Another Round of Breaking and Making Quantum Money: How to Not Build It from Lattices, and More

Public verification of quantum money has been one of the central objects in quantum cryptography ever since Wiesner's pioneering idea of using quantum mechanics to construct banknotes against counterfeiting. So far, we do not know any publicly-verifiable quantum money scheme that is provably secure from standard assumptions. In this work, we provide both negative and positive results for publicly verifiable quantum money. **In the first part, we give a general theorem, showing that a certain natural class of quantum money schemes from lattices cannot be secure. We use this theorem to break the recent quantum money scheme of Khesin, Lu, and Shor. **In the second part, we propose a framework for building quantum money and quantum lightning we call invariant money which abstracts some of the ideas of quantum money from knots by Farhi et al.(ITCS'12). In addition to formalizing this framework, we provide concrete hard computational problems loosely inspired by classical knowledge-of-exponent assumptions, whose hardness would imply the security of quantum lightning, a strengthening of quantum money where not even the bank can duplicate banknotes. **We discuss potential instantiations of our framework, including an oracle construction using cryptographic group actions and instantiations from rerandomizable functional encryption, isogenies over elliptic curves, and knots

Fragmentos autobiográficos de la sociedad tribal bereber marroquí

Taking as a starting point his memories, initiated on to the death of his wife, Ursula, with whom he had shared all his experience of field work in the Moroccan Rif and Atlas, since the late '50, the well-known anthropologist, defender of the theory of tribal segmentarity, DavidMontgomery Hart ( 1927-2001), tracesanautobiographicalpicture, togetherwith anthropological points. This text is part ofhis unpublished autobiography.Tomando como punto de partida sus recuerdos, hilvanados a la muerte de su esposa, Úrsula, con quien había compartido toda su experiencia de trabajo de campo enel Rifyel Atlas marroquí, desde finales de los años cincuenta, el conocido antropólogo, defensor de la teoría de la segmentariedad tribal, David Montgomery Hart ( 1927-2001), traza un cuadro autobiográfico, trufado de puntualizaciones antropológicas. Este texto forma parte de su autobiografía inédita

Full Quantum Equivalence of Group Action DLog and CDH, and More

Cryptographic group actions are a relaxation of standard cryptographic groups that have less structure. This lack of structure allows them to be plausibly quantum resistant despite Shor\u27s algorithm, while still having a number of applications. The most famous example of group actions are built from isogenies on elliptic curves. Our main result is that CDH for abelian group actions is quantumly *equivalent* to discrete log. Galbraith et al. (Mathematical Cryptology) previously showed *perfectly* solving CDH to be equivalent to discrete log quantumly; our result works for any non-negligible advantage. We also explore several other questions about group action and isogeny protocols

A Low-Round Distributed PRF from Lattices and its Application to Distributed Key Management

We initiate the study of lattice-based pseudo-random functions (PRFs) for use in multi-party computation protocols, motivated by their application to distributed key management. We show that the LWE-based PRF of Boneh et al. (CRYPTO\u2713) can be turned into a distributed PRF protocol that runs in only 8 online rounds, improving over the state-of-the-art by an order of magnitude. The resulting protocol can be used as a method for distributed key derivation and reduces the amount of managed key material in distributed key management systems from linear in the number of users to constant. Finally, we support our findings by implementing and evaluating our protocol using the MP-SPDZ framework (CCS\u2720)

Private Puncturable PRFs From Standard Lattice Assumptions

A puncturable pseudorandom function (PRF) has a master key $k$ that enables one to evaluate the PRF at all points of the domain, and has a punctured key $k_x$ that enables one to evaluate the PRF at all points but one. The punctured key $k_x$ reveals no information about the value of the PRF at the punctured point $x$. Punctured PRFs play an important role in cryptography, especially in applications of indistinguishability obfuscation. However, in previous constructions, the punctured key $k_x$ completely reveals the punctured point $x$: given $k_x$ it is easy to determine $x$. A {\em private} puncturable PRF is one where $k_x$ reveals nothing about~$x$. This concept was defined by Boneh, Lewi, and Wu, who showed the usefulness of private puncturing, and gave constructions based on multilinear maps. The question is whether private puncturing can be built from a standard (weaker) cryptographic assumption. We construct the first privately puncturable PRF from standard lattice assumptions, namely from the hardness of learning with errors (LWE) and 1 dimensional short integer solutions (1D-SIS), which have connections to worst-case hardness of general lattice problems. Our starting point is the (non-private) PRF of Brakerski and Vaikuntanathan. We introduce a number of new techniques to enhance this PRF, from which we obtain a privately puncturable PRF. In addition, we also study the simulation based definition of private constrained PRFs for general circuits, and show that the definition is not satisfiable

ALLOSAUR: Accumulator with Low-Latency Oblivious Sublinear Anonymous credential Updates with Revocations

A cryptographic accumulator is a space- and time-efficient data structure with associated algorithms used for secure membership testing. In the growing space of digital credentials, accumulators found in managing a set of valid credentials, giving efficient and anonymous methods for credential holders to prove their validity. Unlike traditional credentials like digital signatures, one can easily revoke credentials with an accumulator; however, each revocation forces existing credential holders to engage in an expensive update process. Previous works make this faster and easier by sacrificing anonymity. To improve performance without compromising privacy, we present ALLOSAUR, a multi-party accumulator based on pairings. In ALLOSAUR, we eliminate the cost of accumulating new credentials, let credential managers manage the accumulator values with secure multiparty computation, and allow anonymous credential updates with a square-root reduction in communication costs as compared to existing work. A deployed digital credential system is a vast and complicated system, and existing formalisms do not fully address the scope or power of a real-world adversary. We develop a thorough UC-style formalism that allows arbitrary malicious behaviour from an adversary controlling a minority of credential managers and arbitrary numbers of users, credentials, and verifiers. In our new formalism we present a novel definition of privacy that captures as much anonymity as possible while accounting for inevitable losses from interaction with the system. The detail in our formalism reveals real-world issues in existing accumulator constructions, all of which ALLOSAUR avoids. Our proof-of-concept implementation can update over 1000 revocations with less than half a second of total computation and 16 kB communication, at least a 5x improvement over the previous state-of-the-art in both metrics

Symmetric Primitives with Structured Secrets

Securely managing encrypted data on an untrusted party is a challenging problem that has motivated the study of a variety of cryptographic primitives. A special class of such primitives allows an untrusted party to transform a ciphertext encrypted under one key to a ciphertext under another key, using some auxiliary information that does not leak the underlying data. Prominent examples of such primitives in the symmetric-key setting are key-homomorphic PRFs, updatable encryption, and proxy re-encryption. Although these primitives differ significantly in terms of their constructions and security requirements, they share two important properties: (a) they have secrets with structure or extra functionality, and (b) all known constructions of these primitives satisfying reasonably strong definitions of security are based on concrete public-key assumptions, e.g., DDH and LWE. This raises the question of whether these objects inherently belong to the world of public-key primitives, or they can potentially be built from simple symmetric-key objects such as pseudorandom functions. In this work, we show that the latter possibility is unlikely. More specifically, we show that: • Any (bounded) key-homomorphic weak PRF with an abelian output group implies a (bounded) input-homomorphic weak PRF, which has recently been shown to imply not only public-key encryption (PKE), but also a variety of primitives such as PIR, lossy TDFs, and even IBE. • Any ciphertext-independent updatable encryption scheme that is forward and post-compromise secure implies PKE. Moreover, any symmetric-key proxy re-encryption scheme with reasonably strong security guarantees implies a forward and post-compromise secure ciphertext-independent updatable encryption, and hence PKE. In addition, we show that unbounded (or exact) key-homomorphic weak PRFs over abelian groups are impossible in the quantum world. In other words, over abelian groups, bounded key-homomorphism is the best that we can hope for in terms of post-quantum security. Our attack also works over other structured primitives with abelian groups and exact homomorphisms, including homomorphic one-way functions and input-homomorphic weak PRFs

Time-release Cryptography from Minimal Circuit Assumptions

Time-release cryptography requires problems that take a long time to solve and take just as long even with significant computational resources. While time-release cryptography originated with the seminal paper of Rivest, Shamir and Wagner (\u2796), it has gained special visibility recently due to new time-release primitives, like verifiable delay functions (VDFs) and sequential proofs of work, and their novel blockchain applications. In spite of this recent progress, security definitions remain inconsistent and fragile, and foundational treatment of these primitives is scarce. Relationships between the various time-release primitives are elusive, with few connections to standard cryptographic assumptions. We systematically address these drawbacks. We define formal notions of sequential functions, the building blocks of time-release cryptography. The new definitions are robust against change of machine models, making them more amenable to complexity theoretic treatment. We demonstrate the equivalence of various types of sequential functions under standard cryptographic assumptions. The time-release primitives in the literature (such as those defined by Bitansky et al. (ITCS \u2716)) imply that these primitives exist, as well as the converse. However, showing that a given construction is a sequential function is a hard circuit lower bound problem. To our knowledge, no results show that standard cryptographic assumptions imply any sequentiality. For example, repeated squaring over RSA groups is assumed to be sequential, but nothing connects this conjecture to standard hardness assumptions. To circumvent this, we construct a function that we prove is sequential if there exists any sequential function, without needing any specific knowledge of this hypothetical function. Our techniques use universal circuits and fully homomorphic encryption and generalize some of the elegant techniques of the recent work on lattice NIZKs (Canetti et al., STOC \u2719). Using our reductions and sequential function constructions, we build VDFs and sequential proofs of work from fully homomorphic encryption, incremental verifiable computation, and the existence of a sequential function. Though our constructions are theoretical in nature and not competitive with existing techniques, they are built from much weaker assumptions than known constructions

Multiparty Noninteractive Key Exchange from Ring Key-Homomorphic Weak PRFs

A weak pseudorandom function $F: \mathcal{K} \times \mathcal{X} \rightarrow \mathcal{Y}$ is said to be ring key-homomorphic if, given $F \left(k_{1}, x \right)$ and $F \left(k_{2}, x \right)$, there are efficient algorithms to compute $F \left(k_{1} \oplus k_{2}, x \right)$ and $F \left(k_{1} \otimes k_{2}, x \right)$ where $\oplus$ and $\otimes$ are the addition and multiplication operations in the ring $\mathcal{K}$, respectively. In this work, we initiate the study of ring key-homomorphic weak PRFs (RKHwPRFs). As our main result, we show that any RKHwPRF implies multiparty noninteractive key exchange (NIKE) for an arbitrary number of parties in the standard model. Our analysis of RKHwPRFs in a sense takes a major step towards the goal of building cryptographic primitives from Minicrypt primitives with structure, which has been studied in a recent line of works. With our result, most of the well-known asymmetric cryptographic primitives can be built from a weak PRF with either a group or ring homomorphism over either the input space or the key space

Algebraic Pseudorandom Functions with Improved Efficiency from the Augmented Cascade

We construct an algebraic pseudorandom function (PRF) that is more efficient than the classic Naor- Reingold algebraic PRF. Our PRF is the result of adapting the cascade construction, which is the basis of HMAC, to the algebraic settings. To do so we define an augmented cascade and prove it secure when the underlying PRF satisfies a property called parallel security. We then use the augmented cascade to build new algebraic PRFs. The algebraic structure of our PRF leads to an efficient large-domain Verifiable Random Function (VRF) and a large-domain simulatable VRF