Vector Forge

Uses mutation testing to systematically identify gaps in test vector coverage, then generates new test vectors that close those gaps. Measures effectiveness by comparing mutation kill rates before and after.

When to Use

• Generating test vectors for cryptographic algorithms or protocols
• Evaluating how well existing test vectors cover an implementation
• Finding implementation code paths that no test vector exercises
• Creating Wycheproof-style cross-implementation test vectors
• Measuring the concrete coverage value of a test vector suite

When NOT to Use

• No implementations exist yet (need code to mutate)
• Single trivial implementation with no edge cases
• Testing application logic rather than algorithm implementations
• The algorithm has no public test vectors to compare against

Prerequisites

• trailmark installed — if uv run trailmark fails, run:

  uv tool install trailmark
  

Python snippets: uv run --with trailmark python - (a tool env is not importable)

- At least one implementation of the target algorithm in a
language with mutation testing support
- A test harness that consumes test vectors and exercises
the implementation
- A mutation testing framework for the target language

---

## Rationalizations to Reject

| Rationalization | Why It's Wrong | Required Action |
|-----------------|----------------|-----------------|
| "We have enough test vectors" | Mutation testing proves otherwise | Run the baseline first |
| "The implementation's own tests are sufficient" | Own tests often share blind spots with the impl | Cross-impl vectors catch different bugs |
| "FFI crates can be mutation tested at the binding layer" | Mutations to wrappers don't affect the underlying impl | Mutate the actual implementation language |
| "Timeouts mean the mutation was caught" | Timeouts are ambiguous — could be killed or alive | Resolve timeouts before drawing conclusions |
| "All mutants are equivalent" | Most aren't — verify by reading the mutation | Classify each escaped mutant individually |
| "Checking valid vectors is enough" | Permissive mutations survive without negative assertions | Assert rejection for every invalid vector |
| "Manual analysis is fine" | Manual analysis misses what tooling catches | Install and run the tools |

---

## Workflow Overview

Phase 1: Discovery → Find implementations to test ↓ Phase 2: Harness → Write/adapt test vector harness for each impl ↓ Phase 3: Baseline → Run mutation testing with existing vectors ↓ Phase 4: Escape Analysis → Classify escaped mutants by code path ↓ Phase 5: Vector Gen → Create test vectors targeting escapes ↓ Phase 6: Validation → Re-run mutation testing, compare before/after ↓ Output: Coverage Report + New Test Vectors

---

## Phase 1: Discovery

Find implementations of the target algorithm. Look for:

1. **Pure implementations** in high-level languages (Go, Rust, Python)
   — these are the best mutation testing targets
2. **FFI wrapper crates** — identify these early so you don't waste
   time mutating wrapper glue code
3. **Reference implementations** — useful for cross-verification but
   may not be the best mutation targets

For each implementation, note:
- Language and mutation testing framework
- Whether it's pure code or FFI wrappers
- Existing test suite size and coverage
- Which API surface the test vectors will exercise

### Implementation Type Classification

| Type | Mutation Value | Example |
|------|---------------|---------|
| Pure implementation | High | zkcrypto/bls12_381 (Rust), gnark-crypto (Go) |
| FFI bindings to C/asm | Low at binding layer | blst Rust crate |
| C/C++ implementation | High (use Mull) | blst C library |
| Generated code | Medium (mutations may be equivalent) | gnark-crypto generated field arithmetic |

**Key insight:** If an implementation delegates to another language
via FFI, you must mutate the *underlying* implementation, not the
bindings. For C/C++ underneath Rust/Go/Python, use Mull or similar.

---

## Phase 2: Harness

For each implementation, create a test harness that:

1. Reads test vectors from JSON files (Wycheproof format recommended)
2. Exercises the implementation's API for each vector
3. Asserts **both acceptance and rejection**:
   - Valid vectors: deserialization succeeds, output matches expected
   - Invalid vectors: deserialization fails or verification rejects
4. Adds **roundtrip assertions** for valid deserialization vectors:
   `serialize(deserialize(bytes)) == bytes`
5. Reports pass/fail per vector with test IDs

**Critical:** A harness that only checks valid vectors will miss all
permissive mutations (e.g., `&` → `|` in validation). See
[references/lessons-learned.md](references/lessons-learned.md) §7.

The harness must be runnable by the mutation testing framework.
For most frameworks this means:
- **Go:** A `_test.go` file in the same package as the implementation
- **Rust:** An integration test in `tests/` or inline `#[test]` functions
- **Python:** A pytest test file
- **C/C++:** A test binary linked against the implementation

### Harness Placement

The harness must live *inside the implementation's package* so the
mutation framework can see it. This usually means:

```bash
# Go: add test file to the package being mutated
cp wycheproof_test.go /path/to/impl/package/

# Rust: add integration test
cp wycheproof.rs /path/to/crate/tests/

# Python: add test to the test directory
cp test_wycheproof.py /path/to/package/tests/

Handling Existing Vectors

If the implementation already has test vectors:

1. Run mutation testing with ONLY the existing vectors (baseline)
2. Run mutation testing with ONLY your new vectors
3. Run mutation testing with BOTH combined
4. The delta between (1) and (3) shows the new vectors' value

---

Phase 3: Baseline

Run mutation testing with existing test vectors only.

Framework Selection

See references/mutation-frameworks.md for language-specific setup.

Language	Framework	Command
Go	gremlins	gremlins unleash ./path/to/package
Rust	cargo-mutants	cargo mutants -j N --timeout T
Python	mutmut	mutmut run --paths-to-mutate src/
C/C++	Mull	mull-runner -test-framework=GoogleTest binary

Parallelism

Always use parallel execution for large codebases:

• cargo mutants -j 8 (Rust, 8 parallel workers)
• gremlins unleash --timeout-coefficient 3 (Go, increase timeouts)
• mutmut run --runner "pytest -x -q" (Python, fail-fast)

Recording Baseline Results

Capture these metrics per implementation:

Metric	Description
Total mutants	Number of mutations generated
Killed	Mutants caught by tests
Survived/Lived	Mutants NOT caught (these are the targets)
Not covered	Code paths no test reaches at all
Timed out	Ambiguous — resolve before comparing
Efficacy %	Killed / (Killed + Survived)
Coverage %	(Total - Not covered) / Total

Save the full mutation log for Phase 4 analysis.

---

Phase 4: Escape Analysis (Graph-Informed Triage)

Classify each escaped (survived + not covered) mutant using the Trailmark call graph for reachability and blast radius analysis.

This phase MUST use the genotoxic skill's triage methodology. The call graph transforms mutation results from a flat list of survived mutants into an actionable, prioritized set of vector targets.

Step 1: Build the Call Graph

Build a Trailmark code graph for each implementation before triaging mutations:

# Go
uv run trailmark analyze --language go --summary {targetDir}

# Rust
uv run trailmark analyze --language rust --summary {targetDir}

The graph provides:

• Caller chains — trace from public API entry points to mutated functions to determine reachability
• Cyclomatic complexity — prioritize high-CC functions
• Blast radius — functions with many callers have wider impact if their mutations survive

Step 2: Filter to Relevant Code

Mutation frameworks test the entire package. Filter results to only the files/functions that test vectors should exercise:

# Go (gremlins)
grep -E "(LIVED|NOT COVERED)" baseline.log \
  | grep -E " at (relevant|files)" \
  | sort

# Rust (cargo-mutants)
cat mutants.out/missed.txt | grep "src/relevant"

Step 3: Graph-Informed Classification

For each escaped mutant, map it to its containing function in the call graph and apply the genotoxic triage criteria:

Graph Signal	Classification	Action
No callers in graph	False Positive	Dead code, skip
Only test callers	False Positive	Test infrastructure
Logging/display/formatting	False Positive	Cosmetic
Cross-package callers but NOT COVERED	Cross-Package Gap	See below
Reachable from public API, low CC	Missing Vector	Design targeted vector
Reachable from public API, high CC (>10)	Fuzzing Target	Both vector + fuzz harness
Validation/error-handling path	Negative Vector	Craft invalid input that triggers path
Optimization path (GLV, SIMD, batch)	Edge-Case Vector	Input that triggers optimization threshold
|→^ after left shift (e.g. (t<<1) | carry)	Equivalent Mutant	Skip — bit 0 always 0, OR=XOR
ct_eq &→| on Montgomery limbs	API-Unreachable	Needs library-internal tests, not vectors
Equivalent mutation (behavior unchanged)	False Positive	Skip

Step 4: Identify Cross-Package Test Gaps

Critical pitfall: Mutation frameworks often only run tests within the same package as the mutation. For Go (gremlins) and Rust (cargo-mutants), this means:

• A mutation in hash_to_curve/g2.go only runs tests in the hash_to_curve package, NOT tests in the parent bls12381 package that imports it
• Functions that are fully exercised by cross-package tests will appear as NOT COVERED — these are false positives
• To confirm: check if the mutated function is called from a test in a different package that wouldn't be run

To resolve cross-package gaps:

1. Add a thin test in the sub-package that calls through the same code path as the cross-package test
2. Or run gremlins with --test-pkg ./... (if supported)
3. Or document as a framework limitation in the report

Step 5: Prioritize by Security Impact

Using the call graph, rank surviving mutants by impact:

Priority	Criteria	Example
P0 — Critical	Mutant weakens validation/equality/authentication	ct_eq: & → | makes equality permissive
P1 — High	Mutant in deserialization flag parsing	from_compressed: & → | accepts invalid flags
P2 — Medium	Mutant in field arithmetic internals	Fp::square: | → ^ corrupts computation
P3 — Low	Mutant in optimization path	phi endomorphism: only affects performance path
Skip	Formatting, display, equivalent mutation	Debug::fmt return value replacement

Step 6: Group by Vector Strategy

Group escaped mutants by the code path they represent and the type of test vector needed:

Deserialization flag validation (P1):
  - g1.rs:339,363-365,384 — from_compressed_unchecked flags
  → Need: valid-point-wrong-flag vectors

Field arithmetic (P2):
  - fp.rs:371-376,406,635-643 — subtract_p, neg, square
  → Need: field arithmetic KATs with edge-case values

Optimization thresholds (P3):
  - g1.go:68, g2.go:75 — GLV vs windowed multiplication
  → Need: scalar multiplication with large scalars

Cross-package (framework limitation):
  - hash_to_curve/g2.go:242-278 — isogeny, sgn0
  → Document as false positive or add sub-package test

Each group becomes a target for new test vectors in Phase 5.

---

Phase 5: Vector Generation

For each escaped code path group, design test vectors that force execution through that path.

Vector Design Patterns

Code Path Type	Vector Strategy
Point deserialization	Malformed points: wrong length, invalid field elements, off-curve, wrong subgroup, identity point
Signature verification	Valid sig + all single-bit corruptions of sig, pk, msg
Hash-to-curve	Known answer tests (KATs) with edge-case inputs: empty, single byte, max length
Aggregate operations	1 signer, many signers, duplicate signers, mixed valid/invalid
Error handling	Every error path should have a vector that triggers it
Arithmetic edge cases	Zero, one, field modulus - 1, points at infinity
Serialization flags	Every valid flag combination + every invalid flag combination
Roundtrip integrity	For every valid deser vector, assert serialize(deserialize(b)) == b
Carry/reduction faults	Reimplement at reduced limb widths, inject faults, extract distinguishing inputs

Single-Fault Negative Vectors

Each negative vector should have exactly one defect with everything else valid — this isolates which validation check is being tested. See references/vector-patterns.md for per-flag construction examples.

Fault Simulation (Limb-Width Reimplementation)

When mutation testing only applies local operator swaps, deeper architectural bugs (carry propagation, reduction overflow) go untested. To close this gap, reimplement the target algorithm at reduced limb widths (8, 16, 25, 32 bits) and deliberately inject faults — then generate vectors that catch them.

See references/fault-simulation.md for the full methodology: limb-width selection, fault injection catalog, vector extraction, and validation workflow.

Cross-Implementation Verification

Every new test vector MUST be verified against at least two independent implementations before being added to the suite:

1. Generate the vector using implementation A
2. Verify with implementation B (different codebase, ideally different language)
3. If B disagrees, investigate — one implementation has a bug

Vector Format

Use Wycheproof JSON format (algorithm, testGroups[].tests[] with tcId, comment, result, flags). See references/vector-patterns.md for the full schema.

Wycheproof contributions: Use Wycheproof's vectorgen tool rather than formatting vector files directly. Supply the generated changes as an envelope. The vectorgen tool can add, update, or replace vectors while handling tcId assignment, test counts, canonical formatting, and schema validation. Go-based generators can avoid the vectorgen CLI tool and instead call the programmatic github.com/c2sp/wycheproof/vectorgen API.

See references/lessons-learned.md §14 and the upstream vectorgen guide for the current workflow and commands.

---

Phase 6: Validation

Re-run mutation testing with the new test vectors included.

Tip: Use per-file mutation testing for fast iteration during vector development (see references/lessons-learned.md §12). Only run full-crate tests for the final comparison.

Before/After Comparison

Metric	Baseline	With New Vectors	Delta
Killed	X	Y	Y - X
Survived	A	B	A - B (should decrease)
Not Covered	C	D	C - D (should decrease)
Efficacy %	E%	F%	F - E

Success Criteria

Vectors have both retroactive value (killing mutants in existing code) and proactive value (catching bugs in future implementations). Generate both kinds — boundary-condition vectors may not improve kill rates in mature libraries but will catch bugs in new implementations. See references/lessons-learned.md §13.

Retroactive (measurable): previously survived/uncovered mutants become killed, no regressions.

If kill rates don't change: the implementation's own tests likely already cover those paths. The vectors still add cross-implementation verification value. Document which case applies.

---

Output Format

Write VECTOR_FORGE_REPORT.md covering: target algorithm, implementations tested, baseline results, escape analysis, new vectors generated, after results, before/after delta, and conclusions. See references/report-template.md for the full template.

---

Quality Checklist

Before delivering:

• At least one pure implementation mutation-tested (not just FFI wrappers)
• Baseline run completed with existing vectors
• Trailmark call graph built for each implementation
• All escaped mutants triaged using graph-informed classification
• Cross-package false positives identified and documented
• Security-critical mutations (ct_eq, validation, auth) prioritized as P0/P1
• Fault simulation and mutation-derived vectors cross-verified against 2+ implementations
• After run completed with new vectors included
• Before/after delta computed and explained
• Report written to VECTOR_FORGE_REPORT.md
• New test vectors saved in standard format (Wycheproof JSON)

---

Integration

Skill	Relationship
genotoxic (required for Phase 4)	Provides graph-informed triage — call graph cuts actionable mutants by 30-50%
mutation-testing (mewt/muton)	Use for Solidity; Vector Forge is language-agnostic
property-based-testing	Better than hand-crafted vectors for bitwise mutations in field arithmetic
testing-handbook-skills (fuzzing)	Functions with CC > 10 and surviving mutants need both vectors and fuzz harnesses

---

Supporting Documentation

• references/mutation-frameworks.md - Language-specific mutation testing framework setup
• references/vector-patterns.md - Common test vector patterns for cryptographic primitives
• references/fault-simulation.md - Limb-width reimplementation for carry, reduction, and overflow faults
• references/report-template.md - Full markdown template for the Vector Forge report
• references/lessons-learned.md - BLS12-381 case study: FFI kill rates, timeout masking, cross-package false positives, bitwise mutation gaps, and security-critical priorities