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Lectures on classical and quantum cryptography. Contents: Private key cryptosystems. Elements of number theory. Public key cryptography and RSA cryptosystem. Shannon`s entropy and mutual information. Entropic uncertainty relations. The no…

Quantum Physics · Physics 2007-07-13 I. V. Volovich , Ya. I. Volovich

Quantum no-cloning theorem gives rise to the intriguing possibility of quantum copy protection where we encode a program or functionality in a quantum state such that a user in possession of k copies cannot create k+1 copies, for any k.…

Cryptography and Security · Computer Science 2024-11-06 Alper Çakan , Vipul Goyal

The phenomenon of quantum erasure has long intrigued physicists, but has surprisingly found limited practical application. Here, we propose an erasure-based protocol for quantum key distribution (QKD) that promises inherent security against…

Quantum Physics · Physics 2016-05-24 Hatim Salih

The capacity of the quantum dense key distribution (QDKD) [Phys. Rev. A69, 032310 (2004)] is doubled by introducing the dense coding. The security of the improved QDKD against eavesdropping is pointed out to be easily proven. In both the…

Quantum Physics · Physics 2007-05-23 Z. J. Zhang , Z. X. Man

We investigate quantum authentication schemes constructed from quantum error-correcting codes. We show that if the code has a property called purity testing, then the resulting authentication scheme guarantees the integrity of ciphertexts,…

Quantum Physics · Physics 2018-04-09 Yfke Dulek , Florian Speelman

Authentication provides the trust people need to engage in transactions. The advent of physical keys that are impossible to copy promises to revolutionize this field. Up to now, such keys have been verified by classical challenge-response…

We present the first leveled fully homomorphic encryption scheme for quantum circuits with classical keys. The scheme allows a classical client to blindly delegate a quantum computation to a quantum server: an honest server is able to run…

Quantum Physics · Physics 2023-12-11 Urmila Mahadev

Public-key cryptography has become a popular way to motivate the teaching of concepts in elementary number theory, abstract algebra, and introduction to proof courses, as well as in cryptography courses. Unfortunately, many experts expect…

History and Overview · Mathematics 2022-10-11 Joshua Holden

We show that encrypted cloning of unknown quantum states is possible. Any number of encrypted clones of a qubit can be created through a unitary transformation, and each of the encrypted clones can be decrypted through a unitary…

Quantum Physics · Physics 2026-01-16 Koji Yamaguchi , Achim Kempf

These lecture notes have been written for courses given at \'Ecole normale sup\'erieure de Lyon and summer school 2022 in post-quantum cryptography that took place in the university of Budapest. Our objective is to give a general…

Cryptography and Security · Computer Science 2023-04-10 Thomas Debris-Alazard

The McEliece public-key encryption scheme has become an interesting alternative to cryptosystems based on number-theoretical problems. Differently from RSA and ElGa- mal, McEliece PKC is not known to be broken by a quantum computer.…

Cryptography and Security · Computer Science 2012-06-04 Nico Döttling , Rafael Dowsley , Jörn Müller-Quade , Anderson C. A. Nascimento

Publicly-verifiable quantum money has been a central and challenging goal in quantum cryptography. To this day, no constructions exist based on standard assumptions. In this study, we propose an alternative notion called quantum cheques…

Quantum Physics · Physics 2024-04-19 Mohammed Barhoush , Louis Salvail

We introduce a simple, practical approach with probabilistic information-theoretic security to solve one of quantum key distribution's major security weaknesses: the requirement of an authenticated classical channel to prevent…

Quantum Physics · Physics 2009-08-27 Travis R. Beals , Kevin P. Hynes , Barry C. Sanders

Post-quantum cryptography studies the security of classical, i.e. non-quantum cryptographic protocols against quantum attacks. Until recently, the considered adversaries were assumed to use quantum computers and behave like classical…

Cryptography and Security · Computer Science 2013-07-16 Maria Velema

We study the practical effectiveness of privacy amplification for classical key-distribution schemes. We find that in contrast to quantum key distribution schemes, the high fidelity of the raw key generated in classical systems allow the…

Cryptography and Security · Computer Science 2015-03-17 Tamas Horvath , Laszlo B. Kish , Jacob Scheuer

Quantum computing threatens the security foundations of consumer electronics (CE). Preparing the diverse CE ecosystem, particularly resource-constrained devices, for the post-quantum era requires quantitative understanding of…

Cryptography and Security · Computer Science 2025-06-16 Daniel Commey , Benjamin Appiah , Griffith S. Klogo , Winful Bagyl-Bac , James D. Gadze , Yousef Alsenani , Garth V. Crosby

A classical obfuscator for quantum circuits is a classical program that, given the classical description of a quantum circuit $Q$, outputs the classical description of a functionally equivalent quantum circuit $\hat{Q}$ that hides as much…

Quantum Physics · Physics 2026-01-14 James Bartusek , Aparna Gupte , Saachi Mutreja , Omri Shmueli

We prove unconditional security for a quantum key distribution (QKD) protocol based on distilling pbits (twisted ebits) [quant-ph/0309110] from an arbitrary untrusted state that is claimed to contain distillable key. Our main result is that…

Quantum Physics · Physics 2016-11-18 Karol Horodecki , Michal Horodecki , Pawel Horodecki , Debbie Leung , Jonathan Oppenheim

Privacy amplification (PA) is an indispensable component in classical and quantum cryptography. Error correction (EC) and data compression (DC) algorithms are also indispensable in classical and quantum information theory. We here study…

Quantum Physics · Physics 2022-02-01 Toyohiro Tsurumaru

We present a quantum digital signature scheme whose security is based on fundamental principles of quantum physics. It allows a sender (Alice) to sign a message in such a way that the signature can be validated by a number of different…

Quantum Physics · Physics 2007-05-23 Daniel Gottesman , Isaac Chuang