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Private Set Intersection (PSI) & Vector OLE Studio
Model privacy-preserving dataset joins. Simulate classical Diffie-Hellman ECDH-PSI, OT-based PaXoS, and modern sub-second VOLE-PSI (Vector Oblivious Linear Evaluation) with zero leakage of non-intersecting records.
Zero-Knowledge PSI
Sub-Second Scaling
VOLE / PaXoS
Underlying cryptographic intersection technique
Volume of records evaluated across parties
Network bandwidth and latency between participants
Verification rigor against actively tampering adversaries
🔒 Blinded Set Intersection & Oblivious Key Exchange Pipeline
VOLE-PSI: Sub-Second 1M Record ProcessingExecution Time
0.38 s
End-to-end intersection computation
Network Data Transferred
14.2 MB
Sub-linear VOLE compression
Evaluation Throughput
2.63 M items/s
Hardware AES-NI accelerated
Information Leakage
0.00%
Zero disclosure of non-matching items
🔬 Mathematical Protocol Mechanics & PaXoS Encoding Analysis
Calculating VOLE correlations and PaXoS hash parameters...
⚠️ 5 Fatal Traps in Private Set Intersection Deployments
1. Using Plain Salted Hashes (The "Fast Hash" Anti-Pattern):
Comparing SHA-256(item + salt) is NOT Private Set Intersection. For low-entropy data (phone numbers, social security numbers, emails, passwords), an attacker precomputes rainbow tables or exhausts the entire search space in seconds. True PSI relies on two-party blinding where neither party can independently compute hashes.
2. Set Size Leakage Exploitation:
Standard PSI protocols reveal the exact size of both sets (|X| and |Y|). If an adversary tracks an individual user whose set size changes dynamically (e.g. contact list adding 1 person), the adversary can correlate network metadata. Production deployments pad sets to fixed bucket thresholds (e.g. powers of two).
3. Cuckoo Hashing Stash Failures in PaXoS:
In OT-based PSI, items are mapped into Cuckoo tables. If the hash load factor is tuned too aggressively, a Cuckoo stash cycle failure can occur, dropping legitimate intersection items. A robust stash or fallback 3-way Cuckoo hash with epsilon slack is mandatory.
4. Malicious Input Substitution without Zero-Knowledge Proofs:
In semi-honest ECDH-PSI, a malicious party can submit fake values $H(x)$ that correlate with target guesses. In security-sensitive enterprise deployments, malicious-secure protocols (like KOS15 or VOLE-PSI with dual checks) must be selected.
5. Omitting Random Oracle Domain Separation:
When hashing raw string data to elliptic curve points (Hash-to-Curve), reusing the same domain separation tag (DST) as other signature schemes creates cross-protocol signature forgery vulnerabilities. Always use an RFC 9380 compliant DST (e.g.
PSI-RISTRETTO255-SHA512-RO-V01).
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