A Spectral Theory of Local-to-Global Leakage

What it is

A preprint (IACR ePrint 2026/2571, received 20 October 2026, approved 21 October 2026, CC BY) by Rei Ueno of Kyoto University. It studies additive secret sharing over a finite abelian group, which the paper treats as a special case of linear secret sharing and side-channel masking. It argues that global leakage from a sharing cannot be predicted from local mutual information (MI) alone.

How it works

The paper gives an exact decomposition of global leakage into two parts: the magnitude of the local leakage, and its spectral alignment across shares. MI captures only the first. The abstract says earlier literature conjectured that local MI suffices, and the paper shows that this fails.

Further results stated in the abstract:

• Two channels with identical local MI can give exponentially different global leakage.
• Local MI does not fix the exponential rate at which leakage vanishes under homomorphic composition.
• A universal separation theorem: the decay rates can still differ exponentially even when all permutation-invariant scalar measures of local leakage agree.
• A characterization of the spectral alignment factor, with a lower bound derived from character-order multiplicity and Möbius inversion.

Preconditions / Affected

The results apply to additive sharing over finite abelian groups. The perfect-cancellation contrast has specific conditions. Automorphism-weighted sharing can cancel leakage perfectly with finitely many shares, even for non-trivial full-support local channels. Ordinary additive sharing cannot do this for non-trivial i.i.d. local leakage channels with finitely many shares.

Caveats

Only the abstract was available, so the theorem statements, constructions and any concrete numbers are not covered here. The paper is marked "Preprint" with no peer-review venue. The abstract gives no experiments on real devices and no guidance on choosing automorphism weights. Its practical message is that masking security bounds based only on local leakage magnitude must optimize over alignments the real channel may not realize.