Pith Number

pith:XXRX6B4A

pith:2026:XXRX6B4ACSZOHJZVFCIZFPB76H

not attested not anchored not stored refs pending

Efficient Quantum Fully Homomorphic Encryption

Fengxia Liu, Kun Tian, Maozhi Xu, Yi Zhang, Zhiming Zheng, Zixian Gong

A novel modular arithmetic program for LWE decryption reduces the quantum resource cost of fully homomorphic encryption to near-linear in the security parameter.

arxiv:2604.23490 v2 · 2026-04-26 · quant-ph · cs.CR

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\usepackage{pith}
\pithnumber{XXRX6B4ACSZOHJZVFCIZFPB76H}

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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

✓ Portable graph bundle live · download bundle · merged state

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

Our central innovation is a novel MAP tailored to the algebraic structure of Learning-with-Errors (LWE) decryption... This yields branching programs of width O(log λ) and length O(λ log λ), thereby reducing the size of the essential quantum gadget from O(λ^{2.58}) to O(λ log² λ) EPR pairs -- a concrete improvement factor of 2^{15} to 2^{18} for standard security parameters.

C2weakest assumption

The assumption that the novel MAP correctly computes the inner product ⟨sk, c⟩ mod q with the claimed O(log q) state width, and that the mapping via the garden-hose model and MBQC incurs no additional exponential overhead beyond the stated bounds.

C3one line summary

A specialized modular arithmetic program for LWE decryption reduces the quantum gadget size in QFHE from O(λ^{2.58}) to O(λ log² λ) EPR pairs.

Receipt and verification

First computed	2026-06-23T02:13:24.255427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bde37f078014b2e3a735289192bc3ff1d5e6d821e911a4e84f927e8d811c94ed

Aliases

arxiv: 2604.23490 · arxiv_version: 2604.23490v2 · doi: 10.48550/arxiv.2604.23490 · pith_short_12: XXRX6B4ACSZO · pith_short_16: XXRX6B4ACSZOHJZV · pith_short_8: XXRX6B4A

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/XXRX6B4ACSZOHJZVFCIZFPB76H \
  | 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: bde37f078014b2e3a735289192bc3ff1d5e6d821e911a4e84f927e8d811c94ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b84f08e68d2266195687faf243bf904f4c1578a5c5bd56b16c1a2dc13a87f167",
    "cross_cats_sorted": [
      "cs.CR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-04-26T01:48:28Z",
    "title_canon_sha256": "d39c823295e8433fb8128f72b23182c5a38d03e1cd07790494160fd37a32bb04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.23490",
    "kind": "arxiv",
    "version": 2
  }
}