XAA","short_pith_number":"pith:D5N6XXSH","canonical_record":{"source":{"id":"1605.04870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-03-22T11:50:01Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"68dd00c2dc4714af7433db1c20c600c4b72abf0a85a64da48fb9ed568aac2042","abstract_canon_sha256":"a22d6384be1b89a769c060c8489fb3ab40846a4f39762f0c773cdf1912cb88f7"},"schema_version":"1.0"},"canonical_sha256":"1f5bebde47a7704e1deb82d7f7577700358b7b6b03c3ba6d8cb9e53077221189","source":{"kind":"arxiv","id":"1605.04870","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04870","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04870v2","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04870","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"D5N6XXSHU5YE","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D5N6XXSHU5YE4HPL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D5N6XXSH","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:D5N6XXSHU5YE4HPLQLL7OV3XAA","target":"record","payload":{"canonical_record":{"source":{"id":"1605.04870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-03-22T11:50:01Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"68dd00c2dc4714af7433db1c20c600c4b72abf0a85a64da48fb9ed568aac2042","abstract_canon_sha256":"a22d6384be1b89a769c060c8489fb3ab40846a4f39762f0c773cdf1912cb88f7"},"schema_version":"1.0"},"canonical_sha256":"1f5bebde47a7704e1deb82d7f7577700358b7b6b03c3ba6d8cb9e53077221189","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:22.535078Z","signature_b64":"KbG90xogV2ykyAelfcZHiiHVvHJZTizdLuIe8RlyrptRgL0QLwJv6oOMJ7JwAtHSxtWzskK98u5ZsZX/Wq5ZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f5bebde47a7704e1deb82d7f7577700358b7b6b03c3ba6d8cb9e53077221189","last_reissued_at":"2026-05-18T00:20:22.534663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:22.534663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.04870","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+dyLpBlr2dldKv2GzVxMeu5ekVrla6jrRmtFJ/flpdwHehYHV2RMLQkOXo28r4bIgponqlnLWJMc3Z2qcyrwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:55:16.461176Z"},"content_sha256":"fcbef320bd89bef8923f57516c1e33f0dd2bf8db9da3db93b7924dc33d74bfbf","schema_version":"1.0","event_id":"sha256:fcbef320bd89bef8923f57516c1e33f0dd2bf8db9da3db93b7924dc33d74bfbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:D5N6XXSHU5YE4HPLQLL7OV3XAA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"t-multiple discrete logarithm problem and solving difficulty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.CR","authors_text":"Jianhong Shi, Wansu Bao, Xiangqun Fu, Xiang Wang","submitted_at":"2016-03-22T11:50:01Z","abstract_excerpt":"Considering the difficult problem under classical computing model can be solved by the quantum algorithm in polynomial time, t-multiple discrete logarithm problems presented. The problem is non-degeneracy and unique solution. We talk about what the parameter effects the problem solving difficulty. Then we pointed out that the index-calculus algorithm is not suitable for the problem, and two sufficient conditions of resistance to the quantum algorithm for the hidden subgroup problem are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04870","kind":"arxiv","version":2},"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":"2026-05-18T00:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZTBbxxQgp2rAFkVIIDCD2qllcawD+HI4/vgYY7md6YJTwwLQQ6R37RKUfTaraHayoJ5POlLAjxQRMkHT923AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:55:16.461585Z"},"content_sha256":"8083271f98ace3107b5ad660b5a48e4392e3394cf5a152334b2719bf65472e91","schema_version":"1.0","event_id":"sha256:8083271f98ace3107b5ad660b5a48e4392e3394cf5a152334b2719bf65472e91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5N6XXSHU5YE4HPLQLL7OV3XAA/bundle.json","state_url":"https://pith.science/pith/D5N6XXSHU5YE4HPLQLL7OV3XAA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5N6XXSHU5YE4HPLQLL7OV3XAA/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":"2026-05-28T16:55:16Z","links":{"resolver":"https://pith.science/pith/D5N6XXSHU5YE4HPLQLL7OV3XAA","bundle":"https://pith.science/pith/D5N6XXSHU5YE4HPLQLL7OV3XAA/bundle.json","state":"https://pith.science/pith/D5N6XXSHU5YE4HPLQLL7OV3XAA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5N6XXSHU5YE4HPLQLL7OV3XAA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:D5N6XXSHU5YE4HPLQLL7OV3XAA","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":"a22d6384be1b89a769c060c8489fb3ab40846a4f39762f0c773cdf1912cb88f7","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-03-22T11:50:01Z","title_canon_sha256":"68dd00c2dc4714af7433db1c20c600c4b72abf0a85a64da48fb9ed568aac2042"},"schema_version":"1.0","source":{"id":"1605.04870","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04870","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04870v2","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04870","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"D5N6XXSHU5YE","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D5N6XXSHU5YE4HPL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D5N6XXSH","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:8083271f98ace3107b5ad660b5a48e4392e3394cf5a152334b2719bf65472e91","target":"graph","created_at":"2026-05-18T00:20:22Z","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":"Considering the difficult problem under classical computing model can be solved by the quantum algorithm in polynomial time, t-multiple discrete logarithm problems presented. The problem is non-degeneracy and unique solution. We talk about what the parameter effects the problem solving difficulty. Then we pointed out that the index-calculus algorithm is not suitable for the problem, and two sufficient conditions of resistance to the quantum algorithm for the hidden subgroup problem are given.","authors_text":"Jianhong Shi, Wansu Bao, Xiangqun Fu, Xiang Wang","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-03-22T11:50:01Z","title":"t-multiple discrete logarithm problem and solving difficulty"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04870","kind":"arxiv","version":2},"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:fcbef320bd89bef8923f57516c1e33f0dd2bf8db9da3db93b7924dc33d74bfbf","target":"record","created_at":"2026-05-18T00:20:22Z","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":"a22d6384be1b89a769c060c8489fb3ab40846a4f39762f0c773cdf1912cb88f7","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2016-03-22T11:50:01Z","title_canon_sha256":"68dd00c2dc4714af7433db1c20c600c4b72abf0a85a64da48fb9ed568aac2042"},"schema_version":"1.0","source":{"id":"1605.04870","kind":"arxiv","version":2}},"canonical_sha256":"1f5bebde47a7704e1deb82d7f7577700358b7b6b03c3ba6d8cb9e53077221189","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f5bebde47a7704e1deb82d7f7577700358b7b6b03c3ba6d8cb9e53077221189","first_computed_at":"2026-05-18T00:20:22.534663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:22.534663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KbG90xogV2ykyAelfcZHiiHVvHJZTizdLuIe8RlyrptRgL0QLwJv6oOMJ7JwAtHSxtWzskK98u5ZsZX/Wq5ZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:22.535078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.04870","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcbef320bd89bef8923f57516c1e33f0dd2bf8db9da3db93b7924dc33d74bfbf","sha256:8083271f98ace3107b5ad660b5a48e4392e3394cf5a152334b2719bf65472e91"],"state_sha256":"e48d97695fdcd6f700f2fb65197bebded5c451fcdc3ad7db5dbc602b00d6570e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L2Pl6FuuUNVeD2FMQ79EHdI3QK7A/Sy8VPu0Gx2zuDWPc01rMlpQCWQVkBVoPfOM4g8RExIpMUSpQ7Gf4ovRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:55:16.463939Z","bundle_sha256":"0df3bfb09763168091b8500634148e23f37c1372ea236edefdf9be65a9ab06bf"}}