Pith Number

pith:V7GK2P7F

pith:2026:V7GK2P7FTKOLOFGL4IR226MDAH

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A Complexity Hierarchy of Shuffles in Card-Based Protocols

Suthee Ruangwises, Tomoki Ono

Shuffles in card-based cryptography form a complexity hierarchy with provable separations between levels.

arxiv:2603.18608 v2 · 2026-03-19 · cs.CR

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\usepackage{pith}
\pithnumber{V7GK2P7FTKOLOFGL4IR226MDAH}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

we classify shuffle operations into several levels according to their implementation complexity [...] prove separation results between several levels by showing that certain shuffles cannot be realized using only operations from lower levels. Finally, we propose a new complexity measure for evaluating card-based protocols based on this hierarchy.

C2weakest assumption

That practical implementation complexity of shuffles can be meaningfully ordered into strict levels with provable separations that hold across all possible physical realizations and human execution variations.

C3one line summary

A new hierarchy classifies card shuffles by complexity with separation proofs, enabling a measure for protocol evaluation.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] Y. Abe, Y. Hayashi, T. Mizuki and H. Sone. Five-Card AND Computations in Com- mitted Format Using Only Uniform Cyclic Shuffles.New Generation Computing, 39(1): 97–114 (2021) 2021

[2] X. Bultel, J. Dreier, J.-G. Dumas, P. Lafourcade, D. Miyahara, T. Mizuki, A. Nagao, T. Sasaki, K. Shinagawa and H. Sone. Physical Zero-Knowledge Proof for Makaro. In Proceedings of the 20th Internatio 2018

[3] B. den Boer. More Efficient Match-Making and Satisfiability: the Five Card Trick. In Proceedings of the Workshop on the Theory and Application of of Cryptographic Tech- niques (EUROCRYPT ’89), pp. 208 1990

[4] R. Gradwohl, M. Naor, B. Pinkas and G.N. Rothblum. Cryptographic and Physical Zero-Knowledge Proof Systems for Solutions of Sudoku Puzzles.Theory of Computing Systems, 44(2): 245–268 (2009) 2009

[5] R. Ishikawa, E. Chida and T. Mizuki. Efficient Card-Based Protocols for Generating a Hidden Random Permutation Without Fixed Points. InProceedings of the 14th Interna- tional Conference on Unconventio 2015

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:38:59.622334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afccad3fe59a9cb714cbe223ad798301ecada5447ea452dc00d3ada0762cf5b9

Aliases

arxiv: 2603.18608 · arxiv_version: 2603.18608v2 · doi: 10.48550/arxiv.2603.18608 · pith_short_12: V7GK2P7FTKOL · pith_short_16: V7GK2P7FTKOLOFGL · pith_short_8: V7GK2P7F

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/V7GK2P7FTKOLOFGL4IR226MDAH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: afccad3fe59a9cb714cbe223ad798301ecada5447ea452dc00d3ada0762cf5b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ce38b535bc38cd8402e30b1fd4281dd29a452ded616a45ed44c677ab80e3e64",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CR",
    "submitted_at": "2026-03-19T08:27:02Z",
    "title_canon_sha256": "3aa58a47fcc13348406abefece7b43d4c8b1bc41100c608c10ae5becbbd222d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.18608",
    "kind": "arxiv",
    "version": 2
  }
}