The impending arrival of cryptographically relevant quantum computing threatens classical public‑key infrastructures. This paper reviews the latest developments (2025–2026) in post‑quantum cryptography (PQC), fully homomorphic encryption (FHE), and zero‑knowledge proofs (ZKP). NIST has advanced nine signature candidates to its third evaluation round and selected HQC as a backup encryption standard. Novel primitives include bio‑inspired RNA‑based cryptography, algebraic hash signatures, and topology‑mined lattice schemes. FHE has reached its fifth generation with the GL scheme and the MadPanthera virtual processor, while lightweight ZKPs such as Microsoft’s Vega enable mobile‑friendly verification. These advances demonstrate rapid maturation toward deployable quantum‑safe systems.
Deoxyribonucleic acid provides unmatched information density and longevity for data storage, yet its easy amplification by polymerase chain reaction enables unauthorized replication at negligible cost. We introduce ZAT-DNA, which encodes information in patterns of canonical adenine and noncanonical 2-aminoadenine. As DNA polymerases cannot distinguish adenine from 2-aminoadenine, polymerase-based amplification erases these patterns, enforcing molecular-layer non-replicability intrinsic to the base-pairing ambiguity. We validate ZAT-DNA for secure key storage, demonstrating error-free encoding, storage, and high-fidelity nanopore retrieval of 32-bit and 64-bit cryptographic keys. ZAT-DNA blocks polymerase-based copying and protects non-fungible tokens by preventing functional duplication. For larger datasets, we present a hybrid “Babel-DNA” architecture: multiple encrypted images are co-encoded in a single regular DNA pool, with each selectively decryptable only via its cognate, non-replicable ZAT-DNA key. This provides a practical framework for molecular access control, secure DNA-encoded databases, and scarce molecular tokens. ZAT-DNA encodes data in A/Z base patterns that PCR erases, ensuring molecular non-replicability. It enables secure 32/64-bit key storage and nanopore retrieval, blocks copying, and protects NFTs. The Babel-DNA hybrid allows selective access to multiple encrypted datasets from a single DNA pool using unique ZAT-DNA keys.
Open access
DNA and Biological Computing
Nanopore and Nanochannel Transport Studies
Physical Unclonable Functions (PUFs) and Hardware Security
Assume that, given a sequence of n integers from 1 to n arranged in random order, we want to sort them, provided that the only acceptable operation is a prefix reversal, which means to take any number of integers (sub-sequence) from the left of the sequence, reverse the order of the sub-sequence, and return them to the original sequence. This problem is called “pancake sorting,” and sorting an arbitrary sequence with the minimum number of operations restricted in this way is known to be NP-hard. In this paper, we consider applying the concept of zero-knowledge proofs to the pancake sorting problem. That is, we design card-based zero-knowledge proof protocols in which a user (the prover) who knows how to sort a given sequence with ℓ operations can convince another user (the verifier) that the prover knows this information without divulging it.
This paper presents a formalised architecture for synthetic agents designed to retain immutable memory, verifiable reasoning, and constrained epistemic growth. Traditional AI systems rely on mutable, opaque statistical models prone to epistemic drift and historical revisionism. In contrast, we introduce the concept of the Merkle Automaton, a cryptographically anchored, deterministic computational framework that integrates formal automata theory with blockchain-based commitments. Each agent transition, memory fragment, and reasoning step is committed within a Merkle structure rooted on-chain, rendering it non-repudiable and auditably permanent. To ensure selective access and confidentiality, we derive symmetric encryption keys from ECDH exchanges contextualised by hierarchical privilege lattices. This enforces cryptographic access control over append-only DAG-structured knowledge graphs. Reasoning is constrained by formal logic systems and verified through deterministic traversal of policy-encoded structures. Updates are non-destructive and historied, preserving epistemic lineage without catastrophic forgetting. Zero-knowledge proofs facilitate verifiable, privacy-preserving inclusion attestations. Collectively, this architecture reframes memory not as a cache but as a ledger - one whose contents are enforced by protocol, bound by cryptography, and constrained by formal logic. The result is not an intelligent agent that mimics thought, but an epistemic entity whose outputs are provably derived, temporally anchored, and impervious to post hoc revision. This design lays foundational groundwork for legal, economic, and high-assurance computational systems that require provable memory, unforgeable provenance, and structural truth.
In an increasingly digital world, establishing secure and reliable methods for verifying identity has become a critical priority across sectors such as finance, healthcare, education, and e-governance. Traditional authentication mechanisms—relying on passwords, personal identification numbers, and physical documents—are increasingly susceptible to fraud, data breaches, and user inconvenience. This paper presents a multi-modal biometric framework for digital identity management, integrating facial recognition and fingerprint verification to enhance accuracy, reduce fraud, and ensure user-centric security. The proposed system includes modules for data acquisition, preprocessing, feature extraction using Convolutional Neural Networks (CNNs) and minutiae detection, score-level fusion, and final authentication decisions. Security and privacy are ensured through AES-256 encryption, differential privacy techniques, and decentralized blockchain-based data storage. This research contributes a scalable, privacy-aware, and highly accurate digital identity model capable of addressing challenges such as interoperability, user trust, and regulatory compliance. Future enhancements include the integration of additional biometric modalities and deployment in mobile and IoT environments.
Currently, PAKE (Password Authenticated Key Exchange) protocols on lattice using a single-server architecture are widely applied. However, such protocols are vulnerable to server leakage attacks, dictionary attacks, and other threats. To address these issues, researchers have proposed multi-server and two-server architecture-based PAKE protocols. However, PAKE protocols in a multi-server architecture require the use of complex cryptographic primitives such as signatures, and zero-knowledge proofs to ensure security, which reduces the execution efficiency of the protocol. To tackle these challenges, we propose two new multi-server password authentication key exchange protocols based on the MLWE (Module learning with errors) problem. Both protocols rely on MLWE instances, using Peikert's error coordination technique to enable two parties with similar values to compute the same result. Furthermore, we introduce the error pairing assumption and proves its security within random oracle model. The proposed protocol divides the password information into different shares and stores them on separate servers. In protocol 1, all servers and user collaboratively generate session keys, making it suitable for high-security application scenarios. In protocol 2, both user and servers generate session keys individually, which is ideal for high-efficiency application scenarios. Compared to similar protocols, both protocols lower computation and communication costs, better addressing practical application needs while providing protection against quantum computing attacks and server leakage threats.
The syndrome decoding problem is one of the NP-complete problems lying at the foundation of code-based cryptography. The variant thereof where the distance between vectors is measured with respect to the Lee metric, rather than the more commonly used Hamming metric, has been analyzed recently in several works due to its potential relevance for building more efficient code-based cryptosystems. The purpose of this article is to present a zero-knowledge proof of knowledge for this variant of the problem.
This paper investigates the use of threshold signature schemes in isogeny-based cryptosystems. By leveraging the distinct features of isogeny graphs, we propose a protocol that offers high security and practical efficiency, making it ideal for distributed ledger technologies and secure multi-party computations. Our scheme is resistant to quantum attacks and maintains minimal computational and communication overheads. We present an extensive analysis of the security and performance of our protocol, emphasizing its relevance to real-world cryptographic systems. MSC 2020: 94A60, 11G07, 68M07.
In the era of Web3, decentralized technologies have emerged as the cornerstone of a new digital paradigm. Backed by a decentralized blockchain architecture, the Web3 space aims to democratize all aspects of the web. From data-sharing to learning models, outsourcing computation is an established, prevalent practice. Verifiable computation makes this practice trustworthy as clients/users can now efficiently validate the integrity of a computation. As verifiable computation gets considered for applications in the Web3 space, decentralization is crucial for system reliability, ensuring that no single entity can suppress clients. At the same time, however, decentralization needs to be balanced with efficiency: clients want their computations done as quickly as possible. Motivated by these issues, we study the trade-off between decentralization and efficiency when outsourcing computational tasks to strategic, rational solution providers. Specifically, we examine this trade-off when the client employs (1) revelation mechanisms, i.e. auctions, where solution providers bid their desired reward for completing the task by a specific deadline and then the client selects which of them will do the task and how much they will be rewarded, and (2) simple, non-revelation mechanisms, where the client commits to the set of rules she will use to map solutions at specific times to rewards and then solution providers decide whether they want to do the task or not. We completely characterize the power and limitations of revelation and non-revelation mechanisms in our model.
Abstract A zero-knowledge proof protocol is a cryptographic protocol in which a prover, who knows the witness to a statement, can convince a verifier that the statement is true without revealing any information about the witness. Although zero-knowledge proof protocols are typically executed on electronic computers, there is a line of research to design zero-knowledge proof protocols based on physical objects (e.g., a deck of cards). This is called physical zero-knowledge proof. In this paper, we construct a physical zero-knowledge proof protocol for a logical puzzle called Sukoro. Sukoro has many cells on the puzzle board, like Sudoku, where each cell must be empty or filled with a number from one to four, and each number must match the number of adjacent filled cells, and the same numbers must not be adjacent to each other. In addition, it has a rule that all filled cells must be connected, which is called the connectivity condition. Although some existing protocols deal with the connectivity condition, all existing methods are interactive , which requires the prover’s knowledge to determine how the cards are manipulated during the execution of the protocols. In this paper, we give a new method for verifying the connectivity condition in the non-interactive setting, which means that the protocol can be executed without the prover’s knowledge, and construct a physical zero-knowledge proof protocol for Sukoro.
The 15-puzzle is a puzzle game played with 15 square tiles numbered from 1 to 15 on a 4 × 4 board. It has been popular for generations because of its simplicity and challenge. The (w × h)-puzzle is a generalization of the 15-puzzle, which is played with wh − 1 square tiles numbered from 1 to wh − 1 on a w × h board. Solving the (w × h)-puzzle is NP-hard, and hence it is valuable to know its solution. In this paper, we apply the concept of zero-knowledge proof to the (w × h)-puzzle. We propose a physical zero-knowledge proof protocol, in which a prover who knows a solution to the (w × h)-puzzle can convince a verifier that the prover knows the solution without revealing any information about it. We also design physical zero-knowledge proof protocols of two token swapping problems closely related to the (w × h)-puzzle.
Sandro Rodriguez Garzon, Dennis Natusch, Artur Philipp, Axel Küpper · 6 authors
Authentication in TLS is predominately carried out with X.509 digital certificates issued by certificate au-thorities (CA). The centralized nature of current public key infrastructures, however, comes along with severe risks, such as single points of failure and susceptibility to cyber-attacks, potentially undermining the security and trustworthiness of the entire system. With Decentralized Identifiers (DID) alongside distributed ledger technology, it becomes technically feasible to prove ownership of a unique identifier without requiring an attestation of the proof's public key by a centralized and therefore vulnerable CA. This article presents DID Link, a novel authentication scheme for TLS 1.3 that empowers entities to authenticate in a TLS-compliant way with self-issued X.509 certificates that are equipped with ledger-anchored DIDs instead of CA-issued identifiers. It facilitates the exchange of tamper-proof and 3rd-party attested claims in the form of DID-bound Verifiable Credentials after the TLS handshake to complete the authentication with a full identification of the communication partner. A prototypical implementation shows comparable TLS handshake durations of DID Link if verification material is cached and reasonable prolongations if it is obtained from a ledger. The significant speed improvement of the resulting TLS channel over a widely used, DID-based alternative transport protocol on the application layer demonstrates the potential of DID Link to become a viable solution for the establishment of secure and trustful end-to-end communication links with decentrally managed digital identities.
Anne M. Luescher, Andreas L. Gimpel, Wendelin J. Stark, Reinhard Heckel · 5 authors
Abstract Physical unclonable functions (PUFs) based on unique tokens generated by random manufacturing processes have been proposed as an alternative to mathematical one-way algorithms. However, these tokens are not distributable, which is a disadvantage for decentralized applications. Finding unclonable, yet distributable functions would help bridge this gap and expand the applications of object-bound cryptography. Here we show that large random DNA pools with a segmented structure of alternating constant and randomly generated portions are able to calculate distinct outputs from millions of inputs in a specific and reproducible manner, in analogy to physical unclonable functions. Our experimental data with pools comprising up to >10 10 unique sequences and encompassing >750 comparisons of resulting outputs demonstrate that the proposed chemical unclonable function (CUF) system is robust, distributable, and scalable. Based on this proof of concept, CUF-based anti-counterfeiting systems, non-fungible objects and decentralized multi-user authentication are conceivable.
Open access
DNA and Biological Computing
Physical Unclonable Functions (PUFs) and Hardware Security
We exploit the idea of [Fen22] which proposes to build an efficient signature scheme based on a zero-knowledge proof of knowledge of a solution of a MinRank instance. The scheme uses the MPCitH paradigm, which is an efficient way to build ZK proofs. We combine this idea with another idea, the hypercube technique introduced in [AMGH+22], which leads to more efficient MPCitH-based scheme. This new approach is more efficient than classical MPCitH, as it allows to reduce the number of party computation. This gives us a first scheme called MIRA-Additive. We then present an other scheme, based on low-threshold secret sharings, called MIRA-Threshold, which is a faster scheme, at the price of larger signatures. The construction of MPCitH using threshold secret sharing is detailed in [FR22]. These two constructions allows us to be faster than classical MPCitH, with a size of signature around 5.6kB with MIRA-Additive, and 8.3kB with MIRA-Threshold. We detail here the constructions and optimizations of the schemes, as well as their security proofs.
Adel Alahmadi, Selda Çalkavur, Patrick Solé, Abdul Nadim Khan · 6 authors
Blockchain is a method of recording information that makes it not feasible for the system to be replaced, attacked, or manipulated. A blockchain is equipped with a notebook that copies and processes the various procedures across the network of computers participating in the blockchain. Digital signature algorithm is one of the cryptographic protocols used by the blockchain. In this work, we introduce a new digital signature scheme based on error correcting codes. In the scheme constructed on a [n, k, d]− code over 𝔽q, which is d ≥ 2t + 1, and the size of the signature length is n − k. The signature verification is based on the bounded distance decoding of the code. Since the verification space is 𝔽qn, the proposed scheme has an improved performance in terms of working in a wider space.
Makaro is a logic puzzle with an objective to fill numbers into a rectangular grid to satisfy certain conditions. In 2018, Bultel et al. developed a physical zero-knowledge proof (ZKP) protocol for Makaro using a deck of cards, which allows a prover to physically convince a verifier that he/she knows a solution of the puzzle without revealing it. However, their protocol requires several identical copies of some cards, making it impractical as a deck of playing cards found in everyday life typically consists of all different cards. In this paper, we propose a new ZKP protocol for Makaro that can be implemented using a standard deck (a deck consisting of all different cards). Our protocol also uses asymptotically less cards than the protocol of Bultel et al. Most importantly, we develop a general method to encode a number with a sequence of all different cards. This allows us to securely compute several numerical functions using a standard deck, such as verifying that two given numbers are different and verifying that a number is the largest one among the given numbers.
A random beacon provides a continuous public source of randomness and its applications range from public lotteries to zero-knowledge proofs. Existing random beacon protocols sacrifice either the fault tolerance or the communication complexity for security, or ease of reconfigurability. This work overcomes the challenges with the existing works through a novel communication efficient combination of state machine replication and (Publicly) Verifiable Secret Sharing (PVSS/VSS).
Classical cryptography has been around for a long time in the documented human history, but most classical ciphers were broken and even solved by hand. Shannon introduced the notion of perfect secrecy that formally defines confidentiality in the information-theoretic sense, which is only possible in the restricted scenarios where the message is no longer than the encryption key. The invention of public-key cryptography (the Diffie-Hellman key exchange protocol in 1976 and the RSA crypto-system in 1977) marks the birth of modern cryptography, allowing parties to exchange messages securely without sharing any secrets in advance. Furthermore, it provides computational security based on the conjectured hardness of mathematical problems such as factorization and the discrete logarithm. Public-key cryptography has found numerous applications in the Internet, financial and banking industry, and blockchains, and it plays a crucial role in protecting information security and asset safety. Unfortunately, in the 1990s, Shor proposed efficient quantum algorithms that solve number-theoretic problems, including factorization and discrete logarithms in polynomial time. Once a quantum computer of a particular scale becomes a reality, it will cause a devastating blow to the existing public-key infrastructure. To deal with such a ‘quantum crisis’, academia and industry are looking into the design, analysis and standardization of cryptographic algorithms that can resist quantum computers referred to as post-quantum cryptography (PQC). The National Institute of Standards and Technology (NIST) has been soliciting proposals for the post-quantum public-key algorithms since 2016. More recently, the Chinese Association for Cryptologic Research (CACR) held a competition on designing cryptographic algorithms whose public-key cryptography track focused on post-quantum cryptographic algorithms. Lattice-based cryptography is considered by most to be the mainstream technical route of post-quantum cryptography, which is reflected in the number of proposals (and their percentage of the total) received in the NIST PQC process. To reflect the status quo of post-quantum cryptography, we invite leading experts in this area to contribute three technical perspectives that aim to help readers understand the algorithms, the underlying basic techniques and different technical routes to achieve quantum resistance. The first perspective, presented by Lu and Zhang, introduces public-key cryptographic algorithms whose quantum security is reducible from the conjectured quantum hardness of lattice problems. In particular, they mainly focus on public-key encryption (PKE) and the key encapsulation mechanism (KEM), which are essential building blocks for securing the confidentiality of communication without pre-shared secrets. Both types of crypto-systems are solicited by the NIST PQC standardization and the CACR algorithm design competition. This perspective gives a comprehensive survey on practical lattice-based PKEs/KEMs, and their best-known quantum and classical attacks. Another important post-quantum crypto-system is digital signature, which ensures that three goals of information security are met other than confidentiality, namely, integrity, authentication and non-repudiation. The second perspective is on lattice-based signature by Lyubashevsky. In this perspective, he surveys different techniques in building lattice-based post-quantum crypto-systems, discusses the challenges in overcoming performance issues and gives us state-of-the-art digital signature schemes. In addition to ensuring the ‘static’ security of information in storage and transmission, advanced cryptographic algorithms and protocols can guarantee information security during the computation process (possibly among multiple parties), referred to as privacy-preserving computation. Cryptographic techniques involved in privacy-preserving computation include secure multi-party computation, zero-knowledge proof and fully homomorphic encryption. There is a pressing need to migrate them to the post-quantum era. The third perspective, by Yu and Xie, presents practical instantiations of these algorithms and discusses possible ways to migrate them to their quantum-resistant counterparts. To summarize, post-quantum cryptography has received widespread attention and made significant progress in recent years. Some post-quantum cryptographic algorithms, such as the lattice-based candidate, also have other advantages (e.g., computational efficiency and full homomorphism) over their classical counterparts. Lattice-based cryptography is an emerging field with high theoretical value and wide application, and we encourage young researchers to enter and explore this new and exciting field.
In addition to their usefulness in proving one’s identity electronically, identification protocols based on zero-knowledge proofs allow designing secure cryptographic signature schemes by means of the Fiat–Shamir transform or other similar constructs. This approach has been followed by many cryptographers during the NIST (National Institute of Standards and Technology) standardization process for quantum-resistant signature schemes. NIST candidates include solutions in different settings, such as lattices and multivariate and multiparty computation. While error-correcting codes may also be used, they do not provide very practical parameters, with a few exceptions. In this manuscript, we explored the possibility of using the error-correcting codes proposed by Stakhov in 2006 to design an identification protocol based on zero-knowledge proofs. We showed that this type of code offers a valid alternative in the error-correcting code setting to build such protocols and, consequently, quantum-resistant signature schemes.
Mit Bitcoin wurde 2008 die erste Kryptowährung veröffentlicht. Mit ihr können Zahlungen getätigt werden, ohne einer zentralen Stelle wie einer Bank vertrauen zu müssen. Dies wird durch einen innovativen Konsensus-Mechanismus ermöglicht, der unter der Bezeichnung Proof-of-Work bekannt ist. Bitcoin ist noch immer die bekannteste und wertvollste Kryptowährung. Über die Jahre sind jedoch einige Probleme offenkundig geworden, wie z.B. der hohe Energieverbrauch und der niedriger Transaktionsdurchsatz. Um das Jahr 2016 kam eine neue Art von Protokollen auf, welche versprach diese beiden Probleme gleichzeitig zu lösen. Diese Protokolle basieren auf dem Proof-of-Stake (PoS) Mechanismus und verwenden gerichtete azyklische Graphen als Datenstruktur. Da es sich hier ebenfalls um Währungen handelt, spielt Sicherheit eine zentrale Rolle. Dies wirft die Frage auf, wie sicher Protokolle dieser Art wirklich sind. Diese Arbeit trägt zur Beantwortung bei, indem Hashgraph im Detail analysiert wird. Hashgraph ist ein vielversprechender Vertreter dieser Protokollart. Die verschiedensten Sicherheits- und Performanceangaben des Protokolls werden mithilfen eines im Zuge der Arbeit entwickelten und veröffentlichten Simulators überprüft. Der Simulator ermöglicht es, das Verhalten des Protokolls unter vier verschiedenen (Angriffs-)Szenarien zu untersuchen. Er bietet dazu umfangreiche Konfigurationsmöglichkeiten an, welche unzählige verschiedene Verläufe ermöglichen. Akteure/Akteurinnen agieren zufällig basierend auf einem veränderbaren Parameter, der Reproduzierbarkeit gewährleistet. Der Simulator selbst verfügt außerdem über eine grafische Benutzerobefläche, wobei Ergebnisse auch als Text-Dateien für weitere Analysen exportiert werden können. In keiner einzigen von tausenden Simulationen wurde der Konsensus-Mechanismus von Hashgraph gebrochen. Basierend auf der Tatsache das Nachrichten zur Synchronsiation beliebig schnell und an beliebige andere Knoten gesendet werden können, kamen jedoch Schwachstellen zu Tage. Diese Arbeit zeigt auf, dass es möglich ist eine widersprüchliche Transaktion zu einer bereits existierenden zu veröffentlichen und diese schneller bestätigt zu bekommen. Weiters wird belohnt, wer Synchronisationen zuerst mit ganz bestimmten Knoten durchführt, was zu einer Überlastung dieser Knoten führen kann. Die präsentierten Ergebnisse zeigen, dass diese Protokollklasse tatsächlich das Potential besitzt, zwei der grundelegenden Probleme von traditionellen Kryptowährungen zu lösen. Die Möglichkeit von Nachrichten-Spam im System kann dies jedoch zunichte machen und ist ein wichtiger Punkt in der Bewertung solcher Protokolle.
Sudoku is a famous logic puzzle where the player has to fill a number between 1 and 9 into each empty cell of a $9 \times 9$ grid such that every number appears exactly once in each row, each column, and each $3 \times 3$ block. In 2020, Sasaki et al. developed a physical card-based protocol of zero-knowledge proof (ZKP) for Sudoku, which enables a prover to convince a verifier that he/she knows a solution of the puzzle without revealing it. Their protocol uses 90 cards, but requires nine identical copies of some cards, which cannot be found in a standard deck of playing cards (consisting of 52 different cards and two jokers). Hence, nine identical standard decks are required to perform that protocol, making the protocol not very practical. In this paper, we propose a new ZKP protocol for Sudoku that can be performed using only two standard decks of playing cards, regardless of whether the two decks are identical or different. In general, we also develop the first ZKP protocol for a generalized $n \times n$ Sudoku that can be performed using a deck of all different cards.