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

Digital signatures are a core enabling technology for the automation and digitization of business and government processes. Despite the slow progress in their use for non-repudiation services, there is little doubt that in a few years digital signatures will be a key mechanism in digital business applications.

Intrinsic Limitations of Digital Signatures and How to Cope with Them

The problem of factoring integers in polynomial time with the help of an infinitely powerful oracle who answers arbitrary questions with yes or no is considered. The goal is to minimize the number of oracle questions. LetN be a given compositen-bit integer to be factored, wheren = ⌈log2N⌉. The trivial method of asking for the bits of the smallest prime factor ofN requiresn/2 questions in the worst case. A non-trivial algorithm of Rivest and Shamir requires onlyn/3 questions for the special case whereN is the product of twon/2-bit primes. In this paper, a polynomial-time oracle factoring algorithm for general integers is presented which, for any e>0, asks at most en oracle questions for sufficiently largeN, thus solving an open problem posed by Rivest and Shamir. Based on a plausible conjecture related to Lenstra's conjecture on the running time of the elliptic curve factoring algorithm, it is shown that the algorithm fails with probability at mostN−e/2 for all sufficiently largeN.

On the oracle complexity of factoring integers

Computational indistinguishability amplification is the problem of strengthening cryptographic primitives whose security is defined by bounding the distinguishing advantage of an efficient distinguisher. Examples include pseudorandom generators (PRGs), pseudorandom functions (PRFs), and pseudorandom permutations (PRPs). The literature on computational indistinguishability amplification consists only of few isolated results. Yao’s XOR-lemma implies, by a hybrid argument, that no efficient distinguisher has advantage better than (roughly) n2m−1δm in distinguishing the XOR of m independent n-bit PRG outputs S1, . . . , Sm from uniform randomness if no efficient distinguisher has advantage more than δ in distinguishing Si from a uniform n-bit string. The factor 2m−1 allows for security amplification only if δ < 12 : For the case of PRFs, a random-offset XOR-construction of Myers was the first result to achieve strong security amplification, i.e., also for 12 ≤ δ < 1. This paper proposes a systematic treatment of computational indistinguishability amplification. We generalize and improve the above product theorem for the XOR of PRGs along five axes. First, we prove the tight information-theoretic bound 2m−1δm (without factor n) also for the computational setting. Second, we prove results for interactive systems (e.g. PRFs or PRPs). Third, we consider the general class of neutralizing combination constructions, not just XOR. As an application, this yields the first indistinguishability amplification results for the cascade of PRPs (i.e., block ciphers) converting a weak PRP into an arbitrarily strong PRP, both for single-sided and two-sided queries. Fourth, strong security amplification is achieved for a subclass of neutralizing constructions which includes as a special case the construction of Myers. As an application we obtain highly practical optimal security amplification for block ciphers, simply by adding random offsets at the input and output of the cascade. Fifth, we show strong security amplification also for weakened assumptions like security against random-input (as opposed to chosen-input) attacks. A key technique is a generalization of Yao’s XOR-lemma to (interactive) systems, which is of independent interest. ∗An extended abstract of this paper appears in the proceedings of CRYPTO 2009. This is the full version.

/pdf/computational-indistinguishability-amplification-tight-51qoikx6b5.pdf

Computational Indistinguishability Amplification: Tight Product Theorems for System Composition.

Extracting essentially uniform randomness from a somewhat random source X is a crucial operation in various applications, in particular in cryptography where an adversary usually possesses some partial information about X. In this paper we formalize and study the most general form of extracting randomness in such a cryptographic setting. Our notion of strong extractors captures in particular the case where the catalyst randomness is neither uniform nor independent of the actual extractor input. This is for example important for privacy amplification, where a uniform cryptographic key is generated by Alice and Bob sharing some partially secret information X by exchanging a catalyst R over an insecure channel accessible to an adversary Eve. Here the authentication information for R creates, from Eve's viewpoint, a dependence between X and R. We provide explicit constructions for this setting based on strong blenders. In addition, we give strong deterministic randomness extractors for lists of random variables, where only an unknown subset of the variables is required to have some amount of min-entropy.

Generalized strong extractors and deterministic privacy amplification

Composable security definitions, at times called simulation-based definitions, provide strong security guarantees that hold in any context. However, they are also met with some skepticism due to many impossibility results; goals such as commitments and zero-knowledge that are achievable in a stand-alone sense were shown to be unachievable composably (without a setup) since provably no efficient simulator exists. In particular, in the context of adaptive security, the so-called “simulator commitment problem” arises: once a party gets corrupted, an efficient simulator is unable to be consistent with its pre-corruption outputs. A natural question is whether such impossibility results are unavoidable or only artifacts of frameworks being too restrictive.

Overcoming Impossibility Results in Composable Security Using Interval-Wise Guarantees

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