Shannon impossibility, revisited

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationInformation Theoretic Security - 6th International Conference, ICITS 2012, Proceedings
Pages100-110
Number of pages11
Volume7412 LNCS
DOIs
StatePublished - 2012
Event6th International Conference on Information Theoretic Security, ICITS 2012 - Montreal, QC, Canada
Duration: Aug 15 2012Aug 17 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7412 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other6th International Conference on Information Theoretic Security, ICITS 2012
CountryCanada
CityMontreal, QC
Period8/15/128/17/12

Fingerprint

Encryption
Cryptography
Limiting
One-way Function
Sufficient
Imply
Necessary
Beliefs

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Dodis, Y. (2012). Shannon impossibility, revisited. In 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.

Information Theoretic Security - 6th International Conference, ICITS 2012, Proceedings. Vol. 7412 LNCS 2012. p. 100-110 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7412 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Dodis, Y 2012, Shannon impossibility, revisited. in 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
Dodis Y. Shannon impossibility, revisited. In Information Theoretic Security - 6th International Conference, ICITS 2012, Proceedings. Vol. 7412 LNCS. 2012. p. 100-110. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-32284-6_6
Dodis, Yevgeniy. / Shannon impossibility, revisited. Information Theoretic Security - 6th International Conference, ICITS 2012, Proceedings. Vol. 7412 LNCS 2012. pp. 100-110 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{b2bce0504e884513bab3d4b43b5ed499,
title = "Shannon impossibility, revisited",
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].)",
author = "Yevgeniy Dodis",
year = "2012",
doi = "10.1007/978-3-642-32284-6_6",
language = "English (US)",
isbn = "9783642322839",
volume = "7412 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "100--110",
booktitle = "Information Theoretic Security - 6th International Conference, ICITS 2012, Proceedings",

}

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

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 -