SECA: Semantically Equivalent & Coherent Attacks

• SECA is a framework of adversarial strategies that preserve meaning and structure to trigger unintended system responses across various domains.
• It employs constraint-driven optimization and verification techniques to generate semantically equivalent yet coherent modifications for attacking systems.
• Applications span quantum cryptography, NLP, hardware verification, and information retrieval, enhancing robustness and exposing hidden vulnerabilities.

Semantically Equivalent and Coherent Attacks (SECA) refer to adversarial strategies, evaluation frameworks, and protection techniques in which modifications to a system's input or execution preserve the original meaning or intended functionality ("semantic equivalence") while ensuring linguistic, structural, or operational naturalness ("coherence"). Unlike classical adversarial attacks that introduce unrealistic artifacts or alter meaning significantly, SECA exploits permissible variations that elicit erroneous or undesired outputs without violating system constraints or expectations. This paradigm emerges in diverse fields, including quantum cryptography, natural language processing, hardware verification, attack tree modeling, and information retrieval.

1. Conceptual Foundations and Definitions

SECA centers on two interrelated properties:

• Semantic Equivalence: The adversarial input, instruction sequence, or query retains the essential informational or operational content of the original. For natural language, this equates to mutual entailment or paraphrase-level similarity; for code, functional preservation; for retrieval, the same informational intent.
• Coherence: Modifications or attacks must maintain well-formedness—syntactic fluency, protocol compliance, or process consistency. Coherence constraints may be enforced via perplexity thresholds for language, protocol monitors in hardware, or consistency of retrieved items for search queries.

The formalization of SECA is context-dependent. For LLMs, the adversarial prompt $x$ for a benign prompt $x_0$ must satisfy: $$\operatorname{SE}(x, x_0) = 1 \quad \land \quad \operatorname{SC}(x) \leq \gamma$$ where $\operatorname{SE}$ is semantic equivalence (as determined by mutual entailment or LLM-based verification) and $\operatorname{SC}$ is a measure of coherence (e.g., linguistic perplexity below threshold $\gamma$) (Liang et al., 5 Oct 2025).

In hardware and verification, semantically equivalent program execution denotes functionally identical but structurally diverse sequences, used to expose bugs or vulnerabilities that uniform duplication may miss (Li et al., 4 Apr 2024). In document retrieval, coherence is induced by penalizing variations in top-ranked document sets for semantically similar queries (Campese et al., 11 Aug 2025).

2. Methodologies and Operationalization

SECA is deployed using constraint-driven or equivalence-aware optimization techniques that search for adversarial, robust, or minimally distinguishable variations within permissible operational boundaries.

2.1 Zeroth-Order Constraint-Preserving Optimization for LLMs

SECA attacks on LLMs are formulated as a constrained search over discrete prompt space. The process leverages auxiliary LLMs for:

• Semantic Proposal: Given prompt $x$, generate $M$ candidate rephrasings.
• Feasibility Check: Verify semantic equivalence and coherence (e.g., using entailment checks and perplexity thresholds).
• Adversarial Selection: Maximize objective (e.g., log-likelihood of hallucinated output) within constraint-satisfying candidates.

This iterative procedure guarantees that all generated adversarial prompts remain meaning-preserving and linguistically plausible, yielding higher attack success rates without semantic or coherence violations (Liang et al., 5 Oct 2025).

2.2 Program Synthesis and Symbolic Quick Error Detection

SEPE-SQED uses program synthesis to construct semantically equivalent instruction sequences for hardware verification:

• Semantic Modeling: Encodes instruction semantics as bit-vector formulas.
• Component Libraries: Uses native, derived, and composite instruction classes to generate alternatives.
• CEGIS with HPF: Employs Counterexample-Guided Inductive Synthesis with Highest Priority First scheduling to efficiently explore the search space, prioritizing diversity and minimizing redundancy.

This enables detection of single-instruction bugs by comparing divergent traces emerging from semantically equivalent but structurally distinct sequences (Li et al., 4 Apr 2024).

2.3 Coherence Losses in Dense Retrieval

Retrieval systems use loss functions explicitly designed to minimize sensitivity to semantic but lexical query variations: $$\mathcal{L}_{CR} = \lambda_1 \sum_{q_i \in \mathcal{C}} \|q - q_i\|_2^2 + \lambda_2 \sum_{q_i \in \mathcal{C}} \sum_{d \in \mathcal{D}^-} (m(q, d^+, d) - m(q_i, d^+, d))^2 + \operatorname{MNR}(q, d^+, \mathcal{D}^-)$$ Here, $q$ and $q_i$ are semantically equivalent queries, and $m(\cdot)$ denotes margin in similarity (Campese et al., 11 Aug 2025).

3. Applications and Domains

Quantum Cryptography: SECA encompasses coherent attacks—those that exploit the ability to apply joint, non-i.i.d. adversarial operations under semantic constraints (e.g., protocol invariance, statistical equivalence of outcomes). These attacks challenge the security of quantum key distribution protocols and require specialized min-entropy bounds and reduction techniques for robust analysis (Mertz et al., 2012, Fröhlich et al., 2017, Lu et al., 2020, Lupo et al., 2017, Sandfuchs et al., 2023).

LLMs and NLP: SECA is relevant for crafting adversarial examples that maintain semantic meaning and coherence. SSCAE, for instance, uses masked LLMs, semantic/syntactic scoring (via embeddings and GPT-2 probabilities), and adaptive search strategies to generate imperceptible, context-aware attacks (Asl et al., 18 Mar 2024). In LLM evaluation, SECA quantifies hallucination risks where meaning-preserving prompt variations can trigger unreliable outputs (Liang et al., 5 Oct 2025).

Hardware Verification: Semantically equivalent program execution in SEPE-SQED enhances bug coverage by decoupling error detection from uniformity and leveraging diverse code paths (Li et al., 4 Apr 2024).

Information Retrieval and Search: Retrieval systems optimized for query coherence exhibit improved stability and robustness to SECA, producing consistent outputs for lexically diverse but semantically equivalent queries (Campese et al., 11 Aug 2025).

Security Analysis and Attack Trees: SAND attack trees introduce sequential conjunction to structurally model coherent and ordered multi-step attacks, formalizing semantic equivalence as canonical forms for risk and cost assessments (Jhawar et al., 2015).

4. Theoretical Insights and Comparative Analyses

The distinguishing feature of SECA is its capacity to expose vulnerabilities, inconsistencies, or security gaps that would remain undetected under traditional adversarial or mutation testing frameworks:

• LLM Sensitivity: Empirical evidence indicates that LLMs are highly sensitive to realistic prompt variations. SECA-based attacks can dramatically increase hallucination rates while preserving semantic and linguistic integrity of prompts (Liang et al., 5 Oct 2025).
• Quantum Protocol Robustness: Methods that reduce coherent-attack analysis to collective attacks via min-entropy bounds and post-selection corrections yield tighter secret key rates and more precise security guarantees for finite-resource scenarios (Mertz et al., 2012, Fröhlich et al., 2017, Lu et al., 2020, Lupo et al., 2017, Sandfuchs et al., 2023).
• Bug Detection Coverage: SEPE-SQED achieves broader error detection by exploiting functional diversity in instruction sequences, outperforming standard SQED, especially for single instruction bugs (Li et al., 4 Apr 2024).
• Retrieval Consistency: CR loss functions reliably produce coherent document lists for semantically equivalent queries, reducing susceptibility to adversarial information manipulation (Campese et al., 11 Aug 2025).

5. Implications for System Design and Security

SECA has direct implications for the development, deployment, and evaluation of high-risk and mission-critical systems:

• Robustness Demands: SECA highlights the need for robust evaluation metrics, constraint-aware adversarial training regimes, and resilience against meaning-preserving input variations.
• Security Proof Reconsiderations: Protocol designers in quantum cryptography, hardware, and software must ensure that reduction techniques account for coordinated operation patterns and classical leakage (e.g., public announcements in DIQKD) (Sandfuchs et al., 2023).
• Monitoring and Enforcement: Game-theoretic enforcement of protocols (e.g., automata monitors or language filters) is essential for mitigating attacks that exploit low-level or surface-form semantic equivalence (Ghica et al., 2012).
• System Reliability: Consistent retrieval and coherent output generation mitigate adversarial exploitation and ensure dependable downstream processing in large-scale IR and QA systems (Campese et al., 11 Aug 2025).

6. Future Directions

Research continues to advance SECA methodologies and their cross-domain interfaces:

• End-to-End Coherence Optimization: Integrating coherence objectives into multiphase pipelines, including dense retrieval, re-ranking, and generative modeling (Campese et al., 11 Aug 2025).
• Automated Synthesis and Verification: Expanded libraries of semantically equivalent program fragments and improved synthesis algorithms for diverse hardware platforms (Li et al., 4 Apr 2024).
• Constraint-Enforced Adversarial Generation: Broader adoption of constraint-preserving, zeroth-order optimizations for both text and code inputs (Liang et al., 5 Oct 2025, Asl et al., 18 Mar 2024).
• Security Proofs for Inter-Round Correlations: Development of analytical techniques to handle classical and quantum correlation structures beyond i.i.d. assumptions in cryptographic protocols (Sandfuchs et al., 2023).

7. Summary Table: SECA Instantiations Across Domains

Domain	SECA Implementation	Main Constraints
Quantum Cryptography	Min-entropy bounds, protocol invariance	Statistical equivalence, protocol coherence
NLP/LLMs	Constraint-driven prompt modification	Semantic equivalence, linguistic coherence
Hardware Verification	Program synthesis (SEPE-SQED)	Functional equivalence, execution trace coherence
Information Retrieval	Coherence-inducing loss functions	Query equivalence, ranked list stability
Attack Tree Modeling	SAND sequential conjunction, term rewriting	Ordered event equivalence

SECA represents a cross-domain principle where attacks, verification strategies, and optimization techniques target operational pathways that are meaning-preserving and structurally consistent. This focus allows for rigorous security assessments and the design of robust systems that can withstand realistic adversarial or perturbative inputs.