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On Kilian's Randomization of Multilinear Map Encodings
Multilinear maps key-exchange Approximate-GCD problem
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 ...
Statistical Zeroizing Attack: Cryptanalysis of Candidates of BP Obfuscation over GGH15 Multilinear Map
Cryptanalysis indistinguishability obfuscation multilinear map
2018/11/12
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...
Quantum Attacks against Indistinguishablility Obfuscators Proved Secure in the Weak Multilinear Map Model
Cryptanalysis Obfuscation
2018/6/5
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...
Generic Hardness of Inversion on Ring and Its Relation to Self-Bilinear Map
MCDH unbalanced modulus
2018/5/22
In this paper, we study the generic hardness of the inversion problem on a ring, which is a problem to compute the inverse of a given prime cc by just using additions, subtractions and multiplications...
Cryptanalyses of Branching Program Obfuscations over GGH13 Multilinear Map from NTRU Attack
Obfuscation multilinear maps graded encoding schemes
2018/5/11
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 ...
On the Statistical Leak of the GGH13 Multilinear Map and some Variants
Cryptanalysis Multilinear Maps Statistical Leaks
2017/5/31
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...
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...
Secure obfuscation in a weak multilinear map model: A simple construction secure against all known attacks
obfuscation multilinear maps annihilating polynomials
2016/6/7
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...
Attribute-Based Signatures for Circuits from Bilinear Map
attribute-based signatures Groth-Sahai proofs Groth-Ostrovsky-Sahai proofs
2016/3/7
In attribute-based signatures, each signer receives a signing key from the authority, which
is associated with the signer’s attribute, and using the signing key, the signer can issue a signature
on ...
Cryptanalysis of the New CLT Multilinear Map over the Integers
Multilinear maps graded encoding schemes
2016/2/23
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...
An Algorithm for NTRU Problems and Cryptanalysis of the GGH Multilinear Map without an encoding of zero
NTRU GGH Multilinear Maps Ideal Lattice
2016/2/23
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...
Statistical Properties of the Square Map Modulo a Power of Two
Square map modulo a power of two Vectorial Boolean function Component Boolean function
2016/1/6
The square map is one of the functions that is used in cryptography. For instance, the square map is used in Rabin encryption scheme, block cipher RC6 and stream cipher Rabbit, in different forms. In ...
Cryptanalysis of the Multilinear Map over the Integers
Multilinear maps graded encoding schemes
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...
Self-bilinear Map on Unknown Order Groups from Indistinguishability Obfuscation and Its Applications
self-bilinear map indistinguishability obfuscation multilinear map
2016/1/4
A self-bilinear map is a bilinear map where the domain and target groups are identical. In
this paper, we introduce a self-bilinear map with auxiliary information which is a weaker variant
of a self...
Cryptanalysis of GGH Map
Multilinear maps Multipartite key exchange (MKE) Witness encryption (WE)
2015/12/31
Multilinear map is a novel primitive which has many cryptographic applications, and GGH map is a major candidate of K-linear maps for K>2. GGH map has two classes of applications, which are applicatio...