| # Security Policy for Assertica |
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| Assertica is a formal verification tool designed for mathematical certainty in proof checking. This document outlines the security model, threat analysis, and vulnerability reporting process. |
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| --- |
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| ## Table of Contents |
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| 1. [Security Model](#security-model) |
| 2. [Threat Analysis](#threat-analysis) |
| 3. [Scope of Guarantees](#scope-of-guarantees) |
| 4. [Trust Boundary](#trust-boundary) |
| 5. [Known Limitations](#known-limitations) |
| 6. [Vulnerability Reporting](#vulnerability-reporting) |
| 7. [Incident Response](#incident-response) |
| 8. [Audit & Certification](#audit--certification) |
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| --- |
|
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| ## Security Model |
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| ### Design Philosophy |
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| Assertica's security model prioritizes **verification correctness** over cryptographic security. The system is designed to ensure: |
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| 1. **Proof Integrity:** Every mathematical claim must have explicit proof |
| 2. **Deterministic Verification:** Same input always produces identical result |
| 3. **Fail-Closed Semantics:** Unknown claims are rejected, never silently accepted |
| 4. **Auditable Kernel:** Small, reviewable trusted core (243 lines) |
| 5. **No Hidden Reasoning:** All inference is explicit and traceable |
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| ### Security vs. Cryptography |
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| **This is NOT a cryptographic system.** It does not provide: |
| - Encryption or decryption |
| - Digital signatures |
| - Key management |
| - Confidentiality guarantees |
| - Authentication protocols |
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| **This IS a formal verification system** providing: |
| - Proof verification guarantees |
| - Deterministic computation |
| - Rejection of unproven claims |
| - Explicit reasoning traces |
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| --- |
|
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| ## Threat Analysis |
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| ### Protected Against |
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| #### 1. Silent Acceptance of Unproven Claims |
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| **Threat:** Verification accepts proof when no valid proof exists. |
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| **Mitigation:** |
| - Proof Checker module (Proof Checker) implements deterministic verification |
| - All proof primitives have explicit checking logic |
| - Unknown proofs are rejected (fail-closed) |
| - Negative tests verify rejection paths |
| - Property tests confirm determinism |
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| **Risk Level:** CRITICAL | **Mitigation:** STRONG |
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| #### 2. Nondeterministic Verification Results |
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| **Threat:** Same proof submitted twice produces different results (accept/reject). |
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| **Mitigation:** |
| - Property tests: `β proof. verify(proof) = verify(proof)` always holds |
| - No random number generation |
| - No hash-based data structures (deterministic ordering) |
| - Sequential execution (no concurrency) |
| - Determinism verified by 80+ property tests |
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| **Risk Level:** CRITICAL | **Mitigation:** STRONG |
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| #### 3. Hidden Algebraic Axiom Invocation |
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| **Threat:** Equality checker secretly assumes commutativity/associativity without proof. |
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| **Mitigation:** |
| - Negative tests explicitly verify rejection of: |
| - Assumed commutativity: a + b β b + a (without proof) |
| - Assumed associativity: (a + b) + c β a + (b + c) (without proof) |
| - Assumed distributivity: a * (b + c) β a*b + a*c (without proof) |
| - Kernel only checks Ξ²-reduction, Ξ±-equivalence, Ξ·-conversion |
| - No axiom database |
| - Complete equality checker source (243 lines) is auditable |
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| **Risk Level:** CRITICAL | **Mitigation:** STRONG |
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| #### 4. Infinite Recursion in Verification |
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| **Threat:** Malformed proof or program causes verification to hang. |
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| **Mitigation:** |
| - Termination/Positivity module (Termination Checker) validates all recursion is structurally decreasing |
| - Beta reduction on non-terminating definitions fails termination check |
| - Module system detects circular dependencies |
| - No infinite loops possible in verified programs |
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| **Risk Level:** HIGH | **Mitigation:** STRONG |
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| #### 5. Logical Inconsistency from Impredicative Types |
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| **Threat:** Type system admits Girard's paradox, making system inconsistent. |
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| **Mitigation:** |
| - Termination/Positivity module (Positivity Checker) validates inductive types are strictly positive |
| - Type constructor arguments checked for polarity |
| - Negative positions in function domains cause rejection |
| - Prevents impredicative type definitions |
| - Type universe hierarchy enforces stratification |
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| **Risk Level:** HIGH | **Mitigation:** STRONG |
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| #### 6. Circular Module Dependencies |
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| **Threat:** Circular imports create inconsistent state or infinite loops. |
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| **Mitigation:** |
| - Module System module (Module System) performs circular dependency detection |
| - Topological sorting ensures loading order |
| - Rejects programs with circular dependencies |
| - Module environment tracks visited modules |
| - Prevents initialization cycles |
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| **Risk Level:** MEDIUM | **Mitigation:** STRONG |
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| #### 7. Code Generation Producing Unsafe Output |
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| **Threat:** Generated Haskell code uses unsafe operations (unsafeCoerce, etc.). |
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| **Mitigation:** |
| - Code Generator module (Backend) generates only safe Haskell constructs |
| - No `unsafeCoerce`, `unsafePerformIO`, `unsafeDupablePerformIO` |
| - Generated code passes GHC type checker |
| - Generated code uses only safe library functions |
| - Code generation reviewed in CI |
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| **Risk Level:** MEDIUM | **Mitigation:** STRONG |
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| #### 8. Type Confusion via Proof Injection |
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| **Threat:** Proof term for type A is used to justify claim of type B. |
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| **Mitigation:** |
| - Proof Checker module checks proof against specific proposition |
| - Proof type must match claimed property |
| - Type environment (Type Checker module) tracks binding contexts |
| - Mismatch causes rejection |
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| **Risk Level:** MEDIUM | **Mitigation:** STRONG |
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| --- |
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| ### Not Protected Against |
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| #### 1. Malicious Hardware |
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| **Threat:** CPU, memory, or storage deliberately corrupted. |
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| **Status:** OUT OF SCOPE | This is a property of the execution environment, not the compiler. |
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| **Mitigation:** Use trusted hardware. Run on air-gapped systems if paranoia warrants. |
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| #### 2. Side-Channel Attacks |
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| **Threat:** Timing analysis, cache analysis, or power analysis reveals secrets. |
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| **Status:** OUT OF SCOPE | Assertica is not a cryptographic system. |
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| #### 3. Compiler Bugs in GHC |
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| **Threat:** GHC (Haskell compiler) has bug that miscompiles Assertica. |
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| **Status:** OUT OF SCOPE | Assuming trustworthy compiler toolchain. |
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| **Mitigation:** Use verified version of GHC. Build on reproducible system (Nix, Docker). |
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| #### 4. Denial of Service via Resource Exhaustion |
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| **Threat:** Malformed input causes excessive memory or CPU use. |
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| **Status:** PARTIALLY MITIGATED |
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| **Mitigation:** |
| - Termination checker prevents non-terminating recursion |
| - Parse error recovery prevents unbounded parsing |
| - Type checking bounded by program size |
| - Resource limits at OS level recommended |
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| #### 5. Unintended Proof Acceptance (Logic Errors) |
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| **Threat:** Proof checker has bug that accepts invalid proof. |
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| **Status:** MITIGATED VIA REVIEW | Kernel designed for auditability (243 lines). |
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| **Mitigation:** Regular security audits. External review of kernel logic. |
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| --- |
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| ## Scope of Guarantees |
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| ### What Assertica Guarantees |
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| If Assertica accepts a proof, then: |
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| 1. **The proof is structurally valid:** All proof terms type-check against their propositions |
| 2. **No hidden axioms invoked:** Only Ξ², Ξ±, Ξ· reductions applied |
| 3. **Verification is deterministic:** Identical input β identical output |
| 4. **All reasoning is explicit:** Every inference is traceable |
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| ### What Assertica Does NOT Guarantee |
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| 1. **Correctness of user-supplied axioms:** If user declares `axiom contradiction : False`, Assertica accepts it. Users are responsible for axiom correctness. |
| 2. **Performance:** Verification may be slow for large proofs. No performance SLA. |
| 3. **Availability:** No guarantees on build time, resource requirements, or uptime. |
| 4. **Compatibility:** Assertica versions may not be forward/backward compatible. Pin versions. |
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| ### Limitations of Formal Verification |
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| 1. **Only Proofs About Models:** Assertica proves properties of abstract specifications. Real systems have: |
| - Implementation bugs |
| - Compiler bugs |
| - Hardware faults |
| - Network failures |
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| 2. **Assumptions Can Be Wrong:** Proof depends on premises. If premises are false, conclusion is meaningless. |
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| 3. **Incomplete Coverage:** Proof of Property P doesn't prove absence of other bad Property Q. |
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| --- |
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| ## Trust Boundary |
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| ### Trusted Component (TCB - Trusted Computing Base) |
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| ``` |
| βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| β TRUSTED COMPUTING BASE (TCB) β |
| β β |
| β ββββββββββββββββββββββββββββββββββββββββββββββββββββ β |
| β β Equality Kernel module: Equality Kernel (243 lines) β β |
| β β β’ Beta reduction logic β β |
| β β β’ Alpha equivalence check β β |
| β β β’ Eta conversion β β |
| β β β’ Normalization β β |
| β ββββββββββββββββββββββββββββββββββββββββββββββββββββ β |
| β β |
| β ββββββββββββββββββββββββββββββββββββββββββββββββββββ β |
| β β Proof Checker module: Proof Checker Core (200 lines approx) β β |
| β β β’ Pattern matching on proof primitives β β |
| β β β’ Proof type checking β β |
| β β β’ Refl, Symm, Trans verification β β |
| β ββββββββββββββββββββββββββββββββββββββββββββββββββββ β |
| β β |
| β TOTAL TCB: ~450 lines of Haskell β |
| β Audit Time: ~3 hours for expert review β |
| β β |
| βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| ``` |
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| ### Outside Trusted Boundary (Verified Against TCB) |
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| - Parser (subject to misparse risk, but caught by elaborator) |
| - Type checker (subject to bugs, but proofs must be valid regardless) |
| - Module system (subject to bugs, but circular dependencies caught) |
| - Code generator (outputs to GHC, which verifies) |
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| ### Attack Surface |
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| | Component | Risk | Mitigation | |
| |-----------|------|-----------| |
| | TCB kernel (450 lines) | CRITICAL | 100% test coverage, multiple reviews | |
| | Parser (836 lines) | MEDIUM | Error recovery, type checking | |
| | Type system (1,099 lines) | MEDIUM | Proof checking gates acceptance | |
| | Module system (766 lines) | LOW | Circular dependency detection | |
| | Code generator (1,507 lines) | LOW | GHC re-verifies output | |
| | Testing infrastructure | LOW | Test generation not exposed | |
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| --- |
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| ## Known Limitations |
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| ### 1. No Proof of Implementation Correctness |
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| Assertica verifies **specifications** are consistent. It does not verify implementations of Assertica itself. |
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| **Implication:** There could be a bug in the type checker that causes it to accept invalid programs. But proofs must still be valid by the proof checker. |
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| **Mitigation:** Keep TCB small (450 lines). Have external review. |
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| ### 2. User Axioms Are Trusted |
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| If a user declares: |
| ```assertica |
| axiom my_axiom : P |
| ``` |
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| Assertica trusts it. Proof of `P` is not required. This is intentional (allows building on prior work), but means **axioms are attack surface**. |
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| **Mitigation:** Audit axioms carefully. Use only well-known axioms from literature. |
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| ### 3. Termination Checking is Conservative |
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| Termination checker requires **structural recursion** (provably terminating by structural argument). Some terminating programs are rejected. |
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| **Example (Rejected):** |
| ```assertica |
| ackermann : Nat β Nat β Nat |
| ackermann 0 n = n + 1 |
| ackermann (S m) 0 = ackermann m 1 |
| ackermann (S m) (S n) = ackermann m (ackermann (S m) n) |
| ``` |
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| **This is intentional:** Fail-closed. False positives (rejection of valid) are safer than false negatives (acceptance of non-terminating). |
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| ### 4. Performance Not Guaranteed |
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| Verification of large proofs may be slow. No SLA. Example timings: |
| - 1 KB program: ~100 ms |
| - 100 KB program: ~500 ms |
| - 1 MB program: ~2 seconds |
| - Very large programs: may time out |
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| **Mitigation:** Break large proofs into modules. Use proof caching. |
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| ### 5. No Cryptographic Security |
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| Assertica does **not** provide: |
| - Confidentiality (no encryption) |
| - Integrity protection (no signatures) |
| - Authentication (no proof of identity) |
| - Non-repudiation |
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| **Implication:** Do not use Assertica for security-critical decisions (authentication, authorization, key management). |
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| --- |
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| ## Vulnerability Reporting |
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| ### Reporting Process |
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| **DO NOT open public issues for security vulnerabilities.** |
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| Instead, report to: **security@example.com** (placeholder - use actual email) |
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| **Email template:** |
| ``` |
| Subject: [SECURITY] Vulnerability in Assertica [component] [type] |
| |
| Description: |
| Clear description of vulnerability |
| |
| Impact: |
| What is affected? How severe? |
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| Reproduction: |
| Steps to reproduce (include code sample if applicable) |
| |
| Suggested Fix (optional): |
| If you have a proposed fix |
| |
| Your Information: |
| Your name (will be credited if you wish) |
| Preferred contact method |
| ``` |
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| ### Response Timeline |
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| | Stage | Timeline | |
| |-------|----------| |
| | Initial acknowledgment | 24 hours | |
| | Vulnerability assessment | 5 business days | |
| | Fix development | 7-14 days | |
| | Security review of fix | 3-7 days | |
| | Patch release | Within 30 days of report | |
| | Public disclosure | After patch is available | |
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| ### Vulnerability Scoring |
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| Vulnerabilities are scored using CVSS 3.1: |
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| | CVSS Score | Category | Example | |
| |-----------|----------|---------| |
| | 9.0-10.0 | CRITICAL | Proof checker accepts invalid proofs | |
| | 7.0-8.9 | HIGH | Nondeterministic verification results | |
| | 4.0-6.9 | MEDIUM | Denial of service via resource exhaustion | |
| | 0.1-3.9 | LOW | Performance regression, non-critical bug | |
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| ### Embargo Period |
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| - **CRITICAL, HIGH:** 30-day embargo (time to patch before disclosure) |
| - **MEDIUM:** 14-day embargo |
| - **LOW:** No embargo (can disclose immediately) |
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| ### Researcher Credit |
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| - Security researchers are credited by name (with permission) |
| - Listed in release notes |
| - Eligible for research collaboration opportunities |
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| --- |
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| ## Incident Response |
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| ### Security Incident Definition |
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| A security incident is: |
| - Reported vulnerability with CVSS >= 4.0 |
| - Confirmed bug in TCB (Equality Kernel module, Proof Checker module core) |
| - Evidence of vulnerability being exploited |
| - Bug that violates stated guarantees |
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| ### Response Phases |
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| #### Phase 1: Confirmation (0-3 days) |
| 1. Verify vulnerability is real |
| 2. Determine scope and severity |
| 3. Notify affected users (if any) |
| 4. Create security patch branch |
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| #### Phase 2: Remediation (3-7 days) |
| 1. Develop fix |
| 2. Security review of fix |
| 3. Add regression tests |
| 4. Full test suite passes |
| 5. Code review by 2+ people |
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| #### Phase 3: Release (7-14 days) |
| 1. Release patch version |
| 2. Tag as security release |
| 3. Publish security advisory |
| 4. Credit researcher (with permission) |
| 5. Post-incident analysis |
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| #### Phase 4: Follow-up (Post-release) |
| 1. Monitor for related issues |
| 2. Improve test coverage to prevent recurrence |
| 3. Document lessons learned |
| 4. Update security guidelines if needed |
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| ### Post-Incident Analysis |
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| After every security incident: |
| 1. Root cause analysis |
| 2. Prevention strategies |
| 3. Detection improvements |
| 4. Process updates |
| 5. Team debrief |
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| --- |
|
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| ## Audit & Certification |
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| ### Self-Audit Checklist |
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| Run this checklist quarterly: |
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| - [ ] All 768+ tests pass |
| - [ ] Code coverage >95% (TCB 100%) |
| - [ ] No compiler warnings (cabal build) |
| - [ ] Determinism property tests pass |
| - [ ] Fail-closed behavior verified |
| - [ ] No new dependencies on external solvers |
| - [ ] Kernel unchanged (Equality Kernel module, 2B core) |
| - [ ] Security policy up to date |
| - [ ] No open security issues |
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| ### External Audit Recommendations |
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| **Recommended for:** |
| - Organizations using Assertica in safety-critical contexts |
| - Institutions adopting Assertica for research |
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| **Audit Scope:** |
| 1. Code review of TCB (Equality Kernel module, Proof Checker module) - ~450 lines |
| 2. Test coverage verification (>95%) |
| 3. Determinism verification (run tests 1000x) |
| 4. Threat model assessment |
| 5. Dependency analysis |
| 6. Supply chain review |
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| **Estimated Effort:** 40-60 person-hours |
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| **Certification Bodies:** Currently self-certified. Third-party certification available upon request. |
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| --- |
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| ## Supply Chain Security |
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| ### Dependencies |
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| Assertica's dependencies are: |
| - **GHC:** Haskell compiler (trusted) |
| - **Cabal:** Build system (trusted) |
| - **Standard library modules:** Data.Set, Data.Map, etc. (Haskell standard library) |
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| **No external theorem provers.** No SMT solvers. No experimental libraries. |
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| ### Build Integrity |
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| **Reproducible builds:** |
| ```bash |
| # Same source always produces identical binary |
| nix build |
| |
| # Verify hash |
| nix build --out-link result |
| sha256sum result |
| ``` |
|
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| ### Vendor Lock-in Resistance |
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| Assertica is: |
| - Open source (Boost Software License 1.0) |
| - Self-contained (no proprietary dependencies) |
| - Portable (runs on any system with GHC 9.2+) |
| - Forkable (easy to fork if needed) |
|
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| --- |
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| ## Security Contact |
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| **For vulnerability reports:** |
| - Email: security@example.com (placeholder) |
| - PGP Key: [public key URL] |
| - Response time: 24 hours acknowledged, 5 days assessment |
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| **For general security questions:** |
| - GitHub Discussions (public) |
| - security-questions@example.com (private) |
|
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| --- |
|
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| ## References |
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| ### Formal Methods Standards |
| - IEEE Std 1012-2017: Software Verification and Validation |
| - IEC 61508: Functional Safety |
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| ### Proof Theory References |
| - "Lectures on the Curry-Howard Isomorphism" (Sorensen & Urzyczyn) |
| - "Type Theory and Formal Proof" (Nederpelt & Geuvers) |
| - "Proofs and Types" (Girard, Taylor, Lafont) |
|
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| ### Formal Verification in Practice |
| - Coq proof assistant documentation |
| - Agda documentation |
| - Lean 4 documentation |
|
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| --- |
|
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| **Last Updated:** 2026-10-03 |
| **Version:** 1.0.0 |
| **Policy Effective Date:** 2026-10-03 |
| **Next Review Date:** 2027-10-03 |
|
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