---
_id: '3281'
abstract:
- lang: eng
text: 'We consider the problem of amplifying the "lossiness" of functions.
We say that an oracle circuit C*: {0,1} m → {0,1}* amplifies relative lossiness
from ℓ/n to L/m if for every function f:{0,1} n → {0,1} n it holds that 1 If f
is injective then so is C f. 2 If f has image size of at most 2 n-ℓ, then C f
has image size at most 2 m-L. The question is whether such C* exists for L/m ≫
ℓ/n. This problem arises naturally in the context of cryptographic "lossy
functions," where the relative lossiness is the key parameter. We show that
for every circuit C* that makes at most t queries to f, the relative lossiness
of C f is at most L/m ≤ ℓ/n + O(log t)/n. In particular, no black-box method making
a polynomial t = poly(n) number of queries can amplify relative lossiness by more
than an O(logn)/n additive term. We show that this is tight by giving a simple
construction (cascading with some randomization) that achieves such amplification.'
acknowledgement: "We would like to thank Oded Goldreich and Omer Rein- gold for discussions
at an early stage of this project, and Scott Aaronson for clarifications regarding
the collision problem.\r\n"
alternative_title:
- LNCS
author:
- first_name: Krzysztof Z
full_name: Pietrzak, Krzysztof Z
id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87
last_name: Pietrzak
- first_name: Alon
full_name: Rosen, Alon
last_name: Rosen
- first_name: Gil
full_name: Segev, Gil
last_name: Segev
citation:
ama: 'Pietrzak KZ, Rosen A, Segev G. Lossy functions do not amplify well. In: Vol
7194. Springer; 2012:458-475. doi:10.1007/978-3-642-28914-9_26'
apa: 'Pietrzak, K. Z., Rosen, A., & Segev, G. (2012). Lossy functions do not
amplify well (Vol. 7194, pp. 458–475). Presented at the TCC: Theory of Cryptography
Conference, Taormina, Sicily, Italy: Springer. https://doi.org/10.1007/978-3-642-28914-9_26'
chicago: Pietrzak, Krzysztof Z, Alon Rosen, and Gil Segev. “Lossy Functions Do Not
Amplify Well,” 7194:458–75. Springer, 2012. https://doi.org/10.1007/978-3-642-28914-9_26.
ieee: 'K. Z. Pietrzak, A. Rosen, and G. Segev, “Lossy functions do not amplify well,”
presented at the TCC: Theory of Cryptography Conference, Taormina, Sicily, Italy,
2012, vol. 7194, pp. 458–475.'
ista: 'Pietrzak KZ, Rosen A, Segev G. 2012. Lossy functions do not amplify well.
TCC: Theory of Cryptography Conference, LNCS, vol. 7194. 458–475.'
mla: Pietrzak, Krzysztof Z., et al. *Lossy Functions Do Not Amplify Well*.
Vol. 7194, Springer, 2012, pp. 458–75, doi:10.1007/978-3-642-28914-9_26.
short: K.Z. Pietrzak, A. Rosen, G. Segev, in:, Springer, 2012, pp. 458–475.
conference:
end_date: 2012-03-21
location: Taormina, Sicily, Italy
name: 'TCC: Theory of Cryptography Conference'
start_date: 2012-03-19
date_created: 2018-12-11T12:02:26Z
date_published: 2012-05-04T00:00:00Z
date_updated: 2019-08-02T12:38:08Z
day: '04'
department:
- _id: KrPi
doi: 10.1007/978-3-642-28914-9_26
intvolume: ' 7194'
language:
- iso: eng
main_file_link:
- url: http://www.iacr.org/archive/tcc2012/tcc2012-index.html
month: '05'
oa_version: None
page: 458 - 475
publication_status: published
publisher: Springer
publist_id: '3365'
quality_controlled: '1'
status: public
title: Lossy functions do not amplify well
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 7194
year: '2012'
...