Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

Semi-Finite Length Analysis for Secure Random Number Generation

Masahito Hayashi

Published Jul 1, 2019• 3 citations
Publisher

Abstract

To discuss secure key generation from imperfect random numbers, we address the secure key generation length. There are several studies for its asymptotic expansion up to the order √n or log n. However, these expansions have errors of the order o(√n) or o(log n), which does not go to zero asymptotically. To resolve this problem, we derive the asymptotic expansion up to the constant order for upper and lower bounds of these optimal values. While the expansions of upper and lower bonds do not match, they clarify the ranges of these optimal values, whose errors go to zero asymptotically.

DOI
10.1109/isit.2019.8849241

Related papers

Truly random number generation: an example

Daniela Frauchiger, Renato Renner

Randomness is crucial for a variety of applications, ranging from gambling to computer simulations, and from cryptography to statistics. However, many of the currently used methods for generating randomness do not meet the criteria that are necessary for these applications to work properly and safely. A common problem is that a sequence of numbers may look random but nevertheless not be truly random. In fact, the sequence may pass all standard statistical tests and yet be perfectly predictable. This renders it useless for many applications. For example, in cryptography, the predictability of a randomly" chosen password is obviously undesirable. Here, we review a recently developed approach to generating true | and hence unpredictable | randomness.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 29, 2013•2 citations

Interactive communication for data exchange

Himanshu Tyagi, Pramod Viswanath, Shun Watanabe

Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Furthermore, we propose an interactive protocol for data exchange which increases the communication size in steps until the task is done and matches the performance of our lower bound. Our single-shot analysis applies to all discrete random variables and yields upper and lower bound of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general sequence such as mixture of IID random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for the IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2015•11 citations

Semi-Quantum Random Number Generation

Julia Guskind, Walter O. Krawec

Semi-quantum cryptography involves at least one user who is semi-quantum or “classical” in nature. Such a user can only interact with the quantum channel in a very restricted way. Many semi-quantum key distribution protocols have been developed, some with rigorous proofs of security. Here we show for the first time that quantum random number generation is possible in the semi-quantum setting. We also develop a rigorous proof of security, deriving a bound on the random bit generation rate of the protocol as a function of noise in the channel. Our protocol and proof may be broadly applicable to other quantum and semi-quantum cryptographic scenarios where users are limited in their capabilities.

arXiv:2210.16427•IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 17, 2023•2 citations

Interactive Communication for Data Exchange

Himanshu Tyagi, Pramod Viswanath, Shun Watanabe

Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We propose a new interactive protocol for data exchange which increases the communication size in steps until the task is done. Next, we derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Our single-shot analysis applies to all discrete random variables and yields upper and lower bound of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general sequence such as mixture of IID random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for the IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.

arXiv:1601.03617•Jan 14, 2016•0 citations

Interactive Communication for Data Exchange

Himanshu Tyagi, Pramod Viswanath, Shun Watanabe

Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We propose a new interactive protocol for data exchange, which increases the communication size in steps until the task is done. We also derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Our single-shot analysis applies to all discrete random variables and yields upper and lower bounds of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general source sequence, such as a mixture of independent and identically distributed (IID) random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.

IEEE Transactions on Information Theory•Nov 2, 2017•6 citations

From uniformity to fluctuations: Quantifying the security cost of imperfect randomness in quantum key distribution

Andrei Gaidash, Pavel V. Yakovlev, George P. Miroshnichenko +1 more

Physical Review A•Feb 4, 2026•1 citation
To discuss secure key generation from imperfect random numbers, we address the secure key generation length. There are several studies for its asymptotic expansion up to the order √n or log n. However, these expansions have errors of the order o(√n) or o(log n), which does not go to zero asymptotically. To resolve this problem, we derive the asymptotic expansion up to the constant order for upper and lower bounds of these optimal values. While the expansions of upper and lower bonds do not match, they clarify the ranges of these optimal values, whose errors go to zero asymptotically.
Randomness is crucial for a variety of applications, ranging from gambling to computer simulations, and from cryptography to statistics. However, many of the currently used methods for generating randomness do not meet the criteria that are necessary for these applications to work properly and safely. A common problem is that a sequence of numbers may look random but nevertheless not be truly random. In fact, the sequence may pass all standard statistical tests and yet be perfectly predictable. This renders it useless for many applications. For example, in cryptography, the predictability of a randomly" chosen password is obviously undesirable. Here, we review a recently developed approach to generating true | and hence unpredictable | randomness.
Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Furthermore, we propose an interactive protocol for data exchange which increases the communication size in steps until the task is done and matches the performance of our lower bound. Our single-shot analysis applies to all discrete random variables and yields upper and lower bound of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general sequence such as mixture of IID random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for the IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.
Semi-quantum cryptography involves at least one user who is semi-quantum or “classical” in nature. Such a user can only interact with the quantum channel in a very restricted way. Many semi-quantum key distribution protocols have been developed, some with rigorous proofs of security. Here we show for the first time that quantum random number generation is possible in the semi-quantum setting. We also develop a rigorous proof of security, deriving a bound on the random bit generation rate of the protocol as a function of noise in the channel. Our protocol and proof may be broadly applicable to other quantum and semi-quantum cryptographic scenarios where users are limited in their capabilities.
Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We propose a new interactive protocol for data exchange which increases the communication size in steps until the task is done. Next, we derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Our single-shot analysis applies to all discrete random variables and yields upper and lower bound of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general sequence such as mixture of IID random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for the IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.
Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We propose a new interactive protocol for data exchange, which increases the communication size in steps until the task is done. We also derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Our single-shot analysis applies to all discrete random variables and yields upper and lower bounds of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general source sequence, such as a mixture of independent and identically distributed (IID) random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.