Computational security in cryptography has a risk that computational assumptions underlying the security are broken in the future. One solution is to construct information-theoretically-secure protocols, but many cryptographic primitives are known to be impossible (or unlikely) to have information-theoretical security even in the quantum world. A nice compromise (intrinsic to quantum) is certified everlasting security, which roughly means the following. A receiver with possession of quantum encrypted data can issue a certificate that shows that the receiver has deleted the encrypted data. If the certificate is valid, the security is guaranteed even if the receiver becomes computationally unbounded. Although several cryptographic primitives, such as commitments and zero-knowledge, have been made certified everlasting secure, there are many other important primitives that are not known to be certified everlasting secure. In this paper, we introduce certified everlasting FE. In this primitive, the receiver with the ciphertext of a message m and the functional decryption key of a function f can obtain f(m) and nothing else. The security holds even if the adversary becomes computationally unbounded after issuing a valid certificate. We, first, construct certified everlasting FE for P/poly circuits where only a single key query is allowed for the adversary. We, then, extend it to q-bounded one for NC1 circuits where q-bounded means that q key queries are allowed for the adversary with an a priori bounded polynomial q. For the construction of certified everlasting FE, we introduce and construct certified everlasting versions of secret-key encryption, public-key encryption, receiver non-committing encryption, and a garbling scheme, which are of independent interest.
Computational security in cryptography has a risk that computational assumptions underlying the security are broken in the future. One solution is to construct information-theoretically-secure protocols, but many cryptographic primitives are known to be impossible (or unlikely) to have information-theoretical security even in the quantum world. A nice compromise (intrinsic to quantum) is certified everlasting security, which roughly means the following. A receiver with possession of quantum encrypted data can issue a certificate that shows that the receiver has deleted the encrypted data. If the certificate is valid, the security is guaranteed even if the receiver becomes computationally unbounded. Although several cryptographic primitives, such as commitments and zero-knowledge, have been made certified everlasting secure, there are many other important primitives that are not known to be certified everlasting secure. In this paper, we introduce certified everlasting FE. In this primitive, the receiver with the ciphertext of a message m and the functional decryption key of a function f can obtain f(m) and nothing else. The security holds even if the adversary becomes computationally unbounded after issuing a valid certificate. We, first, construct certified everlasting FE for P/poly circuits where only a single key query is allowed for the adversary. We, then, extend it to q-bounded one for NC1 circuits where q-bounded means that q key queries are allowed for the adversary with an a priori bounded polynomial q. For the construction of certified everlasting FE, we introduce and construct certified everlasting versions of secret-key encryption, public-key encryption, receiver non-committing encryption, and a garbling scheme, which are of independent interest.
Functional encryption is a powerful cryptographic primitive that enables fine-grained access to encrypted data and underlies numerous applications. Although the ideal security notion for FE, simulation security, has been shown to be impossible in the plain classical setting, those impossibility results rely on inherently classical arguments. This raises a fundamental question: can simulation-secure FE be realized in the quantum regime or in alternative models?
We resolve both directions of this question. On the negative side, we show that the classical impossibility results largely extend to the quantum setting. When the adversary can submit an unbounded number of challenge messages, we establish an unconditional impossibility, matching the classical barrier. In the case where the adversary may obtain many functional keys, classical arguments only yield impossibility under the assumption of pseudorandom functions; we strengthen this by proving impossibility under the potentially weaker assumption of pseudorandom quantum states. We additionally give an independent impossibility based solely on public-key encryption with classical public-keys. Since public-key encryption is not known to imply pseudorandom states, this yields complementary evidence of the barrier and, in particular, establishes unconditional impossibility of public-key functional encryption with classical public-keys. A key technical ingredient in our proofs is a novel incompressibility property for pseudorandom states, which may be of independent interest.
On the positive side, we show how to circumvent these fundamental barriers in memory-restricted models, where the adversary's quantum or classical memory is bounded. In this setting, we obtain new feasibility results for simulation-secure FE that allow many challenge ciphertexts or many functional key queries.
Functional encryption (FE) is a versatile paradigm that enables fine-grained access control over encrypted data. Despite its potential, achieving the gold standard of simulation-based security for FE is impossible in full generality. Known impossibility results demonstrate that simulation security cannot be attained if an adversary in the security experiment is permitted either an unbounded number of functional key queries or an unbounded number of challenge ciphertexts. In this work, we circumvent these fundamental barriers by considering two distinct memory-restricted settings: the Bounded Quantum Storage Model and the Bounded Classical Storage Model. In these settings, the plain model impossibility results no longer apply, allowing us to obtain new positive results. Specifically, we construct two adaptively simulation-secure FE schemes in the Bounded Quantum Storage Model: 1) Many functional key scheme: A construction supporting many functional key queries and a single challenge ciphertext, assuming only the existence of one-way functions. 2) Many ciphertext scheme: An information-theoretic secure construction supporting a single non-adaptive functional key, many challenge ciphertexts, and many adaptive functional key queries. Furthermore, we demonstrate that both schemes can be ported to the Bounded Classical Storage Model, assuming the existence of disappearing grey-box obfuscation.
We address the problem of the-security of cryptographic protocols in face of future advances in computing technology and algorithmic research. The problem stems from the fact may be deemed that computations which at a given point in time may be deemed infeasible, can, in the course of years or decades, be made possible with improved hardware and/or breakthroughs in code-breaking algorithms. In such cases, the security of historical , but nonetheless highly confidential data may be in jeopardy. We present a scheme for efficient secure two-party communication with provable everlasting security. The security is guaranteed in face of any future technological advances, given the current state of of the art. Furthermore, the security of the messages is also guaranteed even if the secret encryption/decryption key is revealed in the future, The scheme is based on the bounded storage model and provides information-theoretic security in this model. The bounded storage model postulates an adversary who is computationally unbounded, and is only bounded in the amount of storage (not computation space) available to store the output of his computation. The bound on the storage can be arbitrarily large (e.g., 100 Tbytes), as long as it is fixed. Given this storage bound, our protocols guarantee that even a computationally all powerful adversary gains no information about a message (except with a probability that is exponentially small in the security parameter k). The bound on storage space need only hold at the time of the message transmission. Thereafter, no additional storage space or, computational power can help the adversary in deciphering the message. We present two protocols. The first protocol, which elaborates on the autoregressive (AR) protocol of Aumann and Rabin (see Advances in Cryptology-Crypto '99, p. 65-79, 1999), employs a short secret key whose size is independent of the length of the message, but uses many public random bits. The second protocol uses an optimal number of public random bits, but employs a longer secret key. Our proof of security utilizes a novel linear algebraic technique.
In recent years, there has been great interest in Functional Encryption (FE), a generaliza-tion of traditional encryption where a token enables a user to learn a specific function of the encrypted data and nothing else. In this paper we put forward a new generalization of FE that we call M ergeable FE (mFE). In a mFE system, given a ciphertext c1 encrypting m1 and a ciphertext c2 encrypting m2, it is possible to produce in an oblivious way (i.e., given only the public-key and without knowledge of the messages, master secret-key or any other aux-iliary information) a ciphertext encrypting the string m1||m2 under the security constraint that this new ciphertext does not leak more information about the original messages than what may be leaked from the new ciphertext using the tokens. For instance, suppose that the adversary is given the token for the function f(·) defined so that for strings x ∈ {0, 1}n, f(x) 4 = g(x) for some function g: {0, 1}n → {0, 1} and for strings y = (x1||x2) ∈ {0, 1}2n, f(x1||x2) 4 = g(x1) ∨ g(x2). Furthermore, suppose that the adversary gets a ciphertext c
In a functional encryption (FE) scheme, a user that holds a ciphertext and a function-key can learn the result of applying the function to the plaintext message. Security requires that the user does not learn anything beyond the function evaluation. We extend this notion to the quantum setting by providing definitions and a construction for a quantum functional encryption (QFE) scheme which allows for the evaluation of polynomially-sized circuits on arbitrary quantum messages. Our construction is built upon quantum garbled circuits [BY20]. We also investigate the relationship of QFE to the seemingly unrelated notion of unclonable encryption (UE) and find that any QFE scheme universally achieves the property of unclonable functional encryption (UFE). In particular we assume the existence of an unclonable encryption scheme with quantum decryption keys which was recently constructed by [AKY24]. Our UFE guarantees that two parties cannot simultaneously recover the correct function outputs using two independently sampled function secret keys. As an application we give the first construction for public-key UE with variable decryption keys. Lastly, we establish a connection between quantum indistinguishability obfuscation (qiO) and quantum functional encryption (QFE); showing that any multi-input indistinguishability-secure quantum functional encryption scheme unconditionally implies the existence of qiO.
We present a unified framework for upgrading a broad class of cryptographic primitives to support constant-rate certified deletion. Previous constructions require a linear number of qubits per encrypted bit of certified-deletable plaintext. In contrast, we obtain the first constant-rate constructions in the plain model that achieve certified deletion while preserving everlasting security.
Our approach applies to a wide range of "all-or-nothing"-type primitives based on BB84-style encodings, including commitment schemes, public-key encryption, attribute-based encryption, and fully homomorphic encryption. Beyond this class, we also obtain constant-rate certified deletion for primitives built from subspace coset states, such as blind delegation, secure software leasing, functional encryption, and differing-inputs iO, and CCA-PKE. Importantly, our framework does not introduce any additional assumptions beyond those required by the underlying certified deletion primitives.
Finally, under the hardness of SIS, we show that public verifiability can be incorporated into BB84- and coset-based certified deletion. In combination with our constant-rate constructions, this yields publicly verifiable certified deletion schemes with constant rate.