Cryptanalysis of the Quadratic Zero-Testing of GGH
نویسندگان
چکیده
In this short note, we analyze the security of the quadratic zero-testing procedure for the GGH13 graded encoding scheme, which was recently proposed by Gentry, Halevi and Lepoint. We show that this modification fails to immunize the GGH13 construction against zeroizing attacks, and that the modified scheme is susceptible to the same attacks as the original one.
منابع مشابه
An Algorithm for NTRU Problems and Cryptanalysis of the GGH Multilinear Map without an encoding of zero
Let h and g be polynomials of bounded Euclidean norm in the ring Z[X]/⟨X+1⟩. Given polynomial [h/g]q ∈ Zq[X]/⟨X+1⟩, the NTRU problem is to find a, b ∈ Z[X]/⟨X + 1⟩ with small Euclidean norm such that [a/b]q = [h/g]q. We propose an algorithm to solve the NTRU problem which runs in 2 2 q) time when ∥g∥, ∥h∥ and ∥g−1∥ are in some range. The main technique of our algorithm is to reduce a problem on...
متن کاملAn Algorithm for NTRU Problems and Cryptanalysis of the GGH Multilinear Map without a Low Level Encoding of Zero
Let f and g be polynomials of a bounded Euclidean norm in the ring Z[X]/⟨X+1⟩. Given the polynomial [f/g]q ∈ Zq[X]/⟨X+1⟩, the NTRU problem is to find a, b ∈ Z[X]/⟨X + 1⟩ with a small Euclidean norm such that [a/b]q = [f/g]q. We propose an algorithm to solve the NTRU problem, which runs in 2 2 λ) time when ∥g∥, ∥f∥, and ∥g−1∥ are within some range. The main technique of our algorithm is the redu...
متن کاملCryptanalysis of the multilinear map on the ideal lattices
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 dimension n of the ideal lattice Z[X]/(X+1) is O(κλ) as suggested for the κ-linear GGH scheme. The zeroizing attack is to recover a basis of an ideal generated by a secret element g ∈ Z[X]/(X + 1) from the...
متن کاملTime and Space Complexity Reduction of a Cryptanalysis Algorithm
Binary Decision Diagram (in short BDD) is an efficient data structure which has been used widely in computer science and engineering. BDD-based attack in key stream cryptanalysis is one of the best forms of attack in its category. In this paper, we propose a new key stream attack which is based on ZDD(Zero-suppressed BDD). We show how a ZDD-based key stream attack is more efficient in time and ...
متن کاملCryptanalysis of the Multilinear Map over the Integers
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 the Garg, Gentry and Halevi (GGH) candidate multilinear map. Zeroizing is much more devastating for CLT than for GGH. In the case of GGH, it allows to break generalizations of the Decision Linear and S...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2015 شماره
صفحات -
تاریخ انتشار 2015