Quantum hashing via ε-universal hashing constructions and Freivalds' fingerprinting schemas

We define the concept of a quantum hash generator and offer a design, which allows one to build a large number of different quantum hash functions. The construction is based on composition of a classical ε-universal hash family and a given family of functions - quantum hash generators. In particular, using the relationship between ε-universal hash families and Freivalds' fingerprinting schemas we present explicit quantum hash function and prove that this construction is optimal with respect to the number of qubits needed for the construction. © 2014 Springer International Publishing

Quantum Hashing for Finite Abelian Groups

We propose a generalization of the quantum hashing technique based on the notion of the small-bias sets. These sets have proved useful in different areas of computer science, and here their properties give an optimal construction for succinct quantum presentation of elements of any finite abelian group, which can be used in various computational and cryptographic scenarios. The known quantum fingerprinting schemas turn out to be the special cases of the proposed quantum hashing for the corresponding abelian group

On Quantum Fingerprinting and Quantum Cryptographic Hashing

Fingerprinting and cryptographic hashing have quite different usages in computer science, but have similar properties. Interpretation of their properties is determined by the area of their usage: fingerprinting methods are methods for constructing efficient randomized and quantum algorithms for computational problems, whereas hashing methods are one of the central cryptographical primitives. Fingerprinting and hashing methods are being developed from the mid of the previous century, whereas quantum fingerprinting and quantum hashing have a short history. In this chapter, we investigate quantum fingerprinting and quantum hashing. We present computational aspects of quantum fingerprinting and quantum hashing and discuss cryptographical properties of quantum hashing

Algebra in Computational Complexity

At its core, much of Computational Complexity is concerned with combinatorial objects and structures. But it has often proven true that the best way to prove things about these combinatorial objects is by establishing a connection to a more well-behaved algebraic setting. Indeed, many of the deepest and most powerful results in Computational Complexity rely on algebraic proof techniques. The Razborov-Smolensky polynomial-approximation method for proving constant-depth circuit lower bounds, the PCP characterization of NP, and the Agrawal-Kayal-Saxena polynomial-time primality test are some of the most prominent examples. The algebraic theme continues in some of the most exciting recent progress in computational complexity. There have been significant recent advances in algebraic circuit lower bounds, and the so-called "chasm at depth 4" suggests that the restricted models now being considered are not so far from ones that would lead to a general result. There have been similar successes concerning the related problems of polynomial identity testing and circuit reconstruction in the algebraic model, and these are tied to central questions regarding the power of randomness in computation. Representation theory has emerged as an important tool in three separate lines of work: the "Geometric Complexity Theory" approach to P vs. NP and circuit lower bounds, the effort to resolve the complexity of matrix multiplication, and a framework for constructing locally testable codes. Coding theory has seen several algebraic innovations in recent years, including multiplicity codes, and new lower bounds. This seminar brought together researchers who are using a diverse array of algebraic methods in a variety of settings. It plays an important role in educating a diverse community about the latest new techniques, spurring further progress

Quantum hashing via ε-universal hashing constructions and Freivalds' fingerprinting schemas

We define the concept of a quantum hash generator and offer a design, which allows one to build a large number of different quantum hash functions. The construction is based on composition of a classical ε-universal hash family and a given family of functions - quantum hash generators. In particular, using the relationship between ε-universal hash families and Freivalds' fingerprinting schemas we present explicit quantum hash function and prove that this construction is optimal with respect to the number of qubits needed for the construction. © 2014 Springer International Publishing

Quantum hashing via ε-universal hashing constructions and Freivalds' fingerprinting schemas

We define the concept of a quantum hash generator and offer a design, which allows one to build a large number of different quantum hash functions. The construction is based on composition of a classical ε-universal hash family and a given family of functions - quantum hash generators. In particular, using the relationship between ε-universal hash families and Freivalds' fingerprinting schemas we present explicit quantum hash function and prove that this construction is optimal with respect to the number of qubits needed for the construction. © 2014 Springer International Publishing

Quantum hashing via ε-universal hashing constructions and Freivalds' fingerprinting schemas

We define the concept of a quantum hash generator and offer a design, which allows one to build a large number of different quantum hash functions. The construction is based on composition of a classical ε-universal hash family and a given family of functions - quantum hash generators. In particular, using the relationship between ε-universal hash families and Freivalds' fingerprinting schemas we present explicit quantum hash function and prove that this construction is optimal with respect to the number of qubits needed for the construction. © 2014 Springer International Publishing

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Actas de las VI Jornadas Nacionales (JNIC2021 LIVE)

Estas jornadas se han convertido en un foro de encuentro de los actores más relevantes en el ámbito de la ciberseguridad en España. En ellas, no sólo se presentan algunos de los trabajos científicos punteros en las diversas áreas de ciberseguridad, sino que se presta especial atención a la formación e innovación educativa en materia de ciberseguridad, y también a la conexión con la industria, a través de propuestas de transferencia de tecnología. Tanto es así que, este año se presentan en el Programa de Transferencia algunas modificaciones sobre su funcionamiento y desarrollo que han sido diseñadas con la intención de mejorarlo y hacerlo más valioso para toda la comunidad investigadora en ciberseguridad