Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Access

Quantum-Assisted Seed Recovery Under Probabilistic Leakage in Post-Quantum Cryptography

Valérie Gauthier–Umaña, Juan D. Sanchez, Ricardo Villanueva-Polanco

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Seed-based key generation is widely used in post-quantum cryptography because it provides compact secret-key representations and deterministic regeneration of cryptographic material. The same design, however, concentrates security on a short secret state: partial or noisy leakage about the seed may sharply reduce the space of plausible secrets. Existing posterior-guided recovery methods exploit such leakage by ranking candidate seeds according to posterior scores and then validating them against the target public key. This work studies how posterior-guided seed recovery changes in the presence of a quantum adversary. Building on the recently introduced Bitwise Bayesian Leakage Model (BBLM) and Seed Recovery Framework (SRF), we keep the leakage-processing stages classical, including posterior inference, candidate generation, ranking, score-band construction, and success-probability estimation. The quantum component is introduced only at the validation stage, where sequential public-key checks over an SRF-selected candidate set are replaced by Grover-assisted search. Instead of applying Grover search to the full seed space $\{0,1\}^{\lambda }$ , we apply it to the index set of the candidate band selected by SRF. For each index $\iota $ , the oracle coherently reconstructs the associated seed candidate $\textsf {seed}_{\iota } $ from the SRF preprocessing structures and evaluates a reversible public-key validation predicate on $\textsf {seed}_{\iota } $ . This yields a band-index oracle whose cost accounts for reversible index-to-seed reconstruction, read-only coherent access to the SRF data structures, seed expansion, scheme-specific public-key validation, comparison with the target public key, conditional phase marking, and uncomputation of all auxiliary workspace. As a concrete case study, we instantiate the seed-level validation component for the RYDE post-quantum signature scheme and develop a logical-oracle-level cost model that separates generic band-index and Grover costs from RYDE-specific validation costs. The analysis includes an explicit access model for the SRF data structures, a full logical-oracle-level cost decomposition, and leakage-driven experiments reporting a representative selected score band, candidate-set size, empirical inclusion probability, oracle cost, Grover iterations, final-check cost, expected validation-stage cost, the corresponding full recovery-cost expression, and calibration trends across leakage parameters. We also compare classical SRF validation, restricted Grover-assisted SRF, and full-space Grover search. The results characterize how posterior-guided candidate restriction and Grover-assisted validation interact under probabilistic leakage at the logical-oracle level, rather than claiming a hardware-level attack estimate.

DOI
10.1109/access.2026.3722424

Related papers

Implementation of Grover’s Algorithm in a Cold-Boot Attack Scenario for RYDE

Juan D. Sanchez

Post-quantum digital signature schemes aim to remain secure against quantum adversaries, yet their practical security may be affected by physical attacks. This work studies the use of Grover’s algorithm in a Cold Boot Attack scenario against the RYDE post-quantum digital signature scheme. We construct a quantum oracle adapted to the RYDE key derivation process and analyze the corresponding Grover operator. Furthermore, we estimate the required quantum resources, including the number of quantum registers and quantum gates. This study provides insight on the feasibility of quantum-assisted attacks on seed-based post-quantum digital signature schemes.

•Jan 28, 2026•0 citations

Quantum-Aware Key Rank for Side-Channel Attacks evaluation

Yevgen Kotukh

Side-channel attacks on block ciphers rarely recover the key outright: they leave a residual key space ordered by subkey posteriors, and evaluation laboratories report the key rank of the true key against thresholds near 2^48 and 2^60. No evaluation framework models an adversary who collects traces classically and finishes the search on a quantum computer, although quantum search with advice provides exactly that. We give such an adversary a cost model and a metric. For a device whose key has rank r, any quantum algorithm with classical access to the posteriors needs Omega(sqrt(r)) cipher evaluations, and block search achieves O(sqrt(r)); the per-instance advantage is exactly quadratic, and the super-quadratic exponents reported for search with advice are averages over the prior that apply to no single device. Under the NIST MAXDEPTH budget D and a Grover iteration of g gates and depth d, the quadratic advantage holds only for ranks up to (4D/(pi d))^2 and collapses to a constant factor beyond; with the best published AES-128 oracle and D = 2^40 the window closes near rank 2^58.6. We define the quantum-aware key rank, the classical rank of equal cost, computable from the rank estimators laboratories already run, and derive the classical rank a device must retain to keep a given threshold against each depth budget. Block search and amplitude amplification from the product-form posterior state are within a factor of two to four of each other on Hamming-weight posteriors, so the cost of coherent indexing decides between them. Experiments on simulated leakage and a toy cipher confirm the predicted window: at SNR 0.125 a depth-limited quantum adversary is worth about 22 traces to a classical one, however large its gate budget.

quant-pharXiv:2610.20537•Oct 15, 2026•0 citations

Q-LEAK: Quantum-Based LEAKage Verification for Side-Channel Countermeasures

Walid El Maouaki, Alberto Marchisio, Muhammad Shafique

Formal verification of power side-channel leakage and its countermeasures in cryptographic algorithms is challenging, as SAT-based methods fail to scale on XOR-heavy, time-unrolled cryptographic circuits with realistic leakage models. We construct compact Conjunctive Normal Form (CNF) cases modeling one-bit leakage under two-trace conditions, linking key dependence and state evolution. Classical solvers quickly reach complexity limits, so we propose Q-LEAK, a quantum-based verification approach using Grover's algorithm, compiling each CNF into an oracle and applying amplitude amplification to search in O(sqrt(N)) oracle calls, with oracles that encode the two-trace leakage predicate and the CNF constraints. Benchmarking against classical SAT shows both potential gains and practical resource limits. In noiseless tests on 5-7 variable benchmarks, Q-LEAK consistently recovered a satisfying assignment within 1-4 tries, with marked bitstrings amplified clearly above the background distribution, exceeding 20 percent probability. The evaluation of Q-LEAK on real quantum hardware revealed at least one classically verified SAT assignment, despite the presence of noise. These results point to a potential path toward quantum-assisted verification of side-channel protections.

quant-pharXiv:2605.25728•May 26, 2026•0 citations

On Quantum Chosen-Ciphertext Attacks and Learning with Errors

Gorjan Alagic, Stacey Jeffery, Māris Ozols +1 more

Large-scale quantum computing poses a major threat to classical public-key cryptography. Recently, strong “quantum access” security models have shown that numerous symmetric-key cryptosystems are also vulnerable. In this paper, we consider classical encryption in a model that grants the adversary quantum oracle access to encryption and decryption, but where we restrict the latter to non-adaptive (i.e., pre-challenge) queries only. We formalize this model using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA 1 in analogy to the classical CCA 1 security model. We show that the standard pseudorandom function ( PRF )-based encryption schemes are QCCA 1 -secure when instantiated with quantum-secure primitives. Our security proofs use a strong bound on quantum random-access codes with shared randomness. Revisiting plain IND − CPA -secure Learning with Errors ( LWE ) encryption, we show that leaking only a single quantum decryption query (and no other leakage or queries of any kind) allows the adversary to recover the full secret key with constant success probability. Information-theoretically, full recovery of the key in the classical setting requires at least a linear number of decryption queries. Our results thus challenge the notion that LWE is unconditionally “just as secure” quantumly as it is classically. The algorithm at the core of our attack is a new variant of the well-known Bernstein–Vazirani algorithm. Finally, we emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.

arXiv:1808.09655•Cryptography•Mar 21, 2020•9 citations

AI-Guided Grover Search for Simulation-Based Evaluation of Post-Quantum Security in CKKS Homomorphic Encryption

Howaida Allam, Sonal Trivedi

The emergence of quantum computing poses fundamental challenges to the security assumptions underlying modern cryptographic systems, particularly Fully Homomorphic Encryption (FHE) schemes that enable computation on encrypted data. While Grover's algorithm provides a theoretical framework for quantum attacks on symmetric cryptographic primitives, its practical application to complex parameter spaces like those in CKKS FHE has remained limited.This paper presents a simulation-based, exploratory hybrid framework that combines deep neural networks with a simplified quantum search model to evaluate the post-quantum security of CKKS bootstrapping parameters under idealised conditions. The AI-enhanced system learns to identify potentially vulnerable parameter configurations through pattern recognition, then uses this knowledge to optimize the quantum oracle construction in a 4-qubit Grover's algorithm simulator. Experiments conducted on 5,000 synthetically generated parameter sets, with evaluation on 100 boundary-region configurations, demonstrate that this hybrid approach achieves a 73.4\% success rate in identifying insecure parameters under the experimental setup, representing a 30.6\% improvement over standard quantum search in the same simulated environment.Within the experimental model, this analysis indicates that under the experimental model, parameter sets nominally targeting 128-bit quantum security may exhibit effective security levels of only 86–101 bits when subjected to AI-guided search, suggesting that current FHE parameter margins warrant further investigation as quantum capabilities mature. The findings are simulation-based and should not be directly extrapolated to real-world deployments without further validation; however, they indicate that security margins may need to be increased by approximately 2.3 times to maintain true 128-bit quantum resistance against intelligent adversaries. These results have implications for post-quantum cryptographic standards and motivate further study at realistic qubit scales.

Journal of Smart Algorithms and Applications (JSAA)•Apr 24, 2026•1 citation

A Note on Quantum Security for Post-Quantum Cryptography.

Fang Song

Shor’s quantum factoring algorithm and a few other efficient quantum algorithms break many clas-sical crypto-systems. In response, people proposed post-quantum cryptography based on computational problems that are believed hard even for quantum computers. However, security of these schemes against quantum attacks is elusive. This is because existing security analysis (almost) only deals with classical attackers and arguing security in the presence of quantum adversaries is challenging due to unique quan-tum features such as no-cloning. This work proposes a general framework to study which classical security proofs can be restored in the quantum setting. Basically, we split a security proof into (a sequence of) classical security reductions, and investigate what security reductions are “quantum-friendly”. We characterize sufficient conditions such that a classical reduction can be “lifted ” to the quantum setting. We then apply our lifting theorems to post-quantum signature schemes. We are able to show that the classical generic construction of hash-tree based signatures from one-way functions and and a more efficient variant proposed in [BDH11] carry over to the quantum setting. Namely, assuming existence of (classical) one-way functions that are resistant to efficient quantum inversion algorithms, there exists a quantum-secure signature scheme. We note that the scheme in [BDH11] is a promising (post-quantum) candidate to be implemented in practice and our result further justifies it. Actually, to obtain these results, we formalize a simple criteria, which is motivated by many classical proofs in the literature and is straightforward to check. This makes our lifting theorem easier to apply, and it should be useful elsewhere to prove quantum security of proposed post-quantum cryptographic schemes. Finally we demonstrate the generality of our framework by showing that several existing works (Full-Domain hash in the quantum random-oracle model [Zha12b] and the simple hybrid arguments framework in [HSS11]) can be reformulated under our unified framework. 1

•Jan 1, 2014•0 citations
Seed-based key generation is widely used in post-quantum cryptography because it provides compact secret-key representations and deterministic regeneration of cryptographic material. The same design, however, concentrates security on a short secret state: partial or noisy leakage about the seed may sharply reduce the space of plausible secrets. Existing posterior-guided recovery methods exploit such leakage by ranking candidate seeds according to posterior scores and then validating them against the target public key. This work studies how posterior-guided seed recovery changes in the presence of a quantum adversary. Building on the recently introduced Bitwise Bayesian Leakage Model (BBLM) and Seed Recovery Framework (SRF), we keep the leakage-processing stages classical, including posterior inference, candidate generation, ranking, score-band construction, and success-probability estimation. The quantum component is introduced only at the validation stage, where sequential public-key checks over an SRF-selected candidate set are replaced by Grover-assisted search. Instead of applying Grover search to the full seed space {0,1}λ\{0,1\}^{\lambda }{0,1}λ , we apply it to the index set of the candidate band selected by SRF. For each index ι\iota ι , the oracle coherently reconstructs the associated seed candidate seedι\textsf {seed}_{\iota } seedι​ from the SRF preprocessing structures and evaluates a reversible public-key validation predicate on seedι\textsf {seed}_{\iota } seedι​ . This yields a band-index oracle whose cost accounts for reversible index-to-seed reconstruction, read-only coherent access to the SRF data structures, seed expansion, scheme-specific public-key validation, comparison with the target public key, conditional phase marking, and uncomputation of all auxiliary workspace. As a concrete case study, we instantiate the seed-level validation component for the RYDE post-quantum signature scheme and develop a logical-oracle-level cost model that separates generic band-index and Grover costs from RYDE-specific validation costs. The analysis includes an explicit access model for the SRF data structures, a full logical-oracle-level cost decomposition, and leakage-driven experiments reporting a representative selected score band, candidate-set size, empirical inclusion probability, oracle cost, Grover iterations, final-check cost, expected validation-stage cost, the corresponding full recovery-cost expression, and calibration trends across leakage parameters. We also compare classical SRF validation, restricted Grover-assisted SRF, and full-space Grover search. The results characterize how posterior-guided candidate restriction and Grover-assisted validation interact under probabilistic leakage at the logical-oracle level, rather than claiming a hardware-level attack estimate.
Post-quantum digital signature schemes aim to remain secure against quantum adversaries, yet their practical security may be affected by physical attacks. This work studies the use of Grover’s algorithm in a Cold Boot Attack scenario against the RYDE post-quantum digital signature scheme. We construct a quantum oracle adapted to the RYDE key derivation process and analyze the corresponding Grover operator. Furthermore, we estimate the required quantum resources, including the number of quantum registers and quantum gates. This study provides insight on the feasibility of quantum-assisted attacks on seed-based post-quantum digital signature schemes.
Side-channel attacks on block ciphers rarely recover the key outright: they leave a residual key space ordered by subkey posteriors, and evaluation laboratories report the key rank of the true key against thresholds near 2^48 and 2^60. No evaluation framework models an adversary who collects traces classically and finishes the search on a quantum computer, although quantum search with advice provides exactly that. We give such an adversary a cost model and a metric. For a device whose key has rank r, any quantum algorithm with classical access to the posteriors needs Omega(sqrt(r)) cipher evaluations, and block search achieves O(sqrt(r)); the per-instance advantage is exactly quadratic, and the super-quadratic exponents reported for search with advice are averages over the prior that apply to no single device. Under the NIST MAXDEPTH budget D and a Grover iteration of g gates and depth d, the quadratic advantage holds only for ranks up to (4D/(pi d))^2 and collapses to a constant factor beyond; with the best published AES-128 oracle and D = 2^40 the window closes near rank 2^58.6. We define the quantum-aware key rank, the classical rank of equal cost, computable from the rank estimators laboratories already run, and derive the classical rank a device must retain to keep a given threshold against each depth budget. Block search and amplitude amplification from the product-form posterior state are within a factor of two to four of each other on Hamming-weight posteriors, so the cost of coherent indexing decides between them. Experiments on simulated leakage and a toy cipher confirm the predicted window: at SNR 0.125 a depth-limited quantum adversary is worth about 22 traces to a classical one, however large its gate budget.
Formal verification of power side-channel leakage and its countermeasures in cryptographic algorithms is challenging, as SAT-based methods fail to scale on XOR-heavy, time-unrolled cryptographic circuits with realistic leakage models. We construct compact Conjunctive Normal Form (CNF) cases modeling one-bit leakage under two-trace conditions, linking key dependence and state evolution. Classical solvers quickly reach complexity limits, so we propose Q-LEAK, a quantum-based verification approach using Grover's algorithm, compiling each CNF into an oracle and applying amplitude amplification to search in O(sqrt(N)) oracle calls, with oracles that encode the two-trace leakage predicate and the CNF constraints. Benchmarking against classical SAT shows both potential gains and practical resource limits. In noiseless tests on 5-7 variable benchmarks, Q-LEAK consistently recovered a satisfying assignment within 1-4 tries, with marked bitstrings amplified clearly above the background distribution, exceeding 20 percent probability. The evaluation of Q-LEAK on real quantum hardware revealed at least one classically verified SAT assignment, despite the presence of noise. These results point to a potential path toward quantum-assisted verification of side-channel protections.
Large-scale quantum computing poses a major threat to classical public-key cryptography. Recently, strong “quantum access” security models have shown that numerous symmetric-key cryptosystems are also vulnerable. In this paper, we consider classical encryption in a model that grants the adversary quantum oracle access to encryption and decryption, but where we restrict the latter to non-adaptive (i.e., pre-challenge) queries only. We formalize this model using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA 1 in analogy to the classical CCA 1 security model. We show that the standard pseudorandom function ( PRF )-based encryption schemes are QCCA 1 -secure when instantiated with quantum-secure primitives. Our security proofs use a strong bound on quantum random-access codes with shared randomness. Revisiting plain IND − CPA -secure Learning with Errors ( LWE ) encryption, we show that leaking only a single quantum decryption query (and no other leakage or queries of any kind) allows the adversary to recover the full secret key with constant success probability. Information-theoretically, full recovery of the key in the classical setting requires at least a linear number of decryption queries. Our results thus challenge the notion that LWE is unconditionally “just as secure” quantumly as it is classically. The algorithm at the core of our attack is a new variant of the well-known Bernstein–Vazirani algorithm. Finally, we emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.
The emergence of quantum computing poses fundamental challenges to the security assumptions underlying modern cryptographic systems, particularly Fully Homomorphic Encryption (FHE) schemes that enable computation on encrypted data. While Grover's algorithm provides a theoretical framework for quantum attacks on symmetric cryptographic primitives, its practical application to complex parameter spaces like those in CKKS FHE has remained limited.This paper presents a simulation-based, exploratory hybrid framework that combines deep neural networks with a simplified quantum search model to evaluate the post-quantum security of CKKS bootstrapping parameters under idealised conditions. The AI-enhanced system learns to identify potentially vulnerable parameter configurations through pattern recognition, then uses this knowledge to optimize the quantum oracle construction in a 4-qubit Grover's algorithm simulator. Experiments conducted on 5,000 synthetically generated parameter sets, with evaluation on 100 boundary-region configurations, demonstrate that this hybrid approach achieves a 73.4\% success rate in identifying insecure parameters under the experimental setup, representing a 30.6\% improvement over standard quantum search in the same simulated environment.Within the experimental model, this analysis indicates that under the experimental model, parameter sets nominally targeting 128-bit quantum security may exhibit effective security levels of only 86–101 bits when subjected to AI-guided search, suggesting that current FHE parameter margins warrant further investigation as quantum capabilities mature. The findings are simulation-based and should not be directly extrapolated to real-world deployments without further validation; however, they indicate that security margins may need to be increased by approximately 2.3 times to maintain true 128-bit quantum resistance against intelligent adversaries. These results have implications for post-quantum cryptographic standards and motivate further study at realistic qubit scales.
Shor’s quantum factoring algorithm and a few other efficient quantum algorithms break many clas-sical crypto-systems. In response, people proposed post-quantum cryptography based on computational problems that are believed hard even for quantum computers. However, security of these schemes against quantum attacks is elusive. This is because existing security analysis (almost) only deals with classical attackers and arguing security in the presence of quantum adversaries is challenging due to unique quan-tum features such as no-cloning. This work proposes a general framework to study which classical security proofs can be restored in the quantum setting. Basically, we split a security proof into (a sequence of) classical security reductions, and investigate what security reductions are “quantum-friendly”. We characterize sufficient conditions such that a classical reduction can be “lifted ” to the quantum setting. We then apply our lifting theorems to post-quantum signature schemes. We are able to show that the classical generic construction of hash-tree based signatures from one-way functions and and a more efficient variant proposed in [BDH11] carry over to the quantum setting. Namely, assuming existence of (classical) one-way functions that are resistant to efficient quantum inversion algorithms, there exists a quantum-secure signature scheme. We note that the scheme in [BDH11] is a promising (post-quantum) candidate to be implemented in practice and our result further justifies it. Actually, to obtain these results, we formalize a simple criteria, which is motivated by many classical proofs in the literature and is straightforward to check. This makes our lifting theorem easier to apply, and it should be useful elsewhere to prove quantum security of proposed post-quantum cryptographic schemes. Finally we demonstrate the generality of our framework by showing that several existing works (Full-Domain hash in the quantum random-oracle model [Zha12b] and the simple hybrid arguments framework in [HSS11]) can be reformulated under our unified framework. 1