Gorjan Alagic

In their seminal work, Gentry and Wichs (STOC'11) established an impossibility result for the task of constructing an adaptively-sound SNARG via black-box reduction from a falsifiable assumption. An exciting set of recent SNARG constructions demonstrated that, if one adopts a weaker but still quite meaningful notion of adaptive soundness, then impossibility no longer holds (Waters-Wu, Waters-Zhandry, Mathialagan-Peters-Vaikunthanathan ePrint'24). These fascinating new results raise an intriguing possibility: is there a way to remove this slight weakening of adaptive soundness, thereby completely circumventing the Gentry-Wichs impossibility? A natural route to closing this gap would be to use a quantum black-box reduction, i.e., a reduction that can query the SNARG adversary on superpositions of inputs. This would take advantage of the fact that Gentry-Wichs only consider classical reductions. In this work, we show that this approach cannot succeed. Specifically, we extend the Gentry-Wichs impossibility result to quantum black-box reductions, and thereby establish an important limit on the power of such reductions.

The National Institute of Standards and Technology is selecting public-key cryptographic algorithms through a public, competition-like process. The new public-key cryptography standards will specify additional digital signatures, public-key encryption, and key-establishment algorithms to supplement Federal Information Processing Standard (FIPS) 186-5, Digital Signature Standard (DSS), as well as NIST Special Publication (SP) 800-56A Revision 3, Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B Revision 2, Recommendation for Pair-Wise Key Establishment Using Integer Factorization Cryptography. It is intended that these algorithms will be capable of protecting sensitive information well into the foreseeable future, including after the advent of quantum computers. After three rounds of evaluation and analysis, NIST announced the selection of the first algorithms to be standardized \cite {NISTIR8413}. The public-key encapsulation mechanism (KEM) selected for standardization was CRYSTALS-Kyber (ML-KEM). The digital signatures selected were CRYSTALS-Di lithium (ML-DSA), Falcon (FN-DSA), and SPHINCS+ (SLH-DSA). In August 2024, NIST published the first three post-quantum cryptography standards based on these algorithms \cite {FIPS203, FIPS204, FIPS205}. Four candidate algorithms for key establishment have continued to be studied in a fourth round of analysis: BIKE, Classic McEliece, HQC, and SIKE. This report describes the evaluation and selection process of these fourth-round candidates based on public feedback and internal review. The report summarizes each of the candidate algorithms and identifies those selected for standardization. The only key-establishment algorithm that will be standardized is HQC. NIST will develop a standard based on HQC to augment and diversify its key-establishment portfolio.

NIST is in the process of evaluating public-key digital signature algorithms for potential standardization to protect sensitive information into the foreseeable future, including after the advent of quantum computers. Any signature scheme that is eventually selected would augment FIPS 204, Module-Lattice-Based Digital Signature Standard; FIPS 205, Stateless Hash-Based Digital Signature Standard; FIPS 186-5, Digital Signature Standard (DSS); and SP 800-208, Recommendation for Stateful Hash-Based Signature Schemes. This report describes the evaluation criteria and selection process of the First Round of the Additional Digital Signatures for the NIST Post-Quantum Cryptography (PQC) Standardization Process. Based on public feedback and internal reviews of the first-round candidates, NIST selected14 candidate algorithms to move forward to the second round of evaluation: CROSS, FAEST, HAWK, LESS, MAYO, Mirath (merger of MIRA/MiRitH), MQOM, PERK, QR-UOV, RYDE, SDitH, SNOVA, SQIsign, and UOV.

In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This fundamental problem in query complexity appears in many contexts, particularly cryptography. In this work, we examine the setting in which the oracle allows for quantum queries to both the forward and the inverse direction of the permutation—except that the challenge value cannot be submitted to the latter. Within that setting, we consider three options for the inversion algorithm: whether it can get quantum advice about the permutation, whether the query algorithm can restrict the distribution with which the challenge input is sampled, and whether it must produce the entire preimage (search) or only the first bit (decision). We prove several theorems connecting the hardness of the resulting variations of the permutation inversion problem and establish lower bounds for them. Our results show that, perhaps surprisingly, the permutation inversion problem does not become significantly easier when the adversary is granted oracle access to the inverse—provided it cannot query the challenge itself.

Cryptography with quantum states exhibits a number of surprising and counterintuitive features. In a 2002 work, Barnum et al. argue that these features imply that digital signatures for quantum states are impossible (Barnum et al., FOCS 2002). In this work, we ask: can all forms of signing quantum data, even in a possibly weak sense, be completely ruled out? We give two results which shed significant light on this basic question. First, we prove an impossibility result for digital signatures for quantum data, which extends the result of Barnum et al. Specifically, we show that no nontrivial combination of correctness and security requirements can be fulfilled, beyond what is achievable simply by measuring the quantum message and then signing the outcome. In other words, only classical signature schemes exist. We then show a positive result: a quantum state can be signed with the same security guarantees as classically, provided that it is also encrypted with the public key of the intended recipient. Following classical nomenclature, we call this notion quantum signcryption. Classically, signcryption is only interesting if it provides superior performance to encypt-then-sign. Quantumly, it is far more interesting: it is the only signing method available. We develop "as-strong-as-classical" security definitions for quantum signcryption and give secure constructions based on post-quantum public-key primitives. Along the way, we show that a natural hybrid method of combining classical and quantum schemes can be used to "upgrade" a secure classical scheme to the fully-quantum setting, in a wide range of cryptographic settings including signcryption, authenticated encryption, and CCA security.

We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i.) ciphertext unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext attack, and (iii.) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All of our new notions also imply QIND-CPA privacy. Combining one-time authentication and classical pseudorandomness, we construct schemes for each of these new quantum security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.