Overview

Documentation Index

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Use this file to discover all available pages before exploring further.

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Architecture

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How it works

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Encryption flow

1. Encode: Convert plaintext values to field elements in Fp
2. Add noise: Generate noise using PRF based on LPN
3. Build hypergraph: Create syndrome graph with random edges
4. Output ciphertext: Layers and edges representing encrypted value

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Homomorphic computation

// Encrypt values (client-side)
Cipher a = enc_value(pk, sk, 42);
Cipher b = enc_value(pk, sk, 17);

// Homomorphic operations (server-side)
Cipher sum  = ct_add(pk, a, b);  // 42 + 17 = 59
Cipher diff = ct_sub(pk, a, b);  // 42 - 17 = 25
Cipher prod = ct_mul(pk, a, b);  // 42 * 17 = 714

// Decrypt results (client-side)
uint64_t result = dec_value(pk, sk, sum);

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Key structures

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Ciphertext

• Layers (L): Computational graph nodes, either BASE or PROD (multiplication)
• Edges (E): Hypergraph edges with weights and syndrome vectors
• Constant term (c0): Plaintext additive constant
• Slots: Number of packed values (for batching)

struct Cipher {
    std::vector<Layer> L;     // Computational layers
    std::vector<Edge> E;      // Hypergraph edges
    std::vector<Fp> c0;       // Constant term
    size_t slots = 1;         // Number of slots
};

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Public key

• Parameters (prm): Security and performance parameters
• Hypergraph matrix (H): Dense random binary matrix
• Generator powers (powg_B): Precomputed powers g^0, g^1, …, g^(B-1)
• Primitives: Root of unity (ω_B) for multiplicative group

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Secret key

• PRF key (prf_k): 256-bit key for pseudorandom functions
• LPN secret (lpn_s_bits): Binary vector for LPN instance

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Performance characteristics

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Design philosophy

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Why hypergraphs?

• Threshold behavior of random hypergraphs
• Fractional colorability results from Moscow Institute of Physics and Technology (MIPT)
• LPN hardness for security guarantees

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Trade-offs

• Fast scalar operations (2.9-14.3× faster multiplication vs RLWE schemes)
• Small fresh ciphertexts (6-85× smaller than BFV/BGV/CKKS)
• No NTT-friendly prime requirements (works with arbitrary uint64)
• Exact arithmetic (no approximation errors)

• Ciphertext growth with depth (exponential in this PoC)
• Slower key generation (22× vs BFV)
• No native SIMD (requires parallelization)
• Less studied security assumption (LPN vs RLWE)

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Next steps