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pith:UA3IMYCV

pith:2026:UA3IMYCVT2Z5L3DQUONG4A5MHX

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Module Lattice Security (Part III): Structured CVP Distance on the Log-Unit Lattice

Ming-Xing Luo

The L² CVP distance from a random short ring element to the log-unit lattice converges to π/(2√6) √n as the dimension n tends to infinity.

arxiv:2605.17404 v1 · 2026-05-17 · cs.DS · cs.CR · math.NT · math.ST · quant-ph · stat.TH

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4 Citations open

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Claims

C1strongest claim

We prove that the L² CVP distance from a random short ring element to the log-unit lattice of Q(ζ_{2^k}) converges to π/(2√6) √n as n=2^{k-1}→∞. ... combined with Parts I and II, we reduce the CDPR factor for ML-KEM from exp(O(√n)) to a sub-polynomial value.

C2weakest assumption

The model of a 'random short ring element' in the ring of integers of Q(ζ_{2^k}) is sufficiently representative that its embedding statistics match the sub-Gaussian coordinates used to derive the limit and the Voronoi cell membership (abstract, first sentence and L^∞ paragraph).

C3one line summary

The L² CVP distance to the log-unit lattice converges to (π/(2√6))√n, enabling sub-polynomial approximation factors for the Short Generator Problem and reducing the CDPR factor for ML-KEM from exp(O(√n)) to sub-polynomial.

References

41 extracted · 41 resolved · 0 Pith anchors

[1] Recovering short generators of principal ideals in cyclotomic rings 2016

[2] Short stickelberger class relations and application to Ideal-SVP 2017

[3] Mildly short vectors in cyclotomic ideal lattices in quantum polynomial time.Journal of the ACM, 68: 1-26, 2021 2021

[4] Efficient quantum algorithms for computing class groups and solving the principal ideal problem in arbitrary degree number fields 2016

[5] Approx-SVP in ideal lattices with pre-processing 2019

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:56.737198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0368660559eb3d5ec70a39a6e03ac3de095de1e3f714c838464f0040db94157

Aliases

arxiv: 2605.17404 · arxiv_version: 2605.17404v1 · doi: 10.48550/arxiv.2605.17404 · pith_short_12: UA3IMYCVT2Z5 · pith_short_16: UA3IMYCVT2Z5L3DQ · pith_short_8: UA3IMYCV

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UA3IMYCVT2Z5L3DQUONG4A5MHX \
  | 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: a0368660559eb3d5ec70a39a6e03ac3de095de1e3f714c838464f0040db94157

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47488b272a599ec7c13ee72bc7026a1cfa6eb61f5faabb9f3520426249913340",
    "cross_cats_sorted": [
      "cs.CR",
      "math.NT",
      "math.ST",
      "quant-ph",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-17T12:00:59Z",
    "title_canon_sha256": "9e03b3f598e3a2b1c01046111eabe8ec452b074f6732dbdead26bdaed7b3bdd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17404",
    "kind": "arxiv",
    "version": 1
  }
}