Post quantum is a general name to all the techniques which are safe against the quantum computer attack. The wireless network is one of the most important means of communication. Wireless network security is a top priority. Wireless networks use conventional cryptography, which has various flaws, whereas quantum cryptography claims to be completely secure. It wasn't long after quantum computers became operational that people began to think about new ways to secure electronic communications. After considering all of the weaknesses in conventional cryptosystems, individuals began to look for new ways to secure electronic communications. Traditional cryptography has many problems, but quantum cryptography addresses nearly all of them.Post quantum is a general name to all the techniques which are safe against the quantum computer attack. The wireless network is one of the most important means of communication. Wireless network security is a top priority. Wireless networks use conventional cryptography, which has various flaws, whereas quantum cryptography claims to be completely secure. It wasn't long after quantum computers became operational that people began to think about new ways to secure electronic communications. After considering all of the weaknesses in conventional cryptosystems, individuals began to look for new ways to secure electronic communications. Traditional cryptography has many problems, but quantum cryptography addresses nearly all of them.

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Cryptography from One-Way Communication: On Completeness of Finite Channels

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Exponential Separation of Quantum and Classical One-Way Numbers-on-Forehead Communication

Guangxu Yang, Jiapeng Zhang

Numbers-on-Forehead (NOF) communication model is a central model in communication complexity. As a restricted variant, one-way NOF model is of particular interest. Establishing strong one-way NOF lower bounds would imply circuit lower bounds, resolve well-known problems in additive combinatorics, and yield wide-ranging applications in areas such as cryptography and distributed computing. However, proving strong lower bounds in one-way NOF communication remains highly challenging; many fundamental questions in one-way NOF communication remain wide open. One of the fundamental questions, proposed by Gavinsky and Pudlák (CCC 2008), is to establish an explicit exponential separation between quantum and classical one-way NOF communication. In this paper, we resolve this open problem by establishing the first exponential separation between quantum and randomized communication complexity in one-way NOF model. Specifically, we define a lifted variant of the Hidden Matching problem of Bar-Yossef, Jayram, and Kerenidis (STOC 2004) and show that it admits an ( $O(\log n)$ )-cost quantum protocol in the one-way NOF setting. By contrast, we prove that any $k$ -party one-way randomized protocol for this problem requires communication $Ω(\frac{n^{1/3}}{2^{k/3}})$ . Notably, our separation applies even to a generalization of $k$ -player one-way communication, where the first player speaks once, and all other $k-1$ players can communicate freely.Numbers-on-Forehead (NOF) communication model is a central model in communication complexity. As a restricted variant, one-way NOF model is of particular interest. Establishing strong one-way NOF lower bounds would imply circuit lower bounds, resolve well-known problems in additive combinatorics, and yield wide-ranging applications in areas such as cryptography and distributed computing. However, proving strong lower bounds in one-way NOF communication remains highly challenging; many fundamental questions in one-way NOF communication remain wide open. One of the fundamental questions, proposed by Gavinsky and Pudlák (CCC 2008), is to establish an explicit exponential separation between quantum and classical one-way NOF communication. In this paper, we resolve this open problem by establishing the first exponential separation between quantum and randomized communication complexity in one-way NOF model. Specifically, we define a lifted variant of the Hidden Matching problem of Bar-Yossef, Jayram, and Kerenidis (STOC 2004) and show that it admits an ($O(\log n)$)-cost quantum protocol in the one-way NOF setting. By contrast, we prove that any $k$-party one-way randomized protocol for this problem requires communication $Ω(\frac{n^{1/3}}{2^{k/3}})$. Notably, our separation applies even to a generalization of $k$-player one-way communication, where the first player speaks once, and all other $k-1$ players can communicate freely.

quant-pharXiv:2603.22795Mar 25, 20260 citations

Cryptographic Protocols

WORLD SCIENTIFIC eBooksDec 11, 20200 citations

O(\log n)

)-cost quantum protocol in the one-way NOF setting. By contrast, we prove that any

k

-party one-way randomized protocol for this problem requires communication

Ω(\frac{n^{1/3}}{2^{k/3}})

. Notably, our separation applies even to a generalization of

k

-player one-way communication, where the first player speaks once, and all other

k-1

players can communicate freely.