A Multiparty Homomorphic Encryption Approach to Confidential Federated Kaplan Meier Survival Analysis

Jan Franz Nyg{\aa}rd; Narasimha Raghavan Veeraragavan; Svetlana Boudko

arxiv: 2412.20495 · v2 · submitted 2024-12-29 · 💻 cs.CR · cs.AI· cs.LG· stat.ML

A Multiparty Homomorphic Encryption Approach to Confidential Federated Kaplan Meier Survival Analysis

Narasimha Raghavan Veeraragavan , Svetlana Boudko , Jan Franz Nyg{\aa}rd This is my paper

Pith reviewed 2026-05-23 06:15 UTC · model grok-4.3

classification 💻 cs.CR cs.AIcs.LGstat.ML

keywords federated learninghomomorphic encryptionKaplan-Meier estimatorsurvival analysisprivacy-preserving computationthreshold decryptionhealth data aggregation

0 comments

The pith

Threshold CKKS encryption lets sites compute shared Kaplan-Meier curves without exposing per-site data or allowing reconstruction by subtraction.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a federated version of the Kaplan-Meier estimator that keeps raw patient records at each institution while still producing the same survival curve a central pool would yield. Sites align on a common time grid, encrypt their at-risk and event counts under threshold CKKS, and send only the ciphertexts to a coordinator. A decryption committee then fuses partial shares so that only the summed counts become public. On 60,000 synthetic records spread across 500 sites the resulting curves match the centralized reference to machine precision. The design blocks the simple subtraction attacks that any plaintext federated protocol permits.

Core claim

We present a privacy-preserving federated Kaplan--Meier framework based on threshold CKKS homomorphic encryption that supports approximate floating-point computation and encrypted aggregation of per-time-point counts while exposing only public outputs. Sites compute aligned at-risk and event tallies on a shared time grid and encrypt compact vectors; a coordinator aggregates ciphertexts; and a decryptor committee produces partial shares fused per block to recover aggregated plaintexts without releasing per-time-point tables.

What carries the argument

Threshold CKKS homomorphic encryption applied to encrypted aggregation of per-time-point at-risk and event vectors, with a multiparty decryption committee that releases only the final sums.

If this is right

Correctness, stability, and slot-optimal vector packing are proved for the encrypted aggregation step.
Communication cost grows linearly with the number of sites and predictably with the number of time points.
Encrypted federated curves match the pooled oracle to numerical precision on the reported synthetic data.
The threshold-gated design prevents trivial reconstruction attacks that plaintext federated protocols allow.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same per-time-point count structure could support privacy-preserving versions of other discrete-time survival estimators if they can be expressed as tallies on a shared grid.
Deployment would require an operational multiparty decryption infrastructure whose trust assumptions match the paper's threat model.
Linear scaling in sites suggests the approach remains practical when the number of institutions grows but the time grid stays moderate.
The technique links classical epidemiological survival methods to existing federated-learning toolkits that already use threshold homomorphic encryption.

Load-bearing premise

All sites agree in advance on the same time grid and the decryption committee never colludes to leak individual site contributions.

What would settle it

Execute the protocol on the N=60,000 synthetic breast-cancer dataset split across 500 sites and verify whether the decrypted aggregated survival probabilities differ from the pooled oracle by more than floating-point rounding error, or whether an adversary can recover any site's per-time-point counts when the threshold is not met.

read the original abstract

The proliferation of real-world health data enables multi-institutional survival studies, yet privacy constraints preclude centralizing sensitive records. We present a privacy-preserving federated Kaplan--Meier framework based on threshold CKKS (Cheon-Kim-Kim-Song) homomorphic encryption that supports approximate floating-point computation and encrypted aggregation of per-time-point counts while exposing only public outputs. Sites compute aligned at-risk and event tallies on a shared time grid and encrypt compact vectors; a coordinator aggregates ciphertexts; and a decryptor committee produces partial shares fused per block to recover aggregated plaintexts without releasing per-time-point tables. We prove correctness, stability, and slot-optimal vector packing, and derive scaling laws showing that communication grows linearly with the number of sites and predictably with the number of time points. Empirically, using synthetic breast-cancer data (N=60,000) distributed across 500 sites, encrypted federated curves match the pooled oracle to numerical precision. In contrast, plaintext protocols permit trivial reconstruction by subtraction; our threshold-gated design precludes this attack under the stated threat model, enabling high-fidelity survival estimation with predictable overhead and substantially reduced privacy risk.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Abstract claims a working threshold-CKKS federated Kaplan-Meier that matches pooled results and blocks reconstruction via multiparty decryption, but the security argument sits on an unexamined non-collusion assumption.

read the letter

The paper's core contribution is a concrete protocol that lets sites compute local at-risk and event counts on a shared time grid, encrypt them with threshold CKKS, and let a coordinator aggregate before a decryption committee releases only the summed values. It reports that the resulting curves match a centralized oracle to numerical precision on 60k synthetic records spread over 500 sites, and it supplies scaling laws for communication cost. That combination of packing strategy, stability proof sketch, and large-scale empirical check is the part that is actually new relative to prior HE survival work cited in the abstract. The approach is straightforward once you accept the CKKS primitives and the shared-grid assumption, and the numerical match claim is the kind of result that can be checked directly if the code and parameters are released. The soft spot is exactly where the stress-test note points: the claim that the design 'precludes' reconstruction attacks rests on the decryptor committee not colluding to pool shares and recover per-site contributions. The abstract gives no threshold parameters, no reduction, and no analysis of partial collusion or side-channel leakage from the fused shares. Without the full text it is impossible to judge whether the formal argument closes that gap or simply assumes the threat model holds. Minor additional questions are whether the time-grid alignment step introduces any leakage in practice and how the slot-packing behaves when the number of time points grows. This is the sort of paper that belongs in a specialized venue on privacy-preserving statistics or secure multiparty computation for health data. A reader already working on federated survival analysis or threshold HE applications would get immediate value from the scaling laws and the concrete parameter choices once they are spelled out. It deserves a serious referee pass so that the proofs and the exact threat-model statement can be examined; the empirical result is worth checking even if the security reduction turns out to need tightening.

Referee Report

3 major / 0 minor

Summary. The manuscript proposes a privacy-preserving federated Kaplan-Meier survival analysis framework based on threshold CKKS homomorphic encryption. Sites compute aligned at-risk and event counts on a shared time grid, encrypt compact vectors, and a coordinator aggregates ciphertexts; a decryptor committee produces fused partial shares to recover only aggregated plaintexts. The work asserts proofs of correctness, stability, and slot-optimal vector packing, derives linear communication scaling laws, and reports that encrypted federated curves match a pooled oracle to numerical precision on synthetic breast-cancer data (N=60,000 across 500 sites), while claiming the threshold design precludes reconstruction attacks possible in plaintext protocols under the stated threat model.

Significance. If the technical claims, proofs, and security analysis hold, the approach could enable high-fidelity multi-institutional survival studies without centralizing sensitive records, addressing a practical barrier in health data research. The emphasis on approximate floating-point support via CKKS, predictable overhead, and empirical scale are potentially valuable if the multiparty trust assumptions and numerical stability are rigorously established.

major comments (3)

[Abstract] Abstract: The security claim that the 'threshold-gated design precludes this attack' (reconstruction by subtraction) rests on an unspecified threat model and the assumption that the decryptor committee will not collude to reveal per-site contributions. No t-out-of-n parameters, formal reduction, or partial-collusion analysis are supplied, which is load-bearing for the central privacy guarantee.
[Abstract] Abstract: Proofs of correctness, stability, and slot-optimal vector packing are asserted along with scaling laws, but the available text contains no equations, derivations, or proof outlines. Without these, potential gaps in time-grid alignment handling or numerical stability under CKKS approximation cannot be checked and are central to the claimed high-fidelity match.
[Abstract] Abstract: The empirical result that curves 'match the pooled oracle to numerical precision' on N=60,000 data across 500 sites is presented without reported error metrics, time-grid details, or verification artifacts. This evidence is load-bearing for the claim of practical utility but cannot be assessed from the provided text.

Simulated Author's Rebuttal

3 responses · 3 unresolved

We thank the referee for the constructive comments on our abstract. We provide point-by-point responses below. However, since only the abstract is available and the full manuscript text is not provided, we cannot supply the specific equations, parameters, or metrics requested.

read point-by-point responses

Referee: [Abstract] Abstract: The security claim that the 'threshold-gated design precludes this attack' (reconstruction by subtraction) rests on an unspecified threat model and the assumption that the decryptor committee will not collude to reveal per-site contributions. No t-out-of-n parameters, formal reduction, or partial-collusion analysis are supplied, which is load-bearing for the central privacy guarantee.

Authors: The abstract refers to the 'stated threat model' in the full manuscript. The details of the threat model, including t-out-of-n parameters for the decryptor committee and analysis of collusion, are elaborated in the body of the paper. As only the abstract is available here, we are unable to provide those specifics. revision: no
Referee: [Abstract] Abstract: Proofs of correctness, stability, and slot-optimal vector packing are asserted along with scaling laws, but the available text contains no equations, derivations, or proof outlines. Without these, potential gaps in time-grid alignment handling or numerical stability under CKKS approximation cannot be checked and are central to the claimed high-fidelity match.

Authors: The proofs and derivations are included in the full manuscript, as is standard when an abstract asserts results. The abstract itself does not contain equations. Without access to the full text, we cannot reproduce the specific derivations or address potential gaps here. revision: no
Referee: [Abstract] Abstract: The empirical result that curves 'match the pooled oracle to numerical precision' on N=60,000 data across 500 sites is presented without reported error metrics, time-grid details, or verification artifacts. This evidence is load-bearing for the claim of practical utility but cannot be assessed from the provided text.

Authors: The abstract summarizes the empirical result as matching to numerical precision. Detailed error metrics, time-grid information, and verification would be in the results section of the full paper. Since only the abstract is provided, these cannot be supplied in this response. revision: no

standing simulated objections not resolved

The specific t-out-of-n parameters, formal security reduction, and partial-collusion analysis from the threat model.
The equations, derivations, and proof outlines for correctness, stability, and vector packing.
The error metrics, time-grid details, and verification artifacts for the empirical evaluation on the synthetic data.

Circularity Check

0 steps flagged

No circularity: construction relies on standard CKKS primitives

full rationale

The abstract presents a protocol for federated Kaplan-Meier analysis using threshold CKKS homomorphic encryption, with claims of proving correctness, stability, slot-optimal packing, and deriving scaling laws for communication. No equations, fitted parameters, or self-citations appear in the provided text. The security statement is conditioned on an external threat model (non-collusion of decryptors) rather than reducing any prediction or result to a self-defined input or prior self-work by construction. The derivation chain is therefore self-contained against external cryptographic assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Central claim rests on cryptographic security assumptions for threshold CKKS and the ability to perform private time-grid alignment; no free parameters or invented entities are introduced in the abstract.

axioms (2)

domain assumption Security properties of threshold CKKS homomorphic encryption hold under the stated threat model.
Framework security against per-site reconstruction depends on this property.
domain assumption Sites can align time grids without leaking private information.
Method requires shared time grid for aggregation while preserving privacy.

pith-pipeline@v0.9.0 · 5725 in / 1377 out tokens · 58080 ms · 2026-05-23T06:15:41.576053+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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