In this paper we consider an application of the recently proposed quantum hashing technique for computing Boolean functions in the quantum communication model. The combination of binary functions on non-binary quantum hash function is done via polynomial presentation, which we have called a characteristic of a Boolean function. Based on the characteristic polynomial presentation of Boolean functions and quantum hashing technique we present a method for computing Boolean functions in the quantum one-way communication model, where one of the parties performs his computations and sends a message to the other party, who must output the result after his part of computations. Some of the results are also true in a more restricted Simultaneous Message Passing model with no shared resources, in which communicating parties can interact only via the referee. We give several examples of Boolean functions whose polynomial presentations have specific properties allowing for construction of quantum communication protocols that are provably exponentially better than classical ones in the simultaneous message passing setting.In this paper we consider an application of the recently proposed quantum hashing technique for computing Boolean functions in the quantum communication model. The combination of binary functions on non-binary quantum hash function is done via polynomial presentation, which we have called a characteristic of a Boolean function. Based on the characteristic polynomial presentation of Boolean functions and quantum hashing technique we present a method for computing Boolean functions in the quantum one-way communication model, where one of the parties performs his computations and sends a message to the other party, who must output the result after his part of computations. Some of the results are also true in a more restricted Simultaneous Message Passing model with no shared resources, in which communicating parties can interact only via the referee. We give several examples of Boolean functions whose polynomial presentations have specific properties allowing for construction of quantum communication protocols that are provably exponentially better than classical ones in the simultaneous message passing setting.

arXiv:1312.1661Dec 5, 20136 citations

Quantum computing cryptography: Unveiling cryptographic Boolean functions with quantum annealing.

Feng Hu, Lucas Lamata, Mikel Sanz +4 more

As the building block in symmetric cryptography, designing Boolean functions satisfying multiple properties is an important problem in sequence ciphers, block ciphers, and hash functions. However, the search of $n$ -variable Boolean functions fulfilling global cryptographic constraints is computationally hard due to the super-exponential size $\mathcal{O}(2^{2^n})$ of the space. Here, we introduce a codification of the cryptographically relevant constraints in the ground state of an Ising Hamiltonian, allowing us to naturally encode it in a quantum annealer, which seems to provide a quantum speedup. Additionally, we benchmark small $n$ cases in a D-Wave machine, showing its capacity of devising bent functions, the most relevant set of cryptographic Boolean functions. We have complemented it with local search and chain repair to improve the D-Wave quantum annealer performance related to the low connectivity. This work shows how to codify super-exponential cryptographic problems into quantum annealers and paves the way for reaching quantum supremacy with an adequately designed chip.As the building block in symmetric cryptography, designing Boolean functions satisfying multiple properties is an important problem in sequence ciphers, block ciphers, and hash functions. However, the search of $n$-variable Boolean functions fulfilling global cryptographic constraints is computationally hard due to the super-exponential size $\mathcal{O}(2^{2^n})$ of the space. Here, we introduce a codification of the cryptographically relevant constraints in the ground state of an Ising Hamiltonian, allowing us to naturally encode it in a quantum annealer, which seems to provide a quantum speedup. Additionally, we benchmark small $n$ cases in a D-Wave machine, showing its capacity of devising bent functions, the most relevant set of cryptographic Boolean functions. We have complemented it with local search and chain repair to improve the D-Wave quantum annealer performance related to the low connectivity. This work shows how to codify super-exponential cryptographic problems into quantum annealers and paves the way for reaching quantum supremacy with an adequately designed chip.

Jun 22, 20183 citations

Boolean Functions and Quantum Gates

WORLD SCIENTIFIC eBooksFeb 20, 20180 citations

Efficient Algorithms for Quantum Hashing

I. Zinnatullin, Kamil Ravilevich Khadiev

arXiv:2507.07002Lecture notes in computer scienceJan 1, 20264 citations

n

-variable Boolean functions fulfilling global cryptographic constraints is computationally hard due to the super-exponential size

\mathcal{O}(2^{2^n})

of the space. Here, we introduce a codification of the cryptographically relevant constraints in the ground state of an Ising Hamiltonian, allowing us to naturally encode it in a quantum annealer, which seems to provide a quantum speedup. Additionally, we benchmark small

n

cases in a D-Wave machine, showing its capacity of devising bent functions, the most relevant set of cryptographic Boolean functions. We have complemented it with local search and chain repair to improve the D-Wave quantum annealer performance related to the low connectivity. This work shows how to codify super-exponential cryptographic problems into quantum annealers and paves the way for reaching quantum supremacy with an adequately designed chip.