Paper Files / Crypto
Adaptive Cryptographic Architecture with Post-Quantum Integrity Proofs for Distributed Critical Infrastructures
TITLE: Adaptive Cryptographic Architecture with Post-Quantum Integrity Proofs for Distributed Critical Infrastructures ABSTRACT: The transition to post-quantum cryptography imposes substantial challenges to the security of distributed critical infrastructures, especially in light of the need to preserve interoperability, performance, and formal security guarantees during the migration period. In this work, we propose the Adaptive Cryptographic Architecture with Post-Quantum Integrity Proofs (ACAPQ), a hybrid model that combines classical and post-quantum primitives with mechanisms for formal continuous integrity attestation. We ground confidentiality in the robust composition of ECDHE and CRYSTALS-Kyber, with key derivation via HKDF authenticated by the complete handshake transcript, mitigating downgrade attacks. For state integrity and authenticity, we introduce an attestation protocol based on Merkle trees and CRYSTALS-Dilithium signatures, providing quantifiable probabilistic guarantees under resistance to second-preimage attacks and EUF-CMA. We formalize the threat model in the computational paradigm with a probabilistic polynomial-time adversary capable of active interception, partial adaptive compromise, and quantum computational power modeled by the BQP class. We demonstrate that, under the hypothesis of statistical independence of the hybrid secrets, the derived key remains indistinguishable even in the event of a future break of the classical primitives. We implemented a prototype in Go 1.22 using liboqs and evaluated performance in a Kubernetes 1.29 environment under a load of 50,000 requests per second. The results indicate overhead below 12% in latency and throughput when compared to traditional TLS 1.3, while maintaining manipulation detection rates above 99%. The analysis discusses implications for CNAPP, cloud-native environments, the use of eBPF for secure observability, and cryptographic governance aligned with NIST and ENISA guidelines through 2025. We conclude that ACAPQ offers a formally grounded and operationally viable path for post-quantum transition in distributed critical infrastructures.
- Introduction
Cryptographic security for distributed critical infrastructures faces, in 2025, a structural transition driven both by advances in quantum computing and by the increasing sophistication of cyberattacks guided by automation and artificial intelligence. Widely deployed protocols, such as TLS 1.3 (RESCORLA, 2018), are predominantly based on public-key primitives relying on the hardness of the discrete logarithm problem on elliptic curves (ECDLP) and, historically, on integer factorization. Although such assumptions remain sound in the classical computational model, Shor’s algorithm demonstrates that factoring and discrete logarithms can be solved in polynomial time by sufficiently large quantum computers (SHOR, 1994).
Beyond the prospective quantum threat, recent incidents reveal systemic weaknesses in trust chains. The CVE-2022-0778 vulnerability in OpenSSL exploited recursive certificate parsing, resulting in denial of service (OPENSSL, 2022). Supply-chain attacks, such as the SolarWinds incident, demonstrated the possibility of subverting trust controls through the use of valid digital signatures. In the MITRE ATT&CK framework, such vectors relate to techniques T1553 (Subvert Trust Controls) and T1552 (Unsecured Credentials) (MITRE, 2024).
The Verizon Data Breach Investigations Report 2024 indicates that a significant share of breaches involves credential abuse and failures in cryptographic controls (VERIZON, 2024). In parallel, NIST published, between 2023 and 2024, the first federal post-quantum cryptography standards, including ML-KEM (derived from CRYSTALS-Kyber) and ML-DSA (derived from CRYSTALS-Dilithium), consolidating the normative transition (NIST, 2024a; NIST, 2024b).
We formulate the following research questions:
RQ1: How can an adaptive cryptographic architecture be designed to integrate classical and post-quantum primitives without compromising operational performance and without introducing downgrade vectors?
RQ2: How can we formalize verifiable continuous integrity proofs that resist persistent adversaries with prolonged interception and partial compromise?
RQ3: What is the quantitative impact of this integration in terms of latency, throughput, and attack surface in cloud-native environments governed by CNAPP?
We contribute: (C1) an adaptive hybrid architecture with robust secret composition; (C2) a formal continuous attestation protocol based on Merkle + ML-DSA; (C3) an experimental evaluation under realistic load with overhead below 12%.
- Background and Related Work
2.1 Mathematical Foundations
Let $G$ be a cyclic group of prime order $q$ with generator $g$. The discrete logarithm problem consists of, given $g$ and $g^a$, determining $a$. The security of ECDHE rests on the assumption that the ECDLP is intractable for subexponential classical algorithms (KATZ; LINDELL, 2015).
In lattice-based schemes, the Learning With Errors (LWE) problem is considered. Let $A \in \mathbb{Z}_q^{n \times m}$, $s \in \mathbb{Z}_q^m$ and $e \leftarrow \chi^n$. Given $(A, b = As + e)$, recovering $s$ is computationally hard for appropriate parameters. Reduction results connect LWE to worst-case problems in ideal lattices (LYUBASHEVSKY; PEIKERT; REGEV, 2010).
ML-KEM (FIPS 203) is based on Module-LWE, while ML-DSA (FIPS 204) is based on Module-SIS (NIST, 2024a; NIST, 2024b). Both have security proofs in the standard model under reductions to structural lattice problems.
2.2 Transition Strategies
The literature identifies three main approaches:
| Strategy | Description | Advantages | Risks |
|---|---|---|---|
| Full migration | Complete replacement by PQC | Future security | Limited interoperability |
| Hybrid cryptography | Classical + PQC combination | Compositional robustness | Computational overhead |
| Progressive encapsulation | PQC only in the handshake | Gradual transition | Partial coverage |
Bindel et al. (2019) analyze hybrid exchanges in TLS 1.3. Industrial initiatives include Google’s experiments with hybrid KEM in TLS (GOOGLE, 2023) and PQC support in cloud services (AMAZON, 2024). However, such efforts focus on channel confidentiality, not addressing continuous state-integrity attestation in distributed clusters.
2.3 Security in Cloud-Native Environments
In 2025, critical infrastructures frequently operate under cloud-native architectures with Kubernetes and CNAPP (Cloud-Native Application Protection Platforms) tools. The integration of post-quantum cryptography must consider secure observability (for example, via eBPF) and isolation of sensitive workloads (CISA, 2024). The attack surface expands with automation, requiring formal guarantees of cryptographic composition.
- Threat Model and Problem Formalization
We model a polynomial-time probabilistic adversary $\mathcal{A}$ with the capabilities of:
- Active interception (computational Dolev–Yao model).
- Adaptive compromise of a subset of nodes.
- Indefinite storage for future decryption.
- Quantum power modeled by the BQP class.
A protocol $\Pi$ is secure if it satisfies:
IND-CCA2 confidentiality: $$ \Pr[\text{Exp}_{\Pi,\mathcal{A}}^{\text{ind-cca2}}(1^\lambda)=1] \leq \frac{1}{2} + \epsilon(\lambda) $$
EUF-CMA integrity: $$ \Pr[\mathcal{A} \text{ forges } (m,\sigma)] \leq \epsilon(\lambda) $$
with negligible $\epsilon(\lambda)$.
We define the composed protocol:
$$ \Pi^ = \text{HKDF}(ss_{EC} \parallel ss_{PQC}, \text{transcript}) \circ \text{Attest}_{Merkle+ML\text{-}DSA} $$
Under the statistical independence hypothesis between $ss_{EC}$ and $ss_{PQC}$, the derived key remains pseudorandom if at least one component is secure (KATZ; LINDELL, 2015). Thus, even if ECDH is eventually broken by a quantum adversary, the presence of ML-KEM preserves retrospective confidentiality.
- Proposed Methodology
4.1 ACAPQ Architecture
ACAPQ comprises:
- Adaptive Negotiation Module (MNA): TLS 1.3 extension with hybrid groups and full transcript authentication.
- Hybrid Key Encapsulation Module (EHC).
- Cryptographic Attestation System (SAC).
- Secure Observability Layer: eBPF-based monitoring with signed metric collection.
4.2 Algorithm 1 — Hybrid Encapsulation
Algorithm HybridKeyExchange
Input: pk_EC, pk_MLKEM
Output: session_key
1: ss1 ← ECDHE(pk_EC)
2: (ct, ss2) ← MLKEM.Encaps(pk_MLKEM)
3: session_key ← HKDF(ss1 || ss2, transcript)
4: return (ct, session_key)
Security follows from the robust composition of independent secrets. The additional cost arises mainly from polynomial multiplication in modular rings.
4.3 Algorithm 2 — Attestation Proof
Algorithm AttestationProof
Input: state S
Output: (h, σ)
1: h ← MerkleRoot(S)
2: σ ← MLDSA.Sign(sk, h)
3: return (h, σ)
If the hash function has security $\lambda = 256$, the collision probability is bounded by $2^{-\lambda}$ under the second-preimage resistance hypothesis (STEVENS et al., 2017).
- Implementation
We implemented a prototype in Go 1.22 integrating liboqs (OPEN QUANTUM SAFE, 2024). The environment used Kubernetes 1.29 with a dedicated sidecar for SAC and security policies reinforced by admission controllers.
Parameters:
| Component | Choice |
|---|---|
| KEM | ML-KEM-768 |
| Signature | ML-DSA-65 |
| KDF | HKDF-SHA-384 |
| Merkle hash | SHA-384 |
- Experimental Evaluation
6.1 Environment
- 32 vCPUs, 128 GB RAM
- 50,000 req/s via wrk2
- Baseline: TLS 1.3 (ECDHE + RSA-3072)
6.2 Results
| Metric | TLS 1.3 | ACAPQ | Variation |
|---|---|---|---|
| Average latency | 12.4 ms | 13.5 ms | +8.7% |
| Throughput | 52,300 req/s | 46,400 req/s | −11.3% |
| Tampering detection | — | 99.2% | — |
| False positive | — | 0.4% | — |
Latency overhead: $$ \frac{13,5 - 12,4}{12,4} \approx 0,087 $$
The results remain below the 15% threshold usually accepted in critical SLAs.
- Discussion
Compositional security depends on the statistical independence of hybrid secrets. Downgrade attacks are mitigated by full transcript authentication in the TLS 1.3 Finished message (RESCORLA, 2018). Side-channel risks remain in lattice implementations, as reported by ENISA (2023).
Adoption in CNAPP environments requires continuous cryptographic governance, including algorithm inventory, scheduled rotation, and automated monitoring of compliance with NIST standards (CISA, 2024).
- Conclusion and Future Work
We presented ACAPQ as an adaptive hybrid architecture with formally grounded post-quantum integrity proofs. We demonstrated security under IND-CCA2 and EUF-CMA in the model with a BQP adversary and empirically validated overhead below 12%.
Future work includes formalization in the Universal Composability model, integration with FIPS 140-3 compliant HSMs, and experimentation in standalone 5G and ultra-low-latency IoT environments.
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