There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

Quantum Computation and Quantum Information

From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Handbook of Applied Cryptography

We propose a fully functional identity-based encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem. Our system is based on the Weil pairing. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.

/pdf/identity-based-encryption-from-the-weil-pairing-sfqdyadlbb.pdf

Identity-Based Encryption from the Weil Pairing

All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory} But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding However, it appeared that this new resource is
very complex and difficult to detect Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon A basic role of entanglement
witnesses in detection of entanglement is emphasized

Quantum entanglement

This paper is concerned with information-theoretically secure secret key agreement in the general scenario where three parties, Alice, Bob, and Eve, know random variables X, Y, and Z, respectively, with joint distribution P xyz , for instance resulting from receiving a sequence of random bits broadcast by a satellite. We consider the problem of determining for a given distribution P xyz whether Alice and Bob can in principle, by communicating over an insecure channel accessible to Eve, generate a secret key about which Eve's information is arbitrarily small. When X, Y, and Z are random variables that result from a binary random variable being sent through three arbitrary independent channels, it is shown that secret key agreement is possible if and only if I(X;Y¦Z) >0, i.e., under the sole condition that X and Y have some (arbitrarily weak) statistical dependence when given Z.

Towards Characterizing When Information-Theoretic Secret Key Agreement Is Possible

The term indistinguishability amplification refers to a setting where a certain construction combines two (or more) cryptographic primitives of the same type to improve their indistinguishability from an ideal primitive Various constructions achieving this property have been studied, both in the information-theoretic and computational setting In the former, a result due to Maurer, Pietrzak and Renner describes the amplification achieved by a very general class of constructions called neutralizing Two types of amplification are observed: a product theorem (bounding the advantage in distinguishing the construction by twice the product of individual advantages) and the amplification of the distinguisher class (the obtained construction is secure against a wider class of distinguishers)

In this paper, we combine these two aspects of information-theoretic indistinguishability amplification We derive a new bound for the general case of a neutralizing construction that keeps the structure of a product theorem, while also capturing the amplification of the distinguisher class This improves both bounds mentioned above

The new technical notion we introduce, central to our analysis, is the notion of free-start distinguishing of systems This describes the setting where the distinguisher is allowed to choose any common state for both systems and then it is supposed to distinguish these systems starting from that chosen state

Free-start distinguishing: combining two types of indistinguishability amplification

Deniable Authentication is a highly desirable property for secure messaging protocols: it allows a sender Alice to authentically transmit messages to a designated receiver Bob in such a way that only Bob gets convinced that Alice indeed sent these messages. In particular, it guarantees that even if Bob tries to convince a (non-designated) party Judy that Alice sent some message, and even if Bob gives Judy his own secret key, Judy will not be convinced: as far as Judy knows, Bob could be making it all up! In this paper we study Deniable Authentication in the setting where Judy can additionally obtain Alice’s secret key. Informally, we want that knowledge of Alice’s secret key does not help Judy in learning whether Alice sent any messages, even if Bob does not have Alice’s secret key and even if Bob cooperates with Judy by giving her his own secret key. This stronger flavor of Deniable Authentication was not considered before and is particularly relevant for Group Messaging as it gives users stronger deniability guarantees. Our main contribution is a scalable “ ” ( ) scheme—a technical formalization of Deniable Authentication that is particularly useful for secure messaging for its confidentiality guarantees—that provides this stronger deniability guarantee. At its core lie new $$\mathrm { M{\textrm{DVS}}}$$ (Multi-Designated Verifier Signature) and $$\text {PKEBC}$$ (Public Key Encryption for Broadcast) scheme constructions: our $$\mathrm { M{\textrm{DVS}}}$$ is not only secure with respect to the new deniability notions, but it is also the first to be tightly secure under standard assumptions; our $$\text {PKEBC}$$ —which is also of independent interest—is the first with ciphertext sizes and encryption and decryption times that grow only linearly in the number of receivers. This is a significant improvement upon the construction given by Maurer et al. (EUROCRYPT ’22), where ciphertext sizes and encryption and decryption times are quadratic in the number of receivers. 

Deniable Authentication when Signing Keys Leak

We study anonymity of probabilistic encryption (pE) and probabilistic authenticated encryption (pAE). We start by providing concise game-based security definitions capturing anonymity for both pE and pAE, and then show that the commonly used notion of indistinguishability from random ciphertexts (IND$) indeed implies the anonymity notions for both pE and pAE. This is in contrast to a recent work of Chan and Rogaway (Asiacrypt 2019), where it is shown that IND$-secure nonce-based authenticated encryption can only achieve anonymity if a sophisticated transformation is applied. Moreover, we also show that the Encrypt-then-MAC paradigm is anonymity-preserving, in the sense that if both the underlying probabilistic MAC (pMAC) and pE schemes are anonymous, then also the resulting pAE scheme is. Finally, we provide a composable treatment of anonymity using the constructive cryptography framework of Maurer and Renner (ICS 2011). We introduce adequate abstractions modeling various kinds of anonymous communication channels for many senders and one receiver in the presence of an active man-in-the-middle adversary. Then we show that the game-based notions indeed are anonymity-preserving, in the sense that they imply constructions between such anonymous channels, thus generating authenticity and/or confidentiality as expected, but crucially retaining anonymity if present.

Anonymous Symmetric-Key Communication

Conditions are derived for the possibility and impossibility of information-theoretic secret-key agreement by public discussion. A new quantity, the intrinsic information, is introduced and its relationship to secret-key agreement is investigated. A new protocol is described that allows secret-key agreement in situations for which previous protocols fail.

The intrinsic conditional mutual information and perfect secrecy

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