Quantum statistical mechanics of encryption: reaching the speed limit of classical block ciphers

• URL: http://arxiv.org/abs/2011.06546v3
• Date: Sun, 6 Mar 2022 16:28:12 GMT
• Title: Quantum statistical mechanics of encryption: reaching the speed limit of classical block ciphers
• Authors: Claudio Chamon, Eduardo R. Mucciolo, and Andrei E. Ruckenstein
• Abstract summary: We cast encryption via classical block ciphers in terms of operator spreading in a dual space of Pauli strings. We quantify the quality of ciphers using measures of delocalization in string space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We cast encryption via classical block ciphers in terms of operator spreading in a dual space of Pauli strings, a formulation which allows us to characterize classical ciphers by using tools well known in the analysis of quantum many-body systems. We connect plaintext and ciphertext attacks to out-of-time order correlators (OTOCs) and quantify the quality of ciphers using measures of delocalization in string space such as participation ratios and corresponding entropies obtained from the wave function amplitudes in string space. The saturation of the string-space information entropy is accompanied by the vanishing of OTOCs. Together these signal irreversibility and chaos, which we take to be the defining properties of good classical ciphers. More precisely, we define a good cipher by requiring that the OTOCs vanish to exponential precision and that the string entropies saturate to the values associated with a random permutation, which are computed explicitly in the paper. We argue that these conditions can be satisfied by $n$-bit block ciphers implemented via random reversible circuits with ${\cal O}(n \log n)$ gates arranged on a tree structure, with layers of $n/3$ 3-bit gates, for which a "key" specifies uniquely the sequence of gates that comprise the circuit. We show that in order to reach this "speed limit" one must employ a three-stage circuit consisting of a stage implemented by layers of nonlinear gates that proliferate the number of strings, flanked by two other stages, each deploying layers of a special set of linear "inflationary" gates that accelerate the growth of small individual strings. A shallow, ${\cal O}(\log n)$-depth cipher of the type described here can be used in constructing a polynomial-overhead scheme for computation on encrypted data proposed in another publication as an alternative to Homomorphic Encryption.

Related papers

• Deterministic identification over channels with finite output: a dimensional perspective on superlinear rates [53.66705737169404]
  We consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets. Our main findings are that the maximum number of messages thus identifiable scales super-exponentially as $2R,nlog n$ with the block length $n$. Results are shown to generalise directly to classical-quantum channels with finite-dimensional output quantum system.
  arXiv  Detail & Related papers  (2024-02-14T11:59:30Z)
• Exact Homomorphic Encryption [0.0]
  This article proposes a framework dubbed Exact Homomorphic Encryption, EHE, enabling exact computations on encrypted data without the need for pre-decryption. Two fundamental traits of quantum gates, invertibility and the noncommutativity, establish the success of EHE.
  arXiv  Detail & Related papers  (2024-01-17T07:48:52Z)
• Publicly-Verifiable Deletion via Target-Collapsing Functions [81.13800728941818]
  We show that targetcollapsing enables publiclyverifiable deletion (PVD) We build on this framework to obtain a variety of primitives supporting publiclyverifiable deletion from weak cryptographic assumptions.
  arXiv  Detail & Related papers  (2023-03-15T15:00:20Z)
• Encryption with Quantum Public Keys [1.7725414095035827]
  We study the question of building quantum public-key encryption schemes from one-way functions and even weaker assumptions. We propose three schemes for quantum public-key encryption from one-way functions, pseudorandom function-like states with proof of deletion and pseudorandom function-like states, respectively.
  arXiv  Detail & Related papers  (2023-03-09T16:17:19Z)
• Revocable Cryptography from Learning with Errors [61.470151825577034]
  We build on the no-cloning principle of quantum mechanics and design cryptographic schemes with key-revocation capabilities. We consider schemes where secret keys are represented as quantum states with the guarantee that, once the secret key is successfully revoked from a user, they no longer have the ability to perform the same functionality as before.
  arXiv  Detail & Related papers  (2023-02-28T18:58:11Z)
• Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption [19.014535120129345]
  Quantum homomorphic encryption allows computation by a server directly on encrypted data. For such constructions to be possible, quantum homomorphic encryption must satisfy two privacy properties. Our work unravels fundamental trade-offs between circuit privacy, data privacy and correctness for a broad family of quantum homomorphic encryption protocols.
  arXiv  Detail & Related papers  (2022-05-24T15:02:34Z)
• A Variational Quantum Attack for AES-like Symmetric Cryptography [69.80357450216633]
  We propose a variational quantum attack algorithm (VQAA) for classical AES-like symmetric cryptography. In the VQAA, the known ciphertext is encoded as the ground state of a Hamiltonian that is constructed through a regular graph.
  arXiv  Detail & Related papers  (2022-05-07T03:15:15Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Quantum Fully Homomorphic Encryption by Integrating Pauli One-time Pad with Quaternions [4.182969308816531]
  Quantum fully homomorphic encryption (QFHE) allows to evaluate quantum circuits on encrypted data. We present a novel QFHE scheme, which extends Pauli one-time pad encryption by relying on the quaternion of SU(2).
  arXiv  Detail & Related papers  (2020-12-08T04:54:02Z)
• A quantum encryption design featuring confusion, diffusion, and mode of operation [0.0]
  We propose a non-OTP quantum encryption scheme utilizing a quantum state creation process to encrypt messages. As essentially a non-OTP quantum block cipher the method stands out against existing methods with the following features.
  arXiv  Detail & Related papers  (2020-10-06T22:23:30Z)
• Backflash Light as a Security Vulnerability in Quantum Key Distribution Systems [77.34726150561087]
  We review the security vulnerabilities of quantum key distribution (QKD) systems. We mainly focus on a particular effect known as backflash light, which can be a source of eavesdropping attacks.
  arXiv  Detail & Related papers  (2020-03-23T18:23:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.