---
_id: '2940'
abstract:
- lang: eng
text: "A chain rule for an entropy notion H(.) states that the entropy H(X) of a
variable X decreases by at most l if conditioned on an l-bit string A, i.e., H(X|A)>=
H(X)-l. More generally, it satisfies a chain rule for conditional entropy if H(X|Y,A)>=
H(X|Y)-l.\r\n\r\nAll natural information theoretic entropy notions we are aware
of (like Shannon or min-entropy) satisfy some kind of chain rule for conditional
entropy. Moreover, many computational entropy notions (like Yao entropy, unpredictability
entropy and several variants of HILL entropy) satisfy the chain rule for conditional
entropy, though here not only the quantity decreases by l, but also the quality
of the entropy decreases exponentially in l. However, for \r\nthe standard notion
of conditional HILL entropy (the computational equivalent of min-entropy) the
existence of such a rule was unknown so far.\r\n\r\nIn this paper, we prove that
for conditional HILL entropy no meaningful chain rule exists, assuming the existence
of one-way permutations: there exist distributions X,Y,A, where A is a distribution
over a single bit, but $H(X|Y)>>H(X|Y,A)$, even if we simultaneously allow
for a massive degradation in the quality of the entropy.\r\n\r\nThe idea underlying
our construction is based on a surprising connection between the chain rule for
HILL entropy and deniable encryption. "
alternative_title:
- LNCS
author:
- first_name: Stephan
full_name: Krenn, Stephan
id: 329FCCF0-F248-11E8-B48F-1D18A9856A87
last_name: Krenn
orcid: 0000-0003-2835-9093
- first_name: Krzysztof Z
full_name: Pietrzak, Krzysztof Z
id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87
last_name: Pietrzak
orcid: 0000-0002-9139-1654
- first_name: Akshay
full_name: Wadia, Akshay
last_name: Wadia
citation:
ama: 'Krenn S, Pietrzak KZ, Wadia A. A counterexample to the chain rule for conditional
HILL entropy, and what deniable encryption has to do with it. In: Sahai A, ed.
Vol 7785. Springer; 2013:23-39. doi:10.1007/978-3-642-36594-2_2'
apa: 'Krenn, S., Pietrzak, K. Z., & Wadia, A. (2013). A counterexample to the
chain rule for conditional HILL entropy, and what deniable encryption has to do
with it. In A. Sahai (Ed.) (Vol. 7785, pp. 23–39). Presented at the TCC: Theory
of Cryptography Conference, Tokyo, Japan: Springer. https://doi.org/10.1007/978-3-642-36594-2_2'
chicago: Krenn, Stephan, Krzysztof Z Pietrzak, and Akshay Wadia. “A Counterexample
to the Chain Rule for Conditional HILL Entropy, and What Deniable Encryption Has
to Do with It.” edited by Amit Sahai, 7785:23–39. Springer, 2013. https://doi.org/10.1007/978-3-642-36594-2_2.
ieee: 'S. Krenn, K. Z. Pietrzak, and A. Wadia, “A counterexample to the chain rule
for conditional HILL entropy, and what deniable encryption has to do with it,”
presented at the TCC: Theory of Cryptography Conference, Tokyo, Japan, 2013, vol.
7785, pp. 23–39.'
ista: 'Krenn S, Pietrzak KZ, Wadia A. 2013. A counterexample to the chain rule for
conditional HILL entropy, and what deniable encryption has to do with it. TCC:
Theory of Cryptography Conference, LNCS, vol. 7785, 23–39.'
mla: Krenn, Stephan, et al. *A Counterexample to the Chain Rule for Conditional
HILL Entropy, and What Deniable Encryption Has to Do with It*. Edited by Amit
Sahai, vol. 7785, Springer, 2013, pp. 23–39, doi:10.1007/978-3-642-36594-2_2.
short: S. Krenn, K.Z. Pietrzak, A. Wadia, in:, A. Sahai (Ed.), Springer, 2013, pp.
23–39.
conference:
end_date: 2013-03-06
location: Tokyo, Japan
name: 'TCC: Theory of Cryptography Conference'
start_date: 2013-03-03
date_created: 2018-12-11T12:00:27Z
date_published: 2013-01-29T00:00:00Z
date_updated: 2021-01-12T07:39:55Z
day: '29'
ddc:
- '000'
department:
- _id: KrPi
doi: 10.1007/978-3-642-36594-2_2
ec_funded: 1
editor:
- first_name: Amit
full_name: Sahai, Amit
last_name: Sahai
file:
- access_level: open_access
checksum: beb0cc1c0579da2d2e84394230a5da78
content_type: application/pdf
creator: dernst
date_created: 2019-01-22T14:11:11Z
date_updated: 2020-07-14T12:45:54Z
file_id: '5875'
file_name: 2013_LNCS_Krenn.pdf
file_size: 414823
relation: main_file
file_date_updated: 2020-07-14T12:45:54Z
has_accepted_license: '1'
intvolume: ' 7785'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Submitted Version
page: 23 - 39
project:
- _id: 258C570E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '259668'
name: Provable Security for Physical Cryptography
publication_status: published
publisher: Springer
publist_id: '3795'
quality_controlled: '1'
related_material:
record:
- id: '1479'
relation: later_version
status: public
scopus_import: 1
status: public
title: A counterexample to the chain rule for conditional HILL entropy, and what deniable
encryption has to do with it
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7785
year: '2013'
...