### Abstract

In this note we revisit the famous result of Shannon [Sha49] stating that any encryption scheme with perfect security against computationally unbounded attackers must have a secret key as long as the message. This result motivated the introduction of modern encryption schemes, which are secure only against a computationally bounded attacker, and allow some small (negligible) advantage to such an attacker. It is a well known folklore that both such relaxations - limiting the power of the attacker and allowing for some small advantage - are necessary to overcome Shannon's result. To our surprise, we could not find a clean and well documented proof of this folklore belief. (In fact, two proofs are required, each showing that only one of the two relaxations above is not sufficient.) Most proofs we saw either made some limiting assumptions (e.g., encryption is deterministic), or proved a much more complicated statement (e.g., beating Shannon's bound implies the existence of one-way functions [IL89].)

Original language | English (US) |
---|---|

Title of host publication | Information Theoretic Security - 6th International Conference, ICITS 2012, Proceedings |

Pages | 100-110 |

Number of pages | 11 |

Volume | 7412 LNCS |

DOIs | |

State | Published - 2012 |

Event | 6th International Conference on Information Theoretic Security, ICITS 2012 - Montreal, QC, Canada Duration: Aug 15 2012 → Aug 17 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 7412 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 6th International Conference on Information Theoretic Security, ICITS 2012 |
---|---|

Country | Canada |

City | Montreal, QC |

Period | 8/15/12 → 8/17/12 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Information Theoretic Security - 6th International Conference, ICITS 2012, Proceedings*(Vol. 7412 LNCS, pp. 100-110). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7412 LNCS). https://doi.org/10.1007/978-3-642-32284-6_6

**Shannon impossibility, revisited.** / Dodis, Yevgeniy.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Information Theoretic Security - 6th International Conference, ICITS 2012, Proceedings.*vol. 7412 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7412 LNCS, pp. 100-110, 6th International Conference on Information Theoretic Security, ICITS 2012, Montreal, QC, Canada, 8/15/12. https://doi.org/10.1007/978-3-642-32284-6_6

}

TY - GEN

T1 - Shannon impossibility, revisited

AU - Dodis, Yevgeniy

PY - 2012

Y1 - 2012

N2 - In this note we revisit the famous result of Shannon [Sha49] stating that any encryption scheme with perfect security against computationally unbounded attackers must have a secret key as long as the message. This result motivated the introduction of modern encryption schemes, which are secure only against a computationally bounded attacker, and allow some small (negligible) advantage to such an attacker. It is a well known folklore that both such relaxations - limiting the power of the attacker and allowing for some small advantage - are necessary to overcome Shannon's result. To our surprise, we could not find a clean and well documented proof of this folklore belief. (In fact, two proofs are required, each showing that only one of the two relaxations above is not sufficient.) Most proofs we saw either made some limiting assumptions (e.g., encryption is deterministic), or proved a much more complicated statement (e.g., beating Shannon's bound implies the existence of one-way functions [IL89].)

AB - In this note we revisit the famous result of Shannon [Sha49] stating that any encryption scheme with perfect security against computationally unbounded attackers must have a secret key as long as the message. This result motivated the introduction of modern encryption schemes, which are secure only against a computationally bounded attacker, and allow some small (negligible) advantage to such an attacker. It is a well known folklore that both such relaxations - limiting the power of the attacker and allowing for some small advantage - are necessary to overcome Shannon's result. To our surprise, we could not find a clean and well documented proof of this folklore belief. (In fact, two proofs are required, each showing that only one of the two relaxations above is not sufficient.) Most proofs we saw either made some limiting assumptions (e.g., encryption is deterministic), or proved a much more complicated statement (e.g., beating Shannon's bound implies the existence of one-way functions [IL89].)

UR - http://www.scopus.com/inward/record.url?scp=84865034944&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865034944&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-32284-6_6

DO - 10.1007/978-3-642-32284-6_6

M3 - Conference contribution

AN - SCOPUS:84865034944

SN - 9783642322839

VL - 7412 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 100

EP - 110

BT - Information Theoretic Security - 6th International Conference, ICITS 2012, Proceedings

ER -