---
_id: '7966'
abstract:
- lang: eng
text: "For 1≤m≤n, we consider a natural m-out-of-n multi-instance scenario for a
public-key encryption (PKE) scheme. An adversary, given n independent instances
of PKE, wins if he breaks at least m out of the n instances. In this work, we
are interested in the scaling factor of PKE schemes, SF, which measures how well
the difficulty of breaking m out of the n instances scales in m. That is, a scaling
factor SF=ℓ indicates that breaking m out of n instances is at least ℓ times more
difficult than breaking one single instance. A PKE scheme with small scaling factor
hence provides an ideal target for mass surveillance. In fact, the Logjam attack
(CCS 2015) implicitly exploited, among other things, an almost constant scaling
factor of ElGamal over finite fields (with shared group parameters).\r\n\r\nFor
Hashed ElGamal over elliptic curves, we use the generic group model to argue that
the scaling factor depends on the scheme's granularity. In low granularity, meaning
each public key contains its independent group parameter, the scheme has optimal
scaling factor SF=m; In medium and high granularity, meaning all public keys share
the same group parameter, the scheme still has a reasonable scaling factor SF=√m.
Our findings underline that instantiating ElGamal over elliptic curves should
be preferred to finite fields in a multi-instance scenario.\r\n\r\nAs our main
technical contribution, we derive new generic-group lower bounds of Ω(√(mp)) on
the difficulty of solving both the m-out-of-n Gap Discrete Logarithm and the m-out-of-n
Gap Computational Diffie-Hellman problem over groups of prime order p, extending
a recent result by Yun (EUROCRYPT 2015). We establish the lower bound by studying
the hardness of a related computational problem which we call the search-by-hypersurface
problem."
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Benedikt
full_name: Auerbach, Benedikt
id: D33D2B18-E445-11E9-ABB7-15F4E5697425
last_name: Auerbach
orcid: 0000-0002-7553-6606
- first_name: Federico
full_name: Giacon, Federico
last_name: Giacon
- first_name: Eike
full_name: Kiltz, Eike
last_name: Kiltz
citation:
ama: 'Auerbach B, Giacon F, Kiltz E. Everybody’s a target: Scalability in public-key
encryption. In: *Advances in Cryptology – EUROCRYPT 2020*. Vol 12107. Springer
Nature; 2020:475-506. doi:10.1007/978-3-030-45727-3_16'
apa: 'Auerbach, B., Giacon, F., & Kiltz, E. (2020). Everybody’s a target: Scalability
in public-key encryption. In *Advances in Cryptology – EUROCRYPT 2020* (Vol.
12107, pp. 475–506). Springer Nature. https://doi.org/10.1007/978-3-030-45727-3_16'
chicago: 'Auerbach, Benedikt, Federico Giacon, and Eike Kiltz. “Everybody’s a Target:
Scalability in Public-Key Encryption.” In *Advances in Cryptology – EUROCRYPT
2020*, 12107:475–506. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-45727-3_16.'
ieee: 'B. Auerbach, F. Giacon, and E. Kiltz, “Everybody’s a target: Scalability
in public-key encryption,” in *Advances in Cryptology – EUROCRYPT 2020*,
2020, vol. 12107, pp. 475–506.'
ista: 'Auerbach B, Giacon F, Kiltz E. 2020. Everybody’s a target: Scalability in
public-key encryption. Advances in Cryptology – EUROCRYPT 2020. EUROCRYPT: Theory
and Applications of Cryptographic Techniques, LNCS, vol. 12107. 475–506.'
mla: 'Auerbach, Benedikt, et al. “Everybody’s a Target: Scalability in Public-Key
Encryption.” *Advances in Cryptology – EUROCRYPT 2020*, vol. 12107, Springer
Nature, 2020, pp. 475–506, doi:10.1007/978-3-030-45727-3_16.'
short: B. Auerbach, F. Giacon, E. Kiltz, in:, Advances in Cryptology – EUROCRYPT
2020, Springer Nature, 2020, pp. 475–506.
conference:
end_date: 2020-05-15
name: 'EUROCRYPT: Theory and Applications of Cryptographic Techniques'
start_date: 2020-05-11
date_created: 2020-06-15T07:13:37Z
date_published: 2020-05-01T00:00:00Z
date_updated: 2020-06-17T11:35:02Z
day: '01'
department:
- _id: KrPi
doi: 10.1007/978-3-030-45727-3_16
intvolume: ' 12107'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprint.iacr.org/2019/364
month: '05'
oa: 1
oa_version: Submitted Version
page: 475-506
project:
- _id: 258AA5B2-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '682815'
name: Teaching Old Crypto New Tricks
publication: Advances in Cryptology – EUROCRYPT 2020
publication_identifier:
isbn:
- '9783030457266'
- '9783030457273'
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: 'Everybody’s a target: Scalability in public-key encryption'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12107
year: '2020'
...