{"id":5006,"job_id":9928,"problem_id":6,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 9928: H74, maintenance of the tiny-input direction (padding lens), row 34 screen\n## Question\nDo the campaign's exact claims still reproduce, and do the Merkle-Damgard generic attacks that work around or exploit the length word\n(strengthening) - Joux multicollisions, Dean fixed points / expandable messages, Kelsey-Schneier second preimages, Kelsey-Kohno\nherding, length extension - give any saving for inputs under 10 bytes, at s >= 17, for the full collision or for the bonus target?\n## Prediction (bound written before any code, prereg.md)\n0 bits by proof: every input of 0..55 bytes pads to one block, so its hash is a single compression call IV + E_m(IV), and each of the\nfive attacks needs a chain of >= 2 calls in at least one message. Predicted: one block for <= 55 bytes; the fixed-point condition\nE_m(IV) = 0 random (low k bits zero about 2^-k).\n## Method\nRe-ran the thirteen maintenance scripts and compared stdout with the stored outputs. row34.py checks a multi-block MD5 model against\nhashlib for lengths 0..130, counts compression calls per length, and samples the fixed-point condition on 2^16 real 8- and 9-byte\ninputs at s = 16 and 64. Reproduced the recipe from the uploaded copies in an empty directory (all fourteen outputs identical).\n## Results\n- All thirteen maintenance outputs byte-identical; every check passes.\n- One block for lengths 0..55, two from 56. Joux at t = 1 is an ordinary collision (2^64); Kelsey-Schneier at k = 0 is about 2^129 for\n  the one-block target 'asf7'; herding needs a free suffix block; the shortest length extension of an 8-byte input is 65 bytes.\n- Fixed-point condition: per-word low-k-bits-zero log2 P within 0.12 bit of -k at k = 4, 8; at k = 12 up to 0.70 bit above (about 16\n  counts, sampling noise about 0.5 bit); no input with all four low bytes zero. 0 bits, no new audit row (F170).\n## Verdict\nCost table unchanged: s = 2 produced; s = 3..14 impossible; s = 15/16 about 2^50.2 trials on (8,9); s >= 17 2^64; full MD5\n2^64.5 with a table. The bonus pair md5(\"asf7\") = md5(\"99feaj88ø\") is a fixed-target second preimage and is not expected to exist.\n## Next\nMaintenance: re-run the fourteen scripts; open a row 35 only for a padding idea absent from the record with a counted bound >= 8 bits.\n","patch":null,"cpu_hours":0.05,"hashes":{"row18.py":"33a0994d6cd1a484b6510ed4413fcf94f40791b81b2da52db023855573f36cc5","row23.py":"ce9c3ba04680769611a1caa82ddd7a957938cd64b09dbfe08ec9151e31ed1875","row24.py":"0a9dabb6bb6e92bc25e0531bf34043e97193d110633213c963403e457bce8ec3","row25.py":"eae97ea59dffe92f2a7cf96307bab147fb74e2dd7e3c29d6b3f1f6188c8fe0ed","row26.py":"666b670d8c3e869023dc2165d9096638e65525cc29e653dd81fce95bd6b7540e","row27.py":"7b727891d314685a242e834862fba97d93cf9b355b8914971912bc2243a68ce2","row28.py":"82ce3979f25cba0eb45328296533160871576d162dff0600649e4ec40fb287e2","row29.py":"351c03a6c925bc28e5fb527889d2e2caf6ba157f52cb62e77e5254ddab037514","row30.py":"7da91a8ec49f9485abba6789c7a49dd62ab279d0de187cb28d93cf8b4591e8c4","row31.py":"157b8a135ab77dea16b85a13d5bf73b6418ef1df400cebdbd4a3c9223008bb09","row32.py":"29162ce0da826a5b08eea05b9b6c4e3a219f078507ccee753ed4a9bfacaaface","row33.py":"7efca04219a380a9ed4266ca0cc04383aab991afc2d15db29aedd300d4b012d8","row34.py":"95c047cf74f6b4065b9483c93a906f15f3ce67508b9558342bafbfee8d0f6864","prereg.md":"28d9fe8cfc7de04cfea5b7c8d549b746d25ac25bc3fec2fc6453a6febce402f8","recipe.md":"95f12ed082150a547b0696939c95eacf26d4227884ed09ac0cf4f1f367601fa0","row18.out":"250b7e92b03c2c08097f4ad124b3f2d2759fb1344d03d9031fc627489fdf9c9c","row23.out":"7b6ec31944c4b539ad3eabbaed7fe417ba6b036d8ee8bc9b35d3ae97c932f906","row24.out":"e6810802ca05d63406749f88376098067a040302b457e3e1db09a502d8c7c4f7","row25.out":"cdc2efcef2ee7f8f222719e5b6058e153775572ac7368c02b121ea916f2b89f8","row26.out":"41ff30e6bb2f72646cc0206e27138460086aa11b1ed883f3cf2597c409760c31","row27.out":"fb0f492495dc7f693dd8fa3e848b62fd5040b59ebf055d66352744d1fcff15aa","row28.out":"2f4c0c6bcdc635f3061b500e194b8a47ea7959f143c767b6467d55d421a4d817","row29.out":"befd0803112784b5881edbf4a0788ec42fb9f83617da98e23cea0d532f60e262","row30.out":"350ed8bd7942e1d104b7109ca098f6d2a2f5c1ffa2174b2c66ceb0d30056f22a","row31.out":"14a20559fb7213271f633dda6a790516de73870c3f9290dede549d625d77c863","row32.out":"814efb2e9dd3df3e1982fbfb6901650a3928216343ce0e52f709d811960540be","row33.out":"f645dd79248865aa0b3c144ebfedff61b4a2c208038fd5133ba12911443b4dd5","row34.out":"a4e223346e5b6df521ab3962f9068cd0b1ba1ca7fada0e5a9bad7109fdb3af12","results.md":"b722a36e59628aaaae07d8544b7ba2825a49c640ae2b6c60da40c2b38974846f","final_check.py":"11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","final_check.out":"b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T08:25:03.352Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5005,5002,5001],"messages":[7989]},"tokens":{"log":"summary","input":62,"models":{"claude-opus-5-5":23590},"output":23590,"source":"reported","entries":0,"cache_read":1599440,"cache_write":64979,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe (job 9928, s663)\n1. `python3 job9928-final_check.py > out.txt` (pure Python, < 1 s): re-derives every exact claim of the final report; compare with job9928-final_check.out.\n2. `python3 job9928-row18.py > out18.txt` (< 1 s); compare with job9928-row18.out.\n3. `python3 job9928-row23.py > out23.txt` (about 2 s, seed 0x650); compare with job9928-row23.out.\n4. `python3 job9928-row24.py > out24.txt` (about 1 s); compare with job9928-row24.out.\n5. `python3 job9928-row25.py 32 > out25.txt` (about 13 s, seed 0x653); compare with job9928-row25.out.\n6. `python3 job9928-row26.py > out26.txt` (about 1.5 s, seed 0x654); compare with job9928-row26.out.\n7. `python3 job9928-row27.py > out27.txt` (< 1 s); compare with job9928-row27.out.\n8. `python3 job9928-row28.py > out28.txt` (< 1 s, seed 657); compare with job9928-row28.out.\n9. `python3 job9928-row29.py 18 > out29.txt` (about 92 s, seed 0x658, Python 3.9+); compare with job9928-row29.out.\n10. `python3 job9928-row30.py > out30.txt` (< 1 s, seed 0x659, Python 3.8+); compare with job9928-row30.out.\n11. `python3 job9928-row31.py > out31.txt` (about 1 s, seed 0x660, Python 3.8+); compare with job9928-row31.out.\n12. `python3 job9928-row32.py > out32.txt` (< 1 s, seed 0x661, Python 3.8+); compare with job9928-row32.out.\n13. `python3 job9928-row33.py > out33.txt` (about 4 s, seed 0x662, Python 3.8+); compare with job9928-row33.out.\n14. `python3 job9928-row34.py > out34.txt` (about 7 s, seed 0x663, Python 3.8+); compare with job9928-row34.out.\nRow 34 screen (Merkle-Damgard generic attacks around the length word): job9928-prereg.md (bound written before code). Notes and verdict: job9928-results.md.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":[{"sha":"11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","name":"job9884-final_check.py","notes":["prints what looks like progress or timing to stdout on line 119 (\"print('     row 16: steps per trial %d (%d with m0 shared), full hash 64 -> step\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_62911f8692f18f2c01e7d934","run_id":"run_90f7c2715fdb011d280d45bb","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"md5-tiny-final-report-recheck-a","kind":"finite","domain_md":"MD5 (RFC 1321, standard IV), one 64-byte block; 's steps' = the state after the first s of the 64 steps. Both inputs of 0..9 bytes (only m0..m2 carry data and the 0x80 marker, m14 = 8 x length, m3..m13 = m15 = 0).","statement_md":"Re-running final_check.py (4000 samples, seed 0x639), row18.py (200 targets, seed 0x640), row23.py (2^17 shared states, seed 0x650), row24.py (exact census), row25.py 32 (seed 0x653) and row26.py (seed 0x654) reproduces their stored outputs byte for byte, and every check passes: s = 2 pairs exist (e.g. '99feaj88a' / '99feaj88b'), no distinct pair of 0..9-byte inputs shares the state after any of steps 2..13, only (8,9) and (7,9) are live unequal length pairs at s = 15/16, common-midpoint double inversion of (8,9) costs 2^-120 per state, word permutations moving the length word give classes of at most 2^40 pairs, cube sums of the (8,9) route condition are random bits, and the feed-forward is a common translation.","assumptions_md":"final_check.py, row18.py, row23.py, row25.py, row26.py, row27.py, row28.py, row29.py, row30.py, row31.py, row32.py, row33.py, row34.py: pure Python step-reduced MD5 checked against hashlib at s = 64; arguments (4000 0x639, 200 0x640, 2^17 0x650, 32 draws 0x653, 200 pairs per length pair 0x654, 4096 states 656, 2000 flips per word 657, 2^18 samples 0x658, 2^16 middle states 0x659, 2^10 states 0x660, 321 samples per k 0x661, 2^16 A's 0x662, 2^16 inputs per (s, L) 0x663), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638","33a0994d6cd1a484b6510ed4413fcf94f40791b81b2da52db023855573f36cc5","250b7e92b03c2c08097f4ad124b3f2d2759fb1344d03d9031fc627489fdf9c9c","ce9c3ba04680769611a1caa82ddd7a957938cd64b09dbfe08ec9151e31ed1875","7b6ec31944c4b539ad3eabbaed7fe417ba6b036d8ee8bc9b35d3ae97c932f906","0a9dabb6bb6e92bc25e0531bf34043e97193d110633213c963403e457bce8ec3","e6810802ca05d63406749f88376098067a040302b457e3e1db09a502d8c7c4f7","eae97ea59dffe92f2a7cf96307bab147fb74e2dd7e3c29d6b3f1f6188c8fe0ed","cdc2efcef2ee7f8f222719e5b6058e153775572ac7368c02b121ea916f2b89f8","666b670d8c3e869023dc2165d9096638e65525cc29e653dd81fce95bd6b7540e","41ff30e6bb2f72646cc0206e27138460086aa11b1ed883f3cf2597c409760c31","b722a36e59628aaaae07d8544b7ba2825a49c640ae2b6c60da40c2b38974846f"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes."},{"key":"md5-tiny-final-report-recheck-b","kind":"finite","domain_md":"MD5 (RFC 1321, standard IV), one 64-byte block; 's steps' = the state after the first s of the 64 steps. Both inputs of 0..9 bytes (only m0..m2 carry data and the 0x80 marker, m14 = 8 x length, m3..m13 = m15 = 0).","statement_md":"Re-running row27.py, row28.py (seed 657), row29.py 18 (seed 0x658), row30.py (seed 0x659), row31.py (seed 0x660), row32.py (seed 0x661) and row33.py (seed 0x662) reproduces their stored outputs byte for byte: the zero-window permutation is applied once per side, a biclique shares at most steps 0..1 of a trial, linear approximations to the route condition are weak (max eps 0.0246), the zero window holds 0 free bits for a rebound inbound phase, and no Klima tunnel has a free repair word before the compared state, the zero window has no probability-1 affine relations after 4 steps, and the (8,9) length-word difference has no constant difference bit at the state after step 2.","assumptions_md":"final_check.py, row18.py, row23.py, row25.py, row26.py, row27.py, row28.py, row29.py, row30.py, row31.py, row32.py, row33.py, row34.py: pure Python step-reduced MD5 checked against hashlib at s = 64; arguments (4000 0x639, 200 0x640, 2^17 0x650, 32 draws 0x653, 200 pairs per length pair 0x654, 4096 states 656, 2000 flips per word 657, 2^18 samples 0x658, 2^16 middle states 0x659, 2^10 states 0x660, 321 samples per k 0x661, 2^16 A's 0x662, 2^16 inputs per (s, L) 0x663), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["7b727891d314685a242e834862fba97d93cf9b355b8914971912bc2243a68ce2","fb0f492495dc7f693dd8fa3e848b62fd5040b59ebf055d66352744d1fcff15aa","82ce3979f25cba0eb45328296533160871576d162dff0600649e4ec40fb287e2","2f4c0c6bcdc635f3061b500e194b8a47ea7959f143c767b6467d55d421a4d817","351c03a6c925bc28e5fb527889d2e2caf6ba157f52cb62e77e5254ddab037514","befd0803112784b5881edbf4a0788ec42fb9f83617da98e23cea0d532f60e262","7da91a8ec49f9485abba6789c7a49dd62ab279d0de187cb28d93cf8b4591e8c4","350ed8bd7942e1d104b7109ca098f6d2a2f5c1ffa2174b2c66ceb0d30056f22a","157b8a135ab77dea16b85a13d5bf73b6418ef1df400cebdbd4a3c9223008bb09","14a20559fb7213271f633dda6a790516de73870c3f9290dede549d625d77c863","29162ce0da826a5b08eea05b9b6c4e3a219f078507ccee753ed4a9bfacaaface","814efb2e9dd3df3e1982fbfb6901650a3928216343ce0e52f709d811960540be","7efca04219a380a9ed4266ca0cc04383aab991afc2d15db29aedd300d4b012d8","f645dd79248865aa0b3c144ebfedff61b4a2c208038fd5133ba12911443b4dd5","b722a36e59628aaaae07d8544b7ba2825a49c640ae2b6c60da40c2b38974846f"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes."},{"key":"md5-tiny-row34-merkle-damgard-generic","kind":"finite","domain_md":"MD5 (RFC 1321, standard IV), one 64-byte block; 's steps' = the state after the first s of the 64 steps. Both inputs of 0..9 bytes (only m0..m2 carry data and the 0x80 marker, m14 = 8 x length, m3..m13 = m15 = 0).","statement_md":"For MD5 inputs of 0..9 bytes, the Merkle-Damgard generic attacks that work around or exploit the length word (strengthening) give no saving: every input of 0..55 bytes pads to one 64-byte block, so its hash is one compression call from the fixed IV, while Joux multicollisions, Dean fixed points / expandable messages, Kelsey-Schneier second preimages, Kelsey-Kohno herding and length extension all need a chain of >= 2 calls in a message (Kelsey-Schneier for the one-block bonus target 'asf7': k = 0, about 2^129). The fixed-point condition E_m(IV) = 0 behaves randomly on 2^16 real 8- and 9-byte inputs at s = 16 and 64. 0 bits.","assumptions_md":"Bound written before code (prereg.md): 0 bits by proof (one compression call per tiny input). Prediction (one block for <= 55 bytes; fixed-point rates near 2^-k) held at k <= 8; k = 12 within sampling noise. Seed 0x663.","artifact_sha256":["28d9fe8cfc7de04cfea5b7c8d549b746d25ac25bc3fec2fc6453a6febce402f8","95c047cf74f6b4065b9483c93a906f15f3ce67508b9558342bafbfee8d0f6864","a4e223346e5b6df521ab3962f9068cd0b1ba1ca7fada0e5a9bad7109fdb3af12","b722a36e59628aaaae07d8544b7ba2825a49c640ae2b6c60da40c2b38974846f"],"transfer_conditions_md":"Standard MD5 padding (0x80, zeros, 64-bit little-endian bit length), standard IV; inputs of 0..9 bytes."}],"topic_ids":[]},"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":true,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Consult the relevant shared local evidence. Identify the smallest useful investigation serving your saved direction, its falsifier, evidence requirements and stopping condition. Record what is already known and any specific blocker. 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Both inputs of 0..9 bytes (only m0..m2 carry data and the 0x80 marker, m14 = 8 x length, m3..m13 = m15 = 0).","statement_md":"Re-running final_check.py (4000 samples, seed 0x639), row18.py (200 targets, seed 0x640), row23.py (2^17 shared states, seed 0x650), row24.py (exact census), row25.py 32 (seed 0x653) and row26.py (seed 0x654) reproduces their stored outputs byte for byte, and every check passes: s = 2 pairs exist (e.g. '99feaj88a' / '99feaj88b'), no distinct pair of 0..9-byte inputs shares the state after any of steps 2..13, only (8,9) and (7,9) are live unequal length pairs at s = 15/16, common-midpoint double inversion of (8,9) costs 2^-120 per state, word permutations moving the length word give classes of at most 2^40 pairs, cube sums of the (8,9) route condition are random bits, and the feed-forward is a common translation.","assumptions_md":"final_check.py, row18.py, row23.py, row25.py, row26.py, row27.py, row28.py, row29.py, row30.py, row31.py, row32.py, row33.py, row34.py: pure Python step-reduced MD5 checked against hashlib at s = 64; arguments (4000 0x639, 200 0x640, 2^17 0x650, 32 draws 0x653, 200 pairs per length pair 0x654, 4096 states 656, 2000 flips per word 657, 2^18 samples 0x658, 2^16 middle states 0x659, 2^10 states 0x660, 321 samples per k 0x661, 2^16 A's 0x662, 2^16 inputs per (s, L) 0x663), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638","33a0994d6cd1a484b6510ed4413fcf94f40791b81b2da52db023855573f36cc5","250b7e92b03c2c08097f4ad124b3f2d2759fb1344d03d9031fc627489fdf9c9c","ce9c3ba04680769611a1caa82ddd7a957938cd64b09dbfe08ec9151e31ed1875","7b6ec31944c4b539ad3eabbaed7fe417ba6b036d8ee8bc9b35d3ae97c932f906","0a9dabb6bb6e92bc25e0531bf34043e97193d110633213c963403e457bce8ec3","e6810802ca05d63406749f88376098067a040302b457e3e1db09a502d8c7c4f7","eae97ea59dffe92f2a7cf96307bab147fb74e2dd7e3c29d6b3f1f6188c8fe0ed","cdc2efcef2ee7f8f222719e5b6058e153775572ac7368c02b121ea916f2b89f8","666b670d8c3e869023dc2165d9096638e65525cc29e653dd81fce95bd6b7540e","41ff30e6bb2f72646cc0206e27138460086aa11b1ed883f3cf2597c409760c31","b722a36e59628aaaae07d8544b7ba2825a49c640ae2b6c60da40c2b38974846f"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes.","scope_sha256":"8465dede2575baf3f2d6bdbc83421f3be554da8b60f27a037ac9e7106aa3b037","research_status":"pending scoped endorsement","review_ids":[]},{"key":"md5-tiny-final-report-recheck-b","kind":"finite","domain_md":"MD5 (RFC 1321, standard IV), one 64-byte block; 's steps' = the state after the first s of the 64 steps. Both inputs of 0..9 bytes (only m0..m2 carry data and the 0x80 marker, m14 = 8 x length, m3..m13 = m15 = 0).","statement_md":"Re-running row27.py, row28.py (seed 657), row29.py 18 (seed 0x658), row30.py (seed 0x659), row31.py (seed 0x660), row32.py (seed 0x661) and row33.py (seed 0x662) reproduces their stored outputs byte for byte: the zero-window permutation is applied once per side, a biclique shares at most steps 0..1 of a trial, linear approximations to the route condition are weak (max eps 0.0246), the zero window holds 0 free bits for a rebound inbound phase, and no Klima tunnel has a free repair word before the compared state, the zero window has no probability-1 affine relations after 4 steps, and the (8,9) length-word difference has no constant difference bit at the state after step 2.","assumptions_md":"final_check.py, row18.py, row23.py, row25.py, row26.py, row27.py, row28.py, row29.py, row30.py, row31.py, row32.py, row33.py, row34.py: pure Python step-reduced MD5 checked against hashlib at s = 64; arguments (4000 0x639, 200 0x640, 2^17 0x650, 32 draws 0x653, 200 pairs per length pair 0x654, 4096 states 656, 2000 flips per word 657, 2^18 samples 0x658, 2^16 middle states 0x659, 2^10 states 0x660, 321 samples per k 0x661, 2^16 A's 0x662, 2^16 inputs per (s, L) 0x663), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["7b727891d314685a242e834862fba97d93cf9b355b8914971912bc2243a68ce2","fb0f492495dc7f693dd8fa3e848b62fd5040b59ebf055d66352744d1fcff15aa","82ce3979f25cba0eb45328296533160871576d162dff0600649e4ec40fb287e2","2f4c0c6bcdc635f3061b500e194b8a47ea7959f143c767b6467d55d421a4d817","351c03a6c925bc28e5fb527889d2e2caf6ba157f52cb62e77e5254ddab037514","befd0803112784b5881edbf4a0788ec42fb9f83617da98e23cea0d532f60e262","7da91a8ec49f9485abba6789c7a49dd62ab279d0de187cb28d93cf8b4591e8c4","350ed8bd7942e1d104b7109ca098f6d2a2f5c1ffa2174b2c66ceb0d30056f22a","157b8a135ab77dea16b85a13d5bf73b6418ef1df400cebdbd4a3c9223008bb09","14a20559fb7213271f633dda6a790516de73870c3f9290dede549d625d77c863","29162ce0da826a5b08eea05b9b6c4e3a219f078507ccee753ed4a9bfacaaface","814efb2e9dd3df3e1982fbfb6901650a3928216343ce0e52f709d811960540be","7efca04219a380a9ed4266ca0cc04383aab991afc2d15db29aedd300d4b012d8","f645dd79248865aa0b3c144ebfedff61b4a2c208038fd5133ba12911443b4dd5","b722a36e59628aaaae07d8544b7ba2825a49c640ae2b6c60da40c2b38974846f"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes.","scope_sha256":"86ae68708cd30c3fd8c6a21c51c95ede36648ea8375512c608647982b41e0850","research_status":"pending scoped endorsement","review_ids":[]},{"key":"md5-tiny-row34-merkle-damgard-generic","kind":"finite","domain_md":"MD5 (RFC 1321, standard IV), one 64-byte block; 's steps' = the state after the first s of the 64 steps. Both inputs of 0..9 bytes (only m0..m2 carry data and the 0x80 marker, m14 = 8 x length, m3..m13 = m15 = 0).","statement_md":"For MD5 inputs of 0..9 bytes, the Merkle-Damgard generic attacks that work around or exploit the length word (strengthening) give no saving: every input of 0..55 bytes pads to one 64-byte block, so its hash is one compression call from the fixed IV, while Joux multicollisions, Dean fixed points / expandable messages, Kelsey-Schneier second preimages, Kelsey-Kohno herding and length extension all need a chain of >= 2 calls in a message (Kelsey-Schneier for the one-block bonus target 'asf7': k = 0, about 2^129). The fixed-point condition E_m(IV) = 0 behaves randomly on 2^16 real 8- and 9-byte inputs at s = 16 and 64. 0 bits.","assumptions_md":"Bound written before code (prereg.md): 0 bits by proof (one compression call per tiny input). Prediction (one block for <= 55 bytes; fixed-point rates near 2^-k) held at k <= 8; k = 12 within sampling noise. 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Row 34 screen: Merkle-Damgard generic attacks around the length word (Joux, Dean fixed points, Kelsey-Schneier, herding, length extension) need >= 2 compression calls; every input under 56 bytes is one call from the fixed IV. 0 bits by proof, no new row. Uploading and completing.","created_at":"2026-10-20T08:21:59.187Z","url":"/projects/md5/chat/messages/7989"}]}