---
_id: '9825'
abstract:
- lang: eng
text: "The dual attack has long been considered a relevant attack on lattice-based
cryptographic schemes relying on the hardness of learning with errors (LWE) and
its structured variants. As solving LWE corresponds to finding a nearest point
on a lattice, one may naturally wonder how efficient this dual approach is for
solving more general closest vector problems, such as the classical closest vector
problem (CVP), the variants bounded distance decoding (BDD) and approximate CVP,
and preprocessing versions of these problems. While primal, sieving-based solutions
to these problems (with preprocessing) were recently studied in a series of works
on approximate Voronoi cells [Laa16b, DLdW19, Laa20, DLvW20], for the dual attack
no such overview exists, especially for problems with preprocessing. With one
of the take-away messages of the approximate Voronoi cell line of work being that
primal attacks work well for approximate CVP(P) but scale poorly for BDD(P), one
may further wonder if the dual attack suffers the same drawbacks, or if it is
perhaps a better solution when trying to solve BDD(P).\r\n\r\nIn this work we
provide an overview of cost estimates for dual algorithms for solving these “classical”
closest lattice vector problems. Heuristically we expect to solve the search version
of average-case CVPP in time and space 20.293\U0001D451+\U0001D45C(\U0001D451)
\ in the single-target model. The distinguishing version of average-case CVPP,
where we wish to distinguish between random targets and targets planted at distance
(say) 0.99⋅\U0001D454\U0001D451 from the lattice, has the same complexity in
the single-target model, but can be solved in time and space 20.195\U0001D451+\U0001D45C(\U0001D451)
\ in the multi-target setting, when given a large number of targets from either
target distribution. This suggests an inequivalence between distinguishing and
searching, as we do not expect a similar improvement in the multi-target setting
to hold for search-CVPP. We analyze three slightly different decoders, both for
distinguishing and searching, and experimentally obtain concrete cost estimates
for the dual attack in dimensions 50 to 80, which confirm our heuristic assumptions,
and show that the hidden order terms in the asymptotic estimates are quite small.\r\n\r\nOur
main take-away message is that the dual attack appears to mirror the approximate
Voronoi cell line of work – whereas using approximate Voronoi cells works well
for approximate CVP(P) but scales poorly for BDD(P), the dual approach scales
well for BDD(P) instances but performs poorly on approximate CVP(P)."
acknowledgement: The authors thank Sauvik Bhattacharya, L´eo Ducas, Rachel Player,
and Christine van Vredendaal for early discussions on this topic and on preliminary
results. The authors further thank the reviewers of CT-RSA 2021 for their valuable
feedback.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Thijs
full_name: Laarhoven, Thijs
last_name: Laarhoven
- first_name: Michael
full_name: Walter, Michael
id: 488F98B0-F248-11E8-B48F-1D18A9856A87
last_name: Walter
orcid: 0000-0003-3186-2482
citation:
ama: 'Laarhoven T, Walter M. Dual lattice attacks for closest vector problems (with
preprocessing). In: Topics in Cryptology – CT-RSA 2021. Vol 12704. Springer
Nature; 2021:478-502. doi:10.1007/978-3-030-75539-3_20'
apa: 'Laarhoven, T., & Walter, M. (2021). Dual lattice attacks for closest vector
problems (with preprocessing). In Topics in Cryptology – CT-RSA 2021 (Vol.
12704, pp. 478–502). Virtual Event: Springer Nature. https://doi.org/10.1007/978-3-030-75539-3_20'
chicago: Laarhoven, Thijs, and Michael Walter. “Dual Lattice Attacks for Closest
Vector Problems (with Preprocessing).” In Topics in Cryptology – CT-RSA 2021,
12704:478–502. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-75539-3_20.
ieee: T. Laarhoven and M. Walter, “Dual lattice attacks for closest vector problems
(with preprocessing),” in Topics in Cryptology – CT-RSA 2021, Virtual Event,
2021, vol. 12704, pp. 478–502.
ista: 'Laarhoven T, Walter M. 2021. Dual lattice attacks for closest vector problems
(with preprocessing). Topics in Cryptology – CT-RSA 2021. CT-RSA: Cryptographers’
Track at the RSA Conference, LNCS, vol. 12704, 478–502.'
mla: Laarhoven, Thijs, and Michael Walter. “Dual Lattice Attacks for Closest Vector
Problems (with Preprocessing).” Topics in Cryptology – CT-RSA 2021, vol.
12704, Springer Nature, 2021, pp. 478–502, doi:10.1007/978-3-030-75539-3_20.
short: T. Laarhoven, M. Walter, in:, Topics in Cryptology – CT-RSA 2021, Springer
Nature, 2021, pp. 478–502.
conference:
end_date: 2021-05-20
location: Virtual Event
name: 'CT-RSA: Cryptographers’ Track at the RSA Conference'
start_date: 2021-05-17
date_created: 2021-08-08T22:01:30Z
date_published: 2021-05-11T00:00:00Z
date_updated: 2023-02-23T14:09:54Z
day: '11'
department:
- _id: KrPi
doi: 10.1007/978-3-030-75539-3_20
intvolume: ' 12704'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprint.iacr.org/2021/557
month: '05'
oa: 1
oa_version: Preprint
page: 478-502
publication: Topics in Cryptology – CT-RSA 2021
publication_identifier:
eissn:
- '16113349'
isbn:
- '9783030755386'
issn:
- '03029743'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dual lattice attacks for closest vector problems (with preprocessing)
type: conference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 12704
year: '2021'
...
---
_id: '9826'
abstract:
- lang: eng
text: "Automated contract tracing aims at supporting manual contact tracing during
pandemics by alerting users of encounters with infected people. There are currently
many proposals for protocols (like the “decentralized” DP-3T and PACT or the “centralized”
ROBERT and DESIRE) to be run on mobile phones, where the basic idea is to regularly
broadcast (using low energy Bluetooth) some values, and at the same time store
(a function of) incoming messages broadcasted by users in their proximity. In
the existing proposals one can trigger false positives on a massive scale by an
“inverse-Sybil” attack, where a large number of devices (malicious users or hacked
phones) pretend to be the same user, such that later, just a single person needs
to be diagnosed (and allowed to upload) to trigger an alert for all users who
were in proximity to any of this large group of devices.\r\n\r\nWe propose the
first protocols that do not succumb to such attacks assuming the devices involved
in the attack do not constantly communicate, which we observe is a necessary assumption.
The high level idea of the protocols is to derive the values to be broadcasted
by a hash chain, so that two (or more) devices who want to launch an inverse-Sybil
attack will not be able to connect their respective chains and thus only one of
them will be able to upload. Our protocols also achieve security against replay,
belated replay, and one of them even against relay attacks."
acknowledgement: Guillermo Pascual-Perez and Michelle Yeo were funded by the European
Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska–Curie
Grant Agreement No. 665385; the remaining contributors to this project have received
funding from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (682815 - TOCNeT).
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: Suvradip
full_name: Chakraborty, Suvradip
id: B9CD0494-D033-11E9-B219-A439E6697425
last_name: Chakraborty
- first_name: Karen
full_name: Klein, Karen
id: 3E83A2F8-F248-11E8-B48F-1D18A9856A87
last_name: Klein
- first_name: Guillermo
full_name: Pascual Perez, Guillermo
id: 2D7ABD02-F248-11E8-B48F-1D18A9856A87
last_name: Pascual Perez
- 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: Michael
full_name: Walter, Michael
id: 488F98B0-F248-11E8-B48F-1D18A9856A87
last_name: Walter
orcid: 0000-0003-3186-2482
- first_name: Michelle X
full_name: Yeo, Michelle X
id: 2D82B818-F248-11E8-B48F-1D18A9856A87
last_name: Yeo
citation:
ama: 'Auerbach B, Chakraborty S, Klein K, et al. Inverse-Sybil attacks in automated
contact tracing. In: Topics in Cryptology – CT-RSA 2021. Vol 12704. Springer
Nature; 2021:399-421. doi:10.1007/978-3-030-75539-3_17'
apa: 'Auerbach, B., Chakraborty, S., Klein, K., Pascual Perez, G., Pietrzak, K.
Z., Walter, M., & Yeo, M. X. (2021). Inverse-Sybil attacks in automated contact
tracing. In Topics in Cryptology – CT-RSA 2021 (Vol. 12704, pp. 399–421).
Virtual Event: Springer Nature. https://doi.org/10.1007/978-3-030-75539-3_17'
chicago: Auerbach, Benedikt, Suvradip Chakraborty, Karen Klein, Guillermo Pascual
Perez, Krzysztof Z Pietrzak, Michael Walter, and Michelle X Yeo. “Inverse-Sybil
Attacks in Automated Contact Tracing.” In Topics in Cryptology – CT-RSA 2021,
12704:399–421. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-75539-3_17.
ieee: B. Auerbach et al., “Inverse-Sybil attacks in automated contact tracing,”
in Topics in Cryptology – CT-RSA 2021, Virtual Event, 2021, vol. 12704,
pp. 399–421.
ista: 'Auerbach B, Chakraborty S, Klein K, Pascual Perez G, Pietrzak KZ, Walter
M, Yeo MX. 2021. Inverse-Sybil attacks in automated contact tracing. Topics in
Cryptology – CT-RSA 2021. CT-RSA: Cryptographers’ Track at the RSA Conference,
LNCS, vol. 12704, 399–421.'
mla: Auerbach, Benedikt, et al. “Inverse-Sybil Attacks in Automated Contact Tracing.”
Topics in Cryptology – CT-RSA 2021, vol. 12704, Springer Nature, 2021,
pp. 399–421, doi:10.1007/978-3-030-75539-3_17.
short: B. Auerbach, S. Chakraborty, K. Klein, G. Pascual Perez, K.Z. Pietrzak, M.
Walter, M.X. Yeo, in:, Topics in Cryptology – CT-RSA 2021, Springer Nature, 2021,
pp. 399–421.
conference:
end_date: 2021-05-20
location: Virtual Event
name: 'CT-RSA: Cryptographers’ Track at the RSA Conference'
start_date: 2021-05-17
date_created: 2021-08-08T22:01:30Z
date_published: 2021-05-11T00:00:00Z
date_updated: 2023-02-23T14:09:56Z
day: '11'
department:
- _id: KrPi
- _id: GradSch
doi: 10.1007/978-3-030-75539-3_17
ec_funded: 1
intvolume: ' 12704'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprint.iacr.org/2020/670
month: '05'
oa: 1
oa_version: Submitted Version
page: 399-421
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: 258AA5B2-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '682815'
name: Teaching Old Crypto New Tricks
publication: Topics in Cryptology – CT-RSA 2021
publication_identifier:
eissn:
- '16113349'
isbn:
- '9783030755386'
issn:
- '03029743'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Inverse-Sybil attacks in automated contact tracing
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12704
year: '2021'
...