Private Information Retrieval (PIR) & Spiral Cryptography Studio
Simulate zero-knowledge database querying with modern cryptographic Private Information Retrieval. Compare Information-Theoretic (Chor-Goldreich) and Single-Server Lattice-Based (Ring-LWE / Spiral) schemes, trace homomorphic inner-product evaluations, and analyze bandwidth scaling versus naive downloads.
1. Database Topology & Cryptographic PIR Scheme
2. Cryptographic Execution & Server Blind Evaluation
3. PIR Scheme Asymptotic & Hardware Trade-off Matrix
| SCHEME | SERVERS | COMMUNICATION | SERVER COMPUTATION | TRUST MODEL |
|---|---|---|---|---|
| Spiral cPIR (2022) | 1 (Single) | O(log N) ~14 KB | O(N) Streaming Ring-LWE | Standard Ring-LWE Hardness |
| Chor-Goldreich (1995) | k ≥ 2 | O(N^(1/k)) | O(N) Bitwise XOR | Zero Collusion between Servers |
| Trivial Download | 1 (Single) | O(N · L) (Full DB) | O(1) Disk read | Information Theoretic |
| Plain SQL Query | 1 (Single) | O(L) Record size | O(1) B-Tree index | Zero Privacy (Server knows ID) |
⚠️ 5 Fatal Traps in Private Information Retrieval
1. The Multi-Server Collusion Catastrophe
Information-theoretic 2-server PIR splits the query into random bitmasks q1 and q2 = q1 ^ e_i. If Server A and Server B secretly share database logs or reside within the same cloud provider VPC, XORing their received queries instantly reveals the exact target index e_i, completely voiding privacy.
2. O(N) Server Memory-Bandwidth Exhaustion
In single-server PIR, the server MUST scan and multiply every single byte of the entire database to evaluate the query. If the database is 100 GB and 1,000 users issue queries per minute, the server requires 100 Terabytes/minute of memory bus throughput. Without high-speed AVX-512 vectorization and optimized SIMD layout, CPU contention causes service denial.
3. Ring-LWE Noise Flooding & Decryption Failure
Lattice-based ciphertexts contain bounded Gaussian noise. Homomorphic multiplications across large hypercubes accumulate noise coefficients. If the polynomial ring modulus q and dimension d (e.g. d=2048, 4096) are under-dimensioned, the final aggregated ciphertext overflows into the plaintext space, producing garbled gibberish upon client decryption.
4. Side-Channel Timing Leaks in Non-Constant-Time SIMD Kernels
If server dot-product implementations skip null or sparse database records to save CPU cycles, the total execution time of the query leaks statistical information regarding the distribution of records accessed. All PIR server evaluation loops must run in strict constant time across every single record partition.
5. Database Modification State Desynchronization
PIR query vectors are tied to fixed index geometries. If an insert, delete, or compaction reorders database row IDs while a client generates or submits a query, the returned decrypted payload will map to an entirely different record, corrupting data integrity without triggering any cryptographic error.