Metrics

Performance measurement and ciphertext analysis utilities

Overview

The metrics utilities provide functions for measuring ciphertext characteristics, validating homomorphic operations, and collecting performance data. These functions are primarily used for debugging, optimization, and analysis of PVAC-HFHE operations.

Functions

dump_metrics

Writes ciphertext metrics to a CSV file for analysis and debugging.

void dump_metrics(
    const PubKey & pk,
    const char * tag,
    const Cipher & C,
    const Fp & val
)

pk · const PubKey & · required

The public key used for density calculations

tag · const char * · required

String identifier for this metric entry (e.g., “after_mul”, “before_recrypt”)

C · const Cipher & · required

The ciphertext to measure

val · const Fp & · required

The actual plaintext value (for verification purposes)

Behavior

• Creates or appends to pvac_metrics.csv in the current directory
• CSV columns: tag, edges, layers, sigma_density, value_lo, value_hi
• Thread-safe with static initialization
• Silently fails if file cannot be opened

Example output

tag,edges,layers,sigma_density,value_lo,value_hi
after_mul,2400,3,0.485231,42,0
before_recrypt,4800,5,0.512847,100,0
after_recrypt,1200,3,0.478934,100,0

This function is intended for development and debugging. Remove calls to dump_metrics in production code to avoid file I/O overhead.

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sigma_density

Calculates the density of noise in a ciphertext by measuring the proportion of set bits in the sigma vectors.

double sigma_density(const PubKey& pk, const Cipher& C)

pk · const PubKey & · required

The public key (used to access prm.m_bits)

C · const Cipher & · required

The ciphertext to analyze

return · double

The density value between 0.0 and 1.0, representing the fraction of set bits across all edge sigma vectors. Returns 0.0 if the ciphertext has no edges.

Calculation

For a ciphertext with edges E₁, E₂, …, Eₙ:

density = (∑ popcount(Eᵢ.s)) / (n × m_bits)

where popcount(Eᵢ.s) is the number of set bits in the sigma bitvector of edge i.

Usage

Density monitoring is critical for determining when to trigger recryption:

Cipher result = mul(pk, evk, A, B);
double d = sigma_density(pk, result);

if (d > 0.52) {
    result = recrypt(pk, evk, result);
}

Density values approaching 0.5 indicate high noise levels. The PVAC-HFHE scheme typically triggers recryption when density exceeds 0.48-0.52.

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sigma_shannon

Computes the Shannon entropy of byte values in the ciphertext’s sigma vectors to assess randomness quality.

double sigma_shannon(const Cipher& C)

C · const Cipher & · required

The ciphertext to analyze

return · double

Shannon entropy in bits (0.0 to 8.0). Higher values indicate better randomness. Returns 0.0 for empty ciphertexts.

Calculation

For byte frequency distribution p₁, p₂, …, p₂₅₆:

H = -∑ pᵢ × log₂(pᵢ)

• Maximum entropy: 8.0 bits (perfectly random)
• Low entropy: < 6.0 bits (may indicate weak randomness)

Use cases

• Validating noise generation quality
• Detecting potential side-channel vulnerabilities
• Analyzing ciphertext compressibility

This function examines the raw byte representation of sigma vectors, not the mathematical field elements. It’s primarily used for cryptographic analysis rather than operational decisions.

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agg_layer_gsum

Aggregates the weighted sum of edges in a specific layer, used for internal validation.

std::vector<Fp> agg_layer_gsum(
    const PubKey& pk,
    const Cipher& X,
    uint32_t lid
)

pk · const PubKey & · required

The public key containing generator powers (powg_B)

X · const Cipher & · required

The ciphertext to analyze

lid · uint32_t · required

The layer ID to aggregate

return · std::vector<Fp>

A vector of field elements (length X.slots) representing the aggregated values for each slot in the specified layer.

Algorithm

For each edge e in layer lid:

s[j] = ∑ sgn(e.ch) × e.w[j] × g^(e.idx)

where sgn(e.ch) is +1 for positive edges, -1 for negative edges.

This function is primarily used internally by check_mul_gsum_all for validation. It’s not typically needed in application code.

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check_mul_gsum_all

Verifies the correctness of a homomorphic multiplication by checking all layer products.

bool check_mul_gsum_all(
    const PubKey & pk,
    const Cipher & A,
    const Cipher & B,
    const Cipher & C
)

pk · const PubKey & · required

The public key used for computation

A · const Cipher & · required

First multiplicand ciphertext

B · const Cipher & · required

Second multiplicand ciphertext

C · const Cipher & · required

Product ciphertext (should equal A × B)

return · bool

true if the multiplication is valid across all layer combinations, false if any discrepancy is detected.

Validation logic

For each pair of layers (la, lb) from A and B:

1. Compute the expected product layer index in C
2. Aggregate the layer sums using agg_layer_gsum
3. Verify that C[lc] = A[la] × B[lb] element-wise

Use cases

• Testing multiplication correctness during development
• Debugging homomorphic operation issues
• Validating parameter choices

This is a computationally expensive validation function. Use it only during testing, not in production code paths.

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Related functions

• sigma_density - Defined in ops/encrypt.hpp, also available here for convenience
• recrypt - Uses density metrics to determine when recryption is needed
• mul - Validated by check_mul_gsum_all

Source location

include/pvac/utils/metrics.hpp