Verifiably Encrypted Signatures with Short Keys based on the Decisional Linear Problem and Obfuscation for Encrypted VES

Verifiably encrypted signatures (VES) are signatures encrypted by a public key of a trusted third party and we can verify their validity without decryption. This paper proposes a new VES scheme which is secure under the decisional linear (DLIN) assumption in the standard model. We also propose new obfuscators for encrypted signatures (ES) and encrypted VES (EVES) which are secure under the DLIN assumption. All previous efficient VES schemes in the standard model are either secure under standard assumptions (such as the computational Diffie-Hellman assumption) with large verification (or secret) keys or secure under \emph{(non-standard) dynamic $q$-type assumptions} (such as the $q$-strong Diffie-Hellman extraction assumption) with short verification keys. Our construction is the first efficient VES scheme with short verification (and secret) keys secure under \emph{a standard assumption (DLIN)}. As by-products of our VES scheme, we construct new obfuscators for ES/EVES based on our new VES scheme. They are more efficient than previous obfuscators with respect to the public key size. Previous obfuscators for EVES are secure under non-standard assumption and use zero-knowledge (ZK) proof systems and Fiat-Shamir heuristics to obtain non-interactive ZK, i.e., its security is considered in the random oracle model. Thus, our construction also has an advantage with respect to assumptions and security models. Our new obfuscator for ES is obtained from our new obfuscator for EVES

Quantum Tokens for Digital Signatures

The fisherman caught a quantum fish. "Fisherman, please let me go", begged the fish, "and I will grant you three wishes". The fisherman agreed. The fish gave the fisherman a quantum computer, three quantum signing tokens and his classical public key. The fish explained: "to sign your three wishes, use the tokenized signature scheme on this quantum computer, then show your valid signature to the king, who owes me a favor". The fisherman used one of the signing tokens to sign the document "give me a castle!" and rushed to the palace. The king executed the classical verification algorithm using the fish's public key, and since it was valid, the king complied. The fisherman's wife wanted to sign ten wishes using their two remaining signing tokens. The fisherman did not want to cheat, and secretly sailed to meet the fish. "Fish, my wife wants to sign ten more wishes". But the fish was not worried: "I have learned quantum cryptography following the previous story (The Fisherman and His Wife by the brothers Grimm). The quantum tokens are consumed during the signing. Your polynomial wife cannot even sign four wishes using the three signing tokens I gave you". "How does it work?" wondered the fisherman. "Have you heard of quantum money? These are quantum states which can be easily verified but are hard to copy. This tokenized quantum signature scheme extends Aaronson and Christiano's quantum money scheme, which is why the signing tokens cannot be copied". "Does your scheme have additional fancy properties?" the fisherman asked. "Yes, the scheme has other security guarantees: revocability, testability and everlasting security. Furthermore, if you're at sea and your quantum phone has only classical reception, you can use this scheme to transfer the value of the quantum money to shore", said the fish, and swam away.Comment: Added illustration of the abstract to the ancillary file

Quantum State Obfuscation from Classical Oracles

A major unresolved question in quantum cryptography is whether it is possible to obfuscate arbitrary quantum computation. Indeed, there is much yet to understand about the feasibility of quantum obfuscation even in the classical oracle model, where one is given for free the ability to obfuscate any classical circuit. In this work, we develop a new array of techniques that we use to construct a quantum state obfuscator, a powerful notion formalized recently by Coladangelo and Gunn (arXiv:2311.07794) in their pursuit of better software copy-protection schemes. Quantum state obfuscation refers to the task of compiling a quantum program, consisting of a quantum circuit $C$ with a classical description and an auxiliary quantum state $\ket{\psi}$, into a functionally-equivalent obfuscated quantum program that hides as much as possible about $C$ and $\ket{\psi}$. We prove the security of our obfuscator when applied to any pseudo-deterministic quantum program, i.e. one that computes a (nearly) deterministic classical input / classical output functionality. Our security proof is with respect to an efficient classical oracle, which may be heuristically instantiated using quantum-secure indistinguishability obfuscation for classical circuits. Our result improves upon the recent work of Bartusek, Kitagawa, Nishimaki and Yamakawa (STOC 2023) who also showed how to obfuscate pseudo-deterministic quantum circuits in the classical oracle model, but only ones with a completely classical description. Furthermore, our result answers a question of Coladangelo and Gunn, who provide a construction of quantum state indistinguishability obfuscation with respect to a quantum oracle. Indeed, our quantum state obfuscator together with Coladangelo-Gunn gives the first candidate realization of a ``best-possible'' copy-protection scheme for all polynomial-time functionalities

Advances in cryptographic voting systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 241-254).Democracy depends on the proper administration of popular elections. Voters should receive assurance that their intent was correctly captured and that all eligible votes were correctly tallied. The election system as a whole should ensure that voter coercion is unlikely, even when voters are willing to be influenced. These conflicting requirements present a significant challenge: how can voters receive enough assurance to trust the election result, but not so much that they can prove to a potential coercer how they voted? This dissertation explores cryptographic techniques for implementing verifiable, secret-ballot elections. We present the power of cryptographic voting, in particular its ability to successfully achieve both verifiability and ballot secrecy, a combination that cannot be achieved by other means. We review a large portion of the literature on cryptographic voting. We propose three novel technical ideas: 1. a simple and inexpensive paper-base cryptographic voting system with some interesting advantages over existing techniques, 2. a theoretical model of incoercibility for human voters with their inherent limited computational ability, and a new ballot casting system that fits the new definition, and 3. a new theoretical construct for shuffling encrypted votes in full view of public observers.by Ben Adida.Ph.D

Indistinguishability Obfuscation of Null Quantum Circuits and Applications

We study the notion of indistinguishability obfuscation for null quantum circuits (quantum null-iO). We present a construction assuming: - The quantum hardness of learning with errors (LWE). - Post-quantum indistinguishability obfuscation for classical circuits. - A notion of "dual-mode" classical verification of quantum computation (CVQC). We give evidence that our notion of dual-mode CVQC exists by proposing a scheme that is secure assuming LWE in the quantum random oracle model (QROM). Then we show how quantum null-iO enables a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Among others, we obtain the first witness encryption scheme for QMA, the first publicly verifiable non-interactive zero-knowledge (NIZK) scheme for QMA, and the first attribute-based encryption (ABE) scheme for BQP

Exploiting loop transformations for the protection of software

Il software conserva la maggior parte del know-how che occorre per svilupparlo. Poich\ue9 oggigiorno il software pu\uf2 essere facilmente duplicato e ridistribuito ovunque, il rischio che la propriet\ue0 intellettuale venga violata su scala globale \ue8 elevato. Una delle pi\uf9 interessanti soluzioni a questo problema \ue8 dotare il software di un watermark. Ai watermark si richiede non solo di certificare in modo univoco il proprietario del software, ma anche di essere resistenti e pervasivi. In questa tesi riformuliamo i concetti di robustezza e pervasivit\ue0 a partire dalla semantica delle tracce. Evidenziamo i cicli quali costrutti di programmazione pervasivi e introduciamo le trasformazioni di ciclo come mattone di costruzione per schemi di watermarking pervasivo. Passiamo in rassegna alcune fra tali trasformazioni, studiando i loro principi di base. Infine, sfruttiamo tali principi per costruire una tecnica di watermarking pervasivo. La robustezza rimane una difficile, quanto affascinante, questione ancora da risolvere.Software retains most of the know-how required fot its development. Because nowadays software can be easily cloned and spread worldwide, the risk of intellectual property infringement on a global scale is high. One of the most viable solutions to this problem is to endow software with a watermark. Good watermarks are required not only to state unambiguously the owner of software, but also to be resilient and pervasive. In this thesis we base resiliency and pervasiveness on trace semantics. We point out loops as pervasive programming constructs and we introduce loop transformations as the basic block of pervasive watermarking schemes. We survey several loop transformations, outlining their underlying principles. Then we exploit these principles to build some pervasive watermarking techniques. Resiliency still remains a big and challenging open issue

Obfuscation and Outsourced Computation with Certified Deletion

Can we outsource computation on encrypted data, while ensuring that the data is certifiably, information-theoretically deleted by the server after computation? Can we encode a computer program in a manner that preserves its functionality, while allowing an evaluator to {\em prove that they deleted the program}? This work answers the above questions, providing the first fully (maliciously) secure solution to the question of blind delegation with certified deletion, and the first solution to the question of obfuscation with certified deletion. Unlike prior work on deletion, these settings require security in the presence of repeated access to partial decryptions of encoded data, followed by certified deletion of the (rest of the) encoded data. To enable security, we introduce a powerful new paradigm for secure information-theoretic deletion of data based on quantum \emph{subspace coset states}. We obtain the following results. Blind Delegation with Certified Deletion - Assuming the quantum hardness of learning with errors, we obtain maliciously-secure blind delegation with certified deletion. This improves upon prior protocols by Poremba (ITCS 2023) and Bartusek and Khurana (arXiv 2022) that we show are insecure against a malicious server. - Assuming sub-exponentially quantum-secure indistinguishability obfuscation, we obtain a \emph{two-message} protocol for blind delegation with certified deletion. All previous protocols required multiple rounds of interaction between the client and server. Obfuscation with Certified Deletion - Assuming post-quantum indistinguishability obfuscation, we obtain a construction of differing-inputs obfuscation with certified deletion, for a polynomial number of differing inputs. As an immediate corollary, we obtain a strong variant of secure software leasing for every differing-inputs circuit family. - We obtain two flavors of functional encryption with certified deletion, one where ciphertexts can be certifiably deleted, and the other where secret keys can be certifiably deleted, assuming appropriate variants of indistinguishability obfuscation and other standard assumptions. - We show how to prepare an ``oracle with certified deletion\u27\u27 implementing any efficient classical functionality. Additional Results - Assuming post-quantum CCA-secure public-key encryption, we obtain a notion of CCA-secure public-key encryption with certified deletion. We view this primarily as a pedagogical tool towards understanding our technique. - Assuming post-quantum indistinguishability obfuscation, we show how to generically add a \emph{publicly-verifiable} certified deletion property to a variety of cryptosystems. Publicly-verifiable deletion schemes prior to our work either relied on unproven conjectures (Poremba, ITCS 2023) or structured oracles (Hiroka et al., Asiacrypt 2021). All our primitives satisfy {\em everlasting security after deletion}, except for functional encryption with deletion for secret keys, where a computational certified deletion guarantee is inherent

Quantum State Obfuscation from Classical Oracles

A major unresolved question in quantum cryptography is whether it is possible to obfuscate arbitrary quantum computation. Indeed, there is much yet to understand about the feasibility of quantum obfuscation even in the classical oracle model, where one is given for free the ability to obfuscate any classical circuit. In this work, we develop a new array of techniques that we use to construct a quantum state obfuscator, a powerful notion formalized recently by Coladangelo and Gunn (arXiv:2311.07794) in their pursuit of better software copy-protection schemes. Quantum state obfuscation refers to the task of compiling a quantum program, consisting of a quantum circuit $C$ with a classical description and an auxiliary quantum state $\ket{\psi}$, into a functionally-equivalent obfuscated quantum program that hides as much as possible about $C$ and $\ket{\psi}$. We prove the security of our obfuscator when applied to any pseudo-deterministic quantum program, i.e. one that computes a (nearly) deterministic classical input / classical output functionality. Our security proof is with respect to an efficient classical oracle, which may be heuristically instantiated using quantum-secure indistinguishability obfuscation for classical circuits. Our result improves upon the recent work of Bartusek, Kitagawa, Nishimaki and Yamakawa (STOC 2023) who also showed how to obfuscate pseudo-deterministic quantum circuits in the classical oracle model, but only ones with a completely classical description. Furthermore, our result answers a question of Coladangelo and Gunn, who provide a construction of quantum state indistinguishability obfuscation with respect to a quantum oracle, but leave the existence of a concrete real-world candidate as an open problem. Indeed, our quantum state obfuscator together with Coladangelo-Gunn gives the first candidate realization of a ``best-possible\u27\u27 copy-protection scheme for all polynomial-time functionalities. Our techniques deviate significantly from previous works on quantum obfuscation. We develop several novel technical tools which we expect to be broadly useful in quantum cryptography. These tools include a publicly-verifiable, linearly-homomorphic quantum authentication scheme with classically-decodable ZX measurements (which we build from coset states), and a method for compiling any quantum circuit into a linear + measurement (\LM) quantum program: an alternating sequence of CNOT operations and partial ZX measurements