High Entropy Random Selection Protocols
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438323" target="_blank" >RIV/00216208:11320/21:10438323 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=aw730U.Cvv" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=aw730U.Cvv</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00453-020-00770-y" target="_blank" >10.1007/s00453-020-00770-y</a>
Alternative languages
Result language
angličtina
Original language name
High Entropy Random Selection Protocols
Original language description
We study the two party problem of randomly selecting a common string among all the strings of length n. We want the protocol to have the property that the output distribution has high Shannon entropy or high min entropy, even when one of the two parties is dishonest and deviates from the protocol. We develop protocols that achieve high, close to n, Shannon entropy and simultaneously min entropy close to n/2. In the literature the randomness guarantee is usually expressed in terms of "resilience". The notion of Shannon entropy is not directly comparable to that of resilience, but we establish a connection between the two that allows us to compare our protocols with the existing ones. We construct an explicit protocol that yields Shannon entropy ????-????(1) and has ????(logASTERISK OPERATOR????) rounds, improving over the protocol of Goldreich et al. (SIAM J Comput 27: 506-544, 1998) that also achieves this entropy but needs O(n) rounds. Both these protocols need ????(????2) bits of communication. Next we reduce the number of rounds and the length of communication in our protocols. We show the existence, non-explicitly, of a protocol that has 6 rounds, O(n) bits of communication and yields Shannon entropy ????-????(log????) and min entropy ????/2-????(log????). Our protocol achieves the same Shannon entropy bound as, also non-explicit, protocol of Gradwohl et al. (in: Dwork (ed) Advances in Cryptology-CRYPTO '06, 409-426, Technical Report , 2006), however achieves much higher min entropy: ????/2-????(log????) versus ????(log????). Finally we exhibit a very simple 3-round explicit "geometric" protocol with communication length O(n). We connect the security parameter of this protocol with the well studied Kakeya problem motivated by Harmonic Analysis and Analytic Number Theory. We prove that this protocol has Shannon entropy ????-????(????). Its relation to the Kakeya problem follows a new and different approach to the random selection problem than any of the previously known protocols.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Algorithmica
ISSN
0178-4617
e-ISSN
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Volume of the periodical
83
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
28
Pages from-to
667-694
UT code for WoS article
000574811400001
EID of the result in the Scopus database
2-s2.0-85091845105