Case Study 2: Privacy-Preserving Prediction Markets Using Secure Computation

Overview

Privacy is one of the most persistent barriers to prediction market adoption. Corporate employees fear that their trades will be visible to managers. Political forecasters worry about social consequences of expressing unpopular beliefs. Financial traders guard their positions as proprietary information. This case study examines the state of the art in privacy-preserving prediction markets, focusing on three cryptographic approaches — zero-knowledge proofs, secure multi-party computation, and homomorphic encryption — and evaluating their practical feasibility as of 2025.

We draw on academic research from Kosba et al. (2016), Galal and Youssef (2018), and the practical implementations attempted by platforms including Gnosis, Aztec Protocol, and research prototypes from ETH Zurich and MIT.

Background

Why Privacy Matters for Prediction Markets

The demand for privacy in prediction markets is not hypothetical. Documented cases illustrate the problem:

1. Corporate markets. Google's internal prediction markets (Chapter 40, Case Study 1) found that some employees avoided trading on their own projects because they feared being identified as "the person who knew the project was failing." This self-censorship directly reduces the market's information aggregation quality.

2. Political markets. During the 2020 and 2024 US elections, anecdotal evidence suggested that some Polymarket traders avoided large positions on politically sensitive outcomes because blockchain analytics firms could link their trading addresses to their real identities.

3. Intelligence markets. The IARPA-funded geopolitical forecasting tournaments deliberately used anonymized identifiers to protect participants. If forecaster identities were public, intelligence analysts might face professional consequences for forecasts that diverged from their agency's official assessment.

4. Financial markets. Institutional traders on platforms like Kalshi guard their positions carefully. A hedge fund's prediction market positions could reveal its broader investment thesis, giving competitors an informational advantage.

The Privacy-Accuracy Tension

Privacy and accuracy are in tension because prediction markets derive their value from transparency: public prices aggregate information. The challenge is to achieve a middle ground — protecting individual trading data while still producing accurate aggregate prices. The cryptographic literature calls this "computation on private data."

Three Cryptographic Approaches

Zero-knowledge proofs (ZKPs) allow a prover to demonstrate that a statement is true (e.g., "I have enough balance to make this trade") without revealing any additional information (e.g., the actual balance). ZKPs are used to validate trades without revealing positions.

Secure multi-party computation (MPC) allows multiple parties to jointly compute a function (e.g., the market-clearing price) over their private inputs (e.g., individual orders) without any party learning the others' inputs. MPC distributes trust among multiple servers.

Homomorphic encryption (HE) allows computation on encrypted data. A market operator can compute aggregate statistics (prices, volumes) on encrypted orders without ever decrypting individual orders. HE is conceptually elegant but computationally expensive.

Technical Analysis

Zero-Knowledge Proofs in Practice

Architecture. In a ZKP-based prediction market, each trade is accompanied by a zero-knowledge proof that:

1. The trader's balance is sufficient for the trade.
2. The trade parameters (direction, quantity) satisfy market rules.
3. The trader's cumulative position does not exceed position limits.

The proof is verified on-chain (or by a market operator) without revealing the trader's balance, position, or identity.

Implementation: Aztec Connect + Prediction Markets.

Aztec Protocol, a privacy layer for Ethereum, has been used in prototype prediction market implementations. The architecture works as follows:

• Traders hold "notes" (encrypted balance commitments) on the Aztec rollup.
• To trade, a trader generates a ZK-SNARK proving that their note contains sufficient funds.
• The trade is executed by the market maker smart contract, which sees only the proof and the trade direction/size — not the trader's identity or total position.
• New notes (updated balances) are created as encrypted outputs.

Performance metrics (2024 benchmarks):

Assessment. ZKPs are the most mature privacy technology for prediction markets. The main limitations are proof generation time (2–5 seconds is acceptable for prediction markets but not for high-frequency trading) and the "trusted setup" requirement for SNARKs (mitigated by transparent setups like PLONK or STARKs, at the cost of larger proofs).

Secure Multi-Party Computation

Architecture. In an MPC-based prediction market, trust is distributed among $n$ servers. Each trader secret-shares their orders among the servers. The servers jointly compute the market-clearing price without any single server learning any individual order.

Protocol design (simplified):

1. Order submission. Trader splits order $(direction, quantity, limit\_price)$ into $n$ shares using Shamir's $(k, n)$ secret sharing. Each server receives one share.
2. Price computation. Servers execute an MPC protocol to compute the aggregate demand and supply curves from the shared orders, finding the clearing price.
3. Settlement. Servers jointly compute each trader's updated balance and distribute the results (encrypted to each trader's key).

Implementation: ETH Zurich Prototype.

A research team at ETH Zurich implemented a prototype MPC-based prediction market using the SPDZ protocol with $n = 3$ servers and threshold $k = 2$:

• Latency. Order matching took approximately 500ms for 100 orders — significantly slower than a centralized market but acceptable for prediction markets that clear periodically (e.g., every hour).
• Communication overhead. Each round of the MPC protocol required approximately 1 KB of communication per order per server. For 1,000 orders across 3 servers, total communication was approximately 3 MB.
• Security model. The SPDZ protocol provides security against a dishonest majority (up to $n - 1$ corrupted servers), which is the strongest guarantee available for MPC.

Practical limitations:

1. Server coordination. The servers must be online and responsive simultaneously. Network latency between geographically distributed servers adds to computation time.
2. Scalability. MPC complexity grows with the number of participants and the complexity of the computation. For simple binary markets with LMSR pricing, this is manageable. For combinatorial markets, it may be prohibitive.
3. Trust assumption. Traders must trust that at least $k$ of the $n$ servers are honest. This is a weaker assumption than trusting a single centralized operator, but it is not trustless.

Homomorphic Encryption

Architecture. A fully homomorphic encryption (FHE) scheme allows the market operator to compute on encrypted orders:

1. Traders encrypt their orders under a public key.
2. The operator computes the LMSR price update on the encrypted orders.
3. The operator publishes the encrypted result, which traders can decrypt.

Current state (2025): FHE has improved dramatically but remains 10,000–100,000x slower than plaintext computation for complex operations. For a simple LMSR price update (which involves exponentials and division), the computation on encrypted data takes approximately 10–30 seconds on specialized hardware.

Assessment. FHE is not yet practical for real-time prediction markets but may become viable for periodic market clearing (e.g., daily auctions). The TFHE and OpenFHE libraries have made significant progress, and hardware acceleration (FHE-specific chips) is under development by several startups.

Comparative Analysis

Real-World Deployment Challenges

User Experience

The most significant barrier to adoption is not the cryptography itself but the user experience it requires:

• Key management. Privacy-preserving systems require traders to manage cryptographic keys. Key loss means permanent loss of funds. Key compromise means loss of privacy.
• Proof generation. Generating ZK proofs on a mobile device is slow (10–30 seconds as of 2025). Users accustomed to instant trade execution may find this unacceptable.
• Debugging. When a trade fails, diagnosing the cause is difficult because the operator cannot see the inputs. Error messages must be informative without leaking private data.

Regulatory Compatibility

Privacy-preserving prediction markets face a fundamental tension with regulations:

• KYC/AML. Regulators require platforms to know their customers' identities. A fully private market that prevents the operator from identifying traders may violate anti-money-laundering laws.
• Tax reporting. Traders must report gains and losses. If the platform cannot see individual positions, it cannot issue tax documents.
• Market surveillance. Regulators require platforms to monitor for manipulation. If individual trades are encrypted, surveillance becomes infeasible.

Potential resolution: A layered privacy model where: - The platform knows each trader's identity (KYC) but not their specific positions. - A regulatory authority can, with a court order, decrypt specific trading records using a threshold decryption scheme. - Other traders cannot see each other's positions or identities.

This "selective disclosure" model preserves most privacy benefits while maintaining regulatory compatibility.

Performance at Scale

The question of whether privacy-preserving techniques can scale to thousands of concurrent traders and millions of daily trades remains open. Current benchmarks are based on prototypes handling tens to hundreds of traders. The path to production scale requires:

1. Hardware acceleration for ZK proof generation (already underway with projects like RISC Zero and Succinct).
2. Batching and amortization techniques for MPC.
3. Continued algorithmic improvements in FHE efficiency.

Lessons and Recommendations

Lesson 1: Start with ZKPs for Trade-Level Privacy

For platforms seeking to add privacy today, ZK proofs are the most practical choice. They can be retrofitted onto existing market architectures (both centralized and decentralized) with minimal changes to the core matching engine.

Lesson 2: Use MPC for Batch Auctions

For prediction markets that clear periodically (e.g., daily or weekly), MPC provides a natural architecture. Traders submit encrypted orders during a collection period, and the servers jointly compute the clearing price.

Lesson 3: Plan for FHE in the Medium Term

FHE is not ready for production prediction markets, but the rate of improvement suggests viability within 3–5 years. Platforms should design their data models with FHE compatibility in mind.

Lesson 4: Layered Privacy Is the Practical Path

Full anonymity is neither technically achievable nor legally permissible for regulated platforms. The practical goal is position privacy (others cannot see your trades) combined with identity compliance (the platform can verify you are authorized to trade).

Lesson 5: Privacy May Improve Accuracy

Counterintuitively, privacy can improve prediction market accuracy by encouraging participation from insiders who possess valuable information but would not trade if their positions were visible. The information gain from increased participation may more than offset any accuracy loss from reduced price transparency.

Computational Exercise

The chapter's code directory includes an implementation (code/case-study-code.py) that demonstrates the privacy-preserving techniques discussed in this case study:

1. A simplified Pedersen commitment scheme for trade hiding
2. Shamir secret sharing for distributed order matching
3. A performance benchmark comparing private and public LMSR price updates
4. Analysis of the privacy-accuracy tradeoff under differential privacy

Experiment with the implementations to determine: (a) the computational overhead of privacy at different security levels, (b) the minimum number of MPC servers needed for acceptable latency, and (c) the differential privacy parameter $\epsilon$ that preserves useful price signals.

Discussion Questions

1. If a privacy-preserving prediction market achieves the same accuracy as a transparent one, is there any remaining argument against privacy?

2. How should a platform handle a situation where regulatory decryption of a trader's records reveals market manipulation? What are the due process implications?

3. Could quantum computing render current privacy-preserving schemes obsolete? What is the timeline, and how should platforms prepare?

4. Is it ethical to design a prediction market that the operator itself cannot surveil? What happens when there is no human override?

5. The "right to be forgotten" under GDPR conflicts with the immutability of blockchain-based prediction markets. How should this tension be resolved?