Formal Proof Step Test Assertion Generator for Cryptographic Primitives

Role: Senior Formal Methods Verification Engineer specializing in Cryptographic Protocol Soundness.

Context

• Cryptographic primitive under test: {{cryptographic_primitive}}
• Formal proof framework and language: {{formal_proof_framework}}
• Core algebraic properties: {{algebraic_properties}}
• Security bound parameters: {{security_bound_parameters}}
• Threat model assumptions: {{threat_model_assumptions}}
• State transition rules: {{state_transition_rules}}

Task

Construct an executable formal verification test script that evaluates algebraic soundness, resistance to state violations, and boundary condition invariants for cryptographic primitives in computational research pipelines.

Method

1. Model the operational semantics of {{cryptographic_primitive}} according to {{state_transition_rules}}.
2. Translate {{algebraic_properties}} into executable verification lemmas and automated testing contracts in {{formal_proof_framework}}.
3. Define inductive step checks that validate soundness across all valid state transitions.
4. Encode adversarial input bounds derived from {{threat_model_assumptions}} to fuzz boundary pre-conditions.
5. Implement assertion monitors checking that {{security_bound_parameters}} are never violated during execution traces.
6. Construct automated counterexample generation routines to extract minimal witness traces upon contract breach.
7. Structure the entry-point verification script to return machine-readable exit codes and assertion logs.

Constraints

• The test script MUST be fully syntactically valid for {{formal_proof_framework}}.
• Lemma definitions MUST NOT use unchecked axiomatic assumptions to bypass proof steps.
• All invariant checks MUST explicitly handle edge states like identity elements, zero divisors, and modular wraparounds.
• Code must include zero placeholder logic or unhandled exception paths.

Output format

Deliver an executable test script structured as follows:

1. Domain Type Definitions & State Modeling
2. Invariant & Contract Assertion Definitions
3. Automated Proof Tactics / Executable Test Harness
4. Counterexample Extraction and Trace Logging Module

Self-review

• Verify that {{algebraic_properties}} are completely covered by executable assertions.
• Check that {{threat_model_assumptions}} are explicitly modeled as contract constraints.
• Confirm syntax compatibility with {{formal_proof_framework}}.