## Abstract

Motivated by a fundamental paradigm in cryptography, we consider a recent variant of the classic problem of bounding the distinguishing advantage between a random function and a random permutation. Specifically, we consider the problem of deciding whether a sequence of q values was sampled uniformly with or without replacement from [N], where the decision is made by a streaming algorithm restricted to using at most s bits of internal memory. In this work, the distinguishing advantage of such an algorithm is measured by the KL divergence between the distributions of its output as induced under the two cases. We show that for any s = Ω(logN) the distinguishing advantage is upper bounded by O(q · s/N), and even by O(q·s/N logN) when q N1 - ϵ for any constant ϵ > 0 where it is nearly tight with respect to the KL divergence.

Original language | American English |
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Title of host publication | 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 858-863 |

Number of pages | 6 |

ISBN (Electronic) | 9781728164328 |

DOIs | |

State | Published - Jun 2020 |

Event | 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2020-June |

ISSN (Print) | 2157-8095 |

### Conference

Conference | 2020 IEEE International Symposium on Information Theory, ISIT 2020 |
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Country/Territory | United States |

City | Los Angeles |

Period | 21/07/20 → 26/07/20 |

### Bibliographical note

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