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On Kilian's Randomization of Multilinear Map Encodings     Multilinear maps  key-exchange  Approximate-GCD problem       font style='font-size:12px;'> 2018/11/29
Indistinguishability obfuscation constructions based on matrix branching programs generally proceed in two steps: first apply Kilian's randomization of the matrix product computation, and then encode ...
We introduce a new type of cryptanalytic algorithm on the obfuscations based on the branching programs. Applying this algorithm to two recent general-purpose obfuscation schemes one by Chen et al. (CR...
We present a quantum polynomial time attack against the GMMSSZ branching program obfuscator of Garg et al. (TCC'16), when instantiated with the GGH13 multilinear map of Garg et al. (EUROCRYPT'13). Thi...
In this paper, we propose cryptanalyses of all existing indistinguishability obfuscation (iO) candidates based on branching programs (BP) over GGH13 multilinear map. To achieve this, we introduce two ...
At EUROCRYPT 2013, Garg, Gentry and Halevi proposed a candidate construction of cryptographic multilinear map (MMap). Despite weaknesses uncovered by Hu and Jia (EUROCRYPT 2016), this candidate is sti...
Secure Obfuscation in a Weak Multilinear Map Model     iO  GGH13       font style='font-size:12px;'> 2016/12/10
All known candidate indistinguishibility obfuscation (iO) schemes rely on candidate multilinear maps. Until recently, the strongest proofs of security available for iO candidates were in a generic mod...
All known candidate indistinguishibility obfuscation (iO) schemes rely on candidate multilinear maps. Until recently, the strongest proofs of security available for iO candidates were in a generic mod...
Multilinear maps serve as a basis for a wide range of cryptographic applications. The first candidate construction of multilinear maps was proposed by Garg, Gentry, and Halevi in 2013, and soon afte...
Let h and g be polynomials of bounded Euclidean norm in the ring Z[X]/. Given polynomial [ h/ g]_q\in Z_q[X]/< X^n+1 >, the NTRU problem is to find a, b\in Z[X]/ with small Euclidean nor...
Cryptanalysis of the Multilinear Map over the Integers     Multilinear maps  graded encoding schemes       font style='font-size:12px;'> 2016/1/6
We describe a polynomial-time cryptanalysis of the (approximate) multilinear map of Coron, Lepoint and Tibouchi (CLT). The attack relies on an adaptation of the so-called zeroizing attack against th...
We improve the zeroizing attack on the multilinear map of Garg, Gentry and Halevi (GGH). Our algorithm can solve the Graded Decisional Diffie-Hellman (GDDH) problem on the GGH scheme when the dimensio...
Cryptanalysis of Gu's ideal multilinear map     Cryptanalysis  multilinear map       font style='font-size:12px;'> 2015/12/24
In March, 2015 Gu Chunsheng proposed a candidate ideal multilinear map [9]. An ideal multilinear map allows to perform as many multiplications as desired, while in κ-multilinear maps like GGH [5] or...
Reducing Multilinear Map Levels in Constrained PRFs and ABE     Constrained PRFs  multilinear maps  ABE       font style='font-size:12px;'> 2015/12/23
The candidate construction of multilinear maps by Garg, Gentry, and Halevi (Eurocrypt 2013) has lead to an explosion of new cryptographic constructions ranging from attribute-based encryption (ABE) ...
Cryptanalysis of the New Multilinear Map over the Integers     Multilinear maps  graded encoding schemes       font style='font-size:12px;'> 2015/12/22
This article describes a polynomial attack on the new multilinear map over the integers presented by Coron, Lepoint and Tibouchi at Crypto 2015 (CLT15). This version is a fix of the first multilinea...
Cryptographic multilinear map is a useful tool for constructing numerous secure protocols and Graded Encoding System (GES) is an approximate concept of multilinear map. In multilinear map context, t...

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