Cryptographic Constructions of Randomness Resources

Alex B. Grilo, Álvaro Yángüez

While one-way functions (OWFs) serve as the minimal assumption for computational cryptography in the classical setting, in quantum cryptography, we have even weaker cryptographic assumptions such as pseudo-random states, and EFI pairs, among others. Moreover, the minimal assumption for computational quantum cryptography remains an open question. Recently, it has been shown that pseudoentanglement is necessary for the existence of quantum cryptography (Goulão and Elkouss 2024), but no cryptographic construction has been built from it. In this work, we study the cryptographic usefulness of quantum pseudoresources—a pair of families of quantum states that exhibit a gap in their resource content yet remain computationally indistinguishable. We show that quantum pseudoresources imply a variant of EFI pairs, which we call EPFI pairs, and that these are equivalent to quantum commitments and thus EFI pairs. Our results suggest that, just as randomness is fundamental to classical cryptography, quantum resources may play a similarly crucial role in the quantum setting. Finally, we focus on the specific case of entanglement, analyzing different definitions of pseudoentanglement and their implications for constructing EPFI pairs. Moreover, we propose a new cryptographic functionality that is intrinsically dependent on entanglement as a resource.

Per Austrin, Kai-Min Chung, Mohammad Mahmoody +2 more

Per Austrin, Kai-Min Chung, Mohammad Mahmoody +2 more

Markulf Kohlweiss, Ueli M. Maurer, Cristina Onete +2 more

Abstract. A receiver-anonymous channel allows a sender to send a message to a receiver without an adversary learning for whom the message is intended. Wireless broadcast channels naturally provide receiver anonymity, as does multi-casting one message to a receiver population containing the intended receiver. While anonymity and confidentiality appear to be orthogonal properties, making anonymous communication confidential is more involved than one might expect, since the ciphertext might reveal which public key has been used to encrypt. To address this problem, public-key cryptosystems with enhanced security properties have been proposed. We investigate constructions as well as limitations for preserving receiver anonymity when using public-key encryption (PKE). We use the constructive cryptography approach by Maurer and Renner and interpret cryptographic schemes as constructions of a certain ideal resource (e.g. a confidential anonymous channel) from given real resources (e.g. a broadcast channel). We define appropriate anonymous communication resources and show that a very natural resource can be constructed by using a PKE scheme which fulfills three properties that appear in cryptographic literature (IND-CCA, key-privacy, weak robustness). We also show that a desirable stronger variant, preventing the adversary from selective “trial-deliveries ” of messages, is unfortunately unachievable by any PKE scheme, no matter how strong. The constructive approach makes the guarantees achieved by applying a cryptographic scheme explicit in the constructed (ideal) resource; this specifies the exact requirements for the applicability of a cryptographic scheme in a given context. It also allows to decide which of the existing security properties of such a cryptographic scheme are adequate for the considered scenario, and which are too weak or too strong. Here, we show that weak robustness is necessary but that so-called strong robustness is unnecessarily strong in that it does not construct a (natural) stronger resource.

Carl A. Miller, Yaoyun Shi

Randomness is a vital resource for modern-day information processing, especially for cryptography. A wide range of applications critically rely on abundant, high-quality random numbers generated securely. Here, we show how to expand a random seed at an exponential rate without trusting the underlying quantum devices. Our approach is secure against the most general adversaries, and has the following new features: cryptographic level of security, tolerating a constant level of imprecision in devices, requiring only unit size quantum memory (for each device component) in an honest implementation, and allowing a large natural class of constructions for the protocol. In conjunction with a recent work by Chung et al. [2014], it also leads to robust unbounded expansion using just 2 multipart devices. When adapted for distributing cryptographic keys, our method achieves, for the first time, exponential expansion combined with cryptographic security and noise tolerance. The proof proceeds by showing that the Rényi divergence of the outputs of the protocol (for a specific bounding operator) decreases linearly as the protocol iterates. At the heart of the proof are a new uncertainty principle on quantum measurements and a method for simulating trusted measurements with untrusted devices.

V. I. SERDOBOLSKII