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Mathematical Analysis of Multilinear Maps over the Integers

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Authors
류한솔
천정희
Major
자연과학대학 수리과학부
Issue Date
2016-08
Publisher
서울대학교 대학원
Keywords
Description
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 천정희.
Abstract
Multilinear maps have lots of cryptographic applications. Until now, there are three types of multilinear maps: the first is constructed using ideal lattices, the second is
defined over the integers, and the last is graph-induced one. However none of them have reduction to well-known hard problems. More serious matter is that they are all proven insecure when low-level encodings of zero are provided .

Especially, for multilinear maps over the integers, construction and analysis are being repeated. At {\sc Crypto} 2013, Coron, Lepoint, and Tibouchi proposed a
multilinear map using CRT (CLT13). However, it was revealed to be insecure so-called CHLRS attack (CHL$^+$15). After then, several attempts have been made to repair the scheme, but quickly proven insecure by extended CHLRS attack. The same authors revised their scheme at {\sc Crypto} 2015 again.

In this thesis, we describe attacks against CLT15. Our attacks share the essence of the cryptanalysis of CLT13 and exploits low level encodings of zero, provided by a ladder, as well as other public parameters. As in
CHL$^+$15, this leads to finding all the secret parameters of $\kappa$-multilinear maps in polynomial time of the security parameter. As a result, CLT15 is fully broken for all possible applications, while the security of CLT13 is not known when low-level encodings are not provided.
Language
English
URI
https://hdl.handle.net/10371/121316
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)