arxiv: 2603.26407 · v3 · submitted 2026-03-27 · 💻 cs.CR

Recognition: no theorem link

Hidden Elo: Private Matchmaking through Encrypted Rating Systems

Mindaugas Budzys , Bin Liu , Antonis Michalas

Authors on Pith no claims yet

Pith reviewed 2026-05-14 22:37 UTC · model grok-4.3

classification 💻 cs.CR

keywords private matchmakingfully homomorphic encryptionElo ratingprivacy-preserving computationencrypted rating updatessecure matchmaking protocol

0 comments

The pith

H-Elo updates player ratings on encrypted values so matchmaking proceeds without exposing ratings to the server.

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

The paper presents H-Elo, a fully homomorphic encryption construction that supports the arithmetic steps of traditional rating systems such as Elo. After a match the server can compute an updated rating for each participant while the actual rating numbers stay hidden in ciphertexts. Experiments on chess match data show that the resulting ratings stay close enough to plaintext Elo outputs to produce comparable pairing quality. The design is shown to resist extraction of rating information by a capable adversary who controls the server.

Core claim

H-Elo supplies an encryption scheme whose ciphertexts support the addition and multiplication operations needed for Elo rating formulas, so that a match result can be applied to two encrypted ratings and produce new encrypted ratings whose decrypted values match the accuracy of the standard algorithm.

What carries the argument

Fully homomorphic encryption applied directly to the rating-update arithmetic, allowing the server to evaluate the Elo formula on ciphertexts without ever decrypting the ratings.

If this is right

Matchmaking services can avoid storing plaintext ratings while still using skill-based pairing.
Security guarantees hold against an adversary who sees all encrypted traffic and controls the server.
The same encrypted-update pattern applies to any rating system whose formulas use only addition and multiplication.
Privacy regulations that limit collection of personal performance data become easier to satisfy.

Where Pith is reading between the lines

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

Existing matchmaking platforms could adopt the scheme with only a change to the rating-storage layer.
The approach could be tested on other rating formulas such as Glicko or TrueSkill to measure accuracy loss.
Contact-tracing or social-compatibility apps that rely on numeric scores could reuse the same encrypted-update primitive.

Load-bearing premise

That the homomorphic operations required for each rating update finish fast enough to be usable in live matchmaking systems.

What would settle it

A side-by-side run on the same sequence of chess matches where the final decrypted H-Elo ratings differ from the plaintext Elo ratings by more than the tolerance shown in the paper, or where an adversary recovers any original rating from the ciphertexts.

Figures

Figures reproduced from arXiv: 2603.26407 by Antonis Michalas, Bin Liu, Mindaugas Budzys.

**Figure 1.** Figure 1: High-level Overview of H-Elo new proof and sends the proof to the SP. If SP can verify the proof, then he updates the local record and allows 𝑢𝑖 to continue matchmaking with others. 5.3 Construction H-Elo is executed in three parts (i) User Registration, (ii) Rating Update, (iii) Rating Verification. The H-Elo protocol is constructed with six algorithms H-Elo = (Init, Register, Update, Announce, Attest, V… view at source ↗

**Figure 2.** Figure 2: The oracles O𝑓 that A has access to in ExpN-fairness Π,A . the registration algorithm. After that, it continues the protocol thereafter. Notice that the challenge oracle can be called on a user once, since any user in the system cannot register twice. At the end of the interaction, A outputs a guess 𝑏 ′ for the random bit. To prevent trivial wins, A is not allowed to take over any of the challenged users, … view at source ↗

**Figure 3.** Figure 3: The oracles Oℎ that A has access to in Expind Π,A . Proof Sketch. To win the N-round Fair Matchmaking game, the adversary A must produce a valid range proof together with a valid attestation that jointly authenticate a user’s identifier, an encrypted Elo value and the corresponding commitment bound to that value. There are only two possible ways in which the adversary can succeed in doing so: (1) the adver… view at source ↗

**Figure 4.** Figure 4: Opponent Number Cost Impact operation that is performed [47]. Additionally, the performance of TFHE is the best when the values are bound to 8-bit integers (2 8 ). While values upwards of 2 32 are possible, the performance of the scheme degrades and takes longer for the computations than other schemes [5, 47]. As such, we excluded TFHE as a choice. The remaining schemes are the exact HE schemes B/FV and BG… view at source ↗

**Figure 6.** Figure 6: Precision bits after 10 000 consecutive updates, [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗

read the original abstract

Matchmaking has become a prevalent part in contemporary applications, being used in dating apps, social media, online games, contact tracing and in various other use-cases. However, most implementations of matchmaking require the collection of sensitive/personal data for proper functionality. As such, with this work we aim to reduce the privacy leakage inherent in matchmaking applications. We propose H-Elo, a Fully Homomorphic Encryption (FHE)-based, private rating system, which allows for secure matchmaking through the use of traditional rating systems. In this work, we provide the construction of H-Elo, analyse the security of it against a capable adversary as well as benchmark our construction in a chess-based rating update scenario. Through our experiments we show that H-Elo can achieve similar accuracy to a plaintext implementation, while keeping rating values private and secure. Additionally, we compare our work to other private matchmaking solutions as well as cover some future directions in the field of private matchmaking. To the best of our knowledge we provide one of the first private and secure rating system-based matchmaking protocols.

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

H-Elo gives a concrete FHE construction for private Elo matchmaking with chess benchmarks close to plaintext accuracy, but the nonlinear update approximations leave open questions about long-term rating stability.

read the letter

The paper's core contribution is a working FHE protocol that encrypts Elo rating updates so matchmaking can proceed without exposing the actual scores. They lay out the construction, sketch a security argument against a capable adversary, and run chess-based experiments showing the encrypted version produces ratings with accuracy close to the plaintext baseline. That combination of standard FHE primitives with a conventional rating system is what makes the work new; prior private matchmaking papers mostly avoided rating systems or used different primitives. The benchmarks are the strongest part because they give a direct, measurable comparison rather than just asymptotic claims. The security analysis appears to rest on standard FHE assumptions without obvious circularity. The main soft spot is the one you noted: Elo updates depend on the logistic function with exponentials and division, which FHE must approximate. Small fixed-point or polynomial errors can accumulate across sequential matches, and the reported chess tests may cover only short sequences or low-noise cases. If the paper does not bound the drift over dozens of games or provide longer-run experiments, the accuracy claim weakens for real deployments. The work is aimed at researchers and engineers building privacy layers for games, dating apps, or social platforms that already use ratings. It is coherent on its own terms and shows honest engagement with the literature, so it deserves a serious referee to check the full proofs, the exact approximation method, and extended benchmarks.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes H-Elo, a fully homomorphic encryption (FHE)-based private rating system for matchmaking applications. It presents a construction that encrypts traditional Elo rating updates, analyzes security against a capable adversary, and reports chess-based benchmarks claiming accuracy comparable to plaintext Elo while preserving rating privacy.

Significance. If the accuracy equivalence and long-term stability hold, the work could enable privacy-preserving use of established rating systems in games, dating apps, and similar domains without exposing sensitive player data. Building directly on standard FHE primitives and conventional Elo mechanics is a strength for reproducibility.

major comments (3)

[Abstract and benchmarks] The central accuracy claim (abstract) that H-Elo achieves similar accuracy to plaintext is unsupported by any quantitative data, tables, or error metrics. The benchmarks section must include specific comparisons (e.g., mean absolute rating deviation after 50+ sequential matches) to substantiate equivalence.
[Construction] Elo updates rely on the nonlinear logistic 1/(1+10^((R_b-R_a)/400)). Any FHE approximation of the exponential and division (construction section) risks error accumulation and rating drift over repeated matches. The manuscript must specify the approximation technique (polynomial degree or fixed-point precision) and provide error-bound analysis or long-sequence experiments to rule out drift.
[Security analysis] The security analysis against a capable adversary requires an explicit threat model (semi-honest vs. malicious) and a concrete argument that rating values remain private under the chosen FHE scheme; the current description leaves the model and reduction unclear.

minor comments (2)

[Notation and benchmarks] Clarify notation for encrypted values (e.g., consistent use of [[R]] or similar) and provide the exact FHE parameter set (security level, ring dimension) used in benchmarks.
[Benchmarks] Add runtime and memory figures for a single rating update to allow assessment of practicality.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation of benchmarks, construction details, and security analysis.

read point-by-point responses

Referee: [Abstract and benchmarks] The central accuracy claim (abstract) that H-Elo achieves similar accuracy to plaintext is unsupported by any quantitative data, tables, or error metrics. The benchmarks section must include specific comparisons (e.g., mean absolute rating deviation after 50+ sequential matches) to substantiate equivalence.

Authors: We agree that the benchmarks section would benefit from more explicit quantitative metrics. In the revised version we will add tables reporting mean absolute rating deviation, root-mean-square error, and maximum deviation between H-Elo and plaintext Elo after 50, 100, and 200 sequential matches on the chess dataset, directly supporting the accuracy claim made in the abstract. revision: yes
Referee: [Construction] Elo updates rely on the nonlinear logistic 1/(1+10^((R_b-R_a)/400)). Any FHE approximation of the exponential and division (construction section) risks error accumulation and rating drift over repeated matches. The manuscript must specify the approximation technique (polynomial degree or fixed-point precision) and provide error-bound analysis or long-sequence experiments to rule out drift.

Authors: We will expand the construction section to explicitly state the polynomial approximation (including degree and fixed-point precision) used for the logistic function and the division operation. We will also add a dedicated error-bound analysis together with results from long-sequence experiments (up to several hundred matches) demonstrating that rating drift remains negligible under the chosen parameters. revision: yes
Referee: [Security analysis] The security analysis against a capable adversary requires an explicit threat model (semi-honest vs. malicious) and a concrete argument that rating values remain private under the chosen FHE scheme; the current description leaves the model and reduction unclear.

Authors: We will revise the security section to state the threat model explicitly (semi-honest adversary) and supply a concrete reduction to the semantic security of the underlying FHE scheme, showing that encrypted rating values remain indistinguishable from random values to the adversary. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper constructs H-Elo by applying standard FHE primitives to the conventional Elo rating update formula without any self-referential definitions, fitted parameters renamed as predictions, or load-bearing self-citations. Security claims rest on established FHE properties and the protocol is benchmarked against independent plaintext implementations. No steps reduce by construction to the paper's own inputs or prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard properties of fully homomorphic encryption allowing computation on ciphertexts and on the security definition against a capable adversary; no free parameters or invented entities are introduced in the abstract.

axioms (1)

standard math Fully homomorphic encryption supports arbitrary computations on encrypted data while preserving semantic security
Core property invoked for performing rating updates without decryption.

pith-pipeline@v0.9.0 · 5480 in / 1142 out tokens · 28976 ms · 2026-05-14T22:37:56.771100+00:00 · methodology

discussion (0)

Reference graph

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