Source-pinned research
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ArkLib.Lattices.CyclotomicModulus.Rq.eq_zero_of_l2NormSq_eq_zero
Plain-language statement
A ring element with zero centered squared ℓ₂ norm is 0: every centered coefficient representative below deg φ vanishes (ZMod.valMinAbs_eq_zero), and the representative is reduced (degree < deg φ), so the underlying polynomial is 0.
Source project: ArkLib
Person-level attribution pending.
ArkLib.Lattices.CyclotomicModulus.Rq.l1Norm_one
Plain-language statement
The centered ℓ₁ norm of 1 : Rq Φ is 1 (when 1 ≤ deg φ): the trivial challenge c = 1 used by the honest committer is nonzero and ℓ₁-short.
Source project: ArkLib
Person-level attribution pending.
ArkLib.Lattices.CyclotomicModulus.Rq.l2NormSq_le_natDegree_mul_lInftyNorm_sq
Plain-language statement
ℓ∞ → ℓ₂² bridge (ring element): ‖x‖₂² ≤ deg φ · ‖x‖∞² , each of the deg φ centered coefficients contributes at most ‖x‖∞².
Source project: ArkLib
Person-level attribution pending.
ArkLib.Lattices.CyclotomicModulus.Rq.l2NormSq_mul_le
Plain-language statement
Per-entry product norm bound (Micciancio/Young, cf. [Mic07, ineqs. (2.6)–(2.7)]). Over the negacyclic ring X^{2^α}+1, ‖d·w‖₂² ≤ ‖d‖₁²·‖w‖₂².
Source project: ArkLib
Person-level attribution pending.
ArkLib.Lattices.CyclotomicModulus.Rq.l2NormSq_sub_le
Plain-language statement
Per-element subtraction bound: ‖a - b‖₂² ≤ 2·(‖a‖₂² + ‖b‖₂²).
Source project: ArkLib
Person-level attribution pending.
ArkLib.Lattices.CyclotomicModulus.Rq.lInftyNorm_sub_le
Plain-language statement
Per-element ℓ∞ triangle inequality: ‖a - b‖∞ ≤ ‖a‖∞ + ‖b‖∞.
Source project: ArkLib
Person-level attribution pending.