WebNov 30, 2024 · Arora and Ge showed that the problem can be solved in polynomial time given a number of samples quadratic in the dimension n. On the other hand, the problem is known to be as hard as standard LWE given only slightly more than n samples. Binary error LWE is the particular case of the learning with errors (LWE) problem in which errors are chosen in \ {0,1\}. It has various cryptographic applications, and in particular, has been used to construct efficient encryption schemes for use in constrained devices. See more Slightly informally, Hilbert’s Nullstellensatz essentially states that the ideal generated by a family of polynomials f_1,\dots ,f_m\in \mathbb {Z}_q[x_1,\dots ,x_n] coincides with the ideal of polynomials that vanish on the set … See more The Arora-Ge polynomial system arising from binary error LWE is a polynomial system as above with d_{1} = \cdots = d_{m} = 2. Therefore, we can sum up the results of this section … See more Now consider the Arora-Ge approach of linearizing the polynomial system, except that we do not apply it to the quadratic system directly, but instead to an equivalent, … See more We can completely determine the cost of the approach above provided that we can determine the minimal value D sufficient to recover \mathbf {s}, … See more
Indistinguishability Obfuscation from Simple-to-State Hard …
WebPaper: Indistinguishability Obfuscation from Simple-to-State Hard Problems: New Assumptions, New Techniques, and Simplification WebApr 13, 2016 · However, recent results show that some subclasses are weaker than expected. In this work we show that LWE with binary error, introduced by Micciancio and Peikert, is one such subclass. We achieve this by applying the Howgrave-Graham attack on NTRU, which is a combination of lattice techniques and a Meet-in-the-Middle approach, … how to sell oil and gas royalties
On the Hardness of Learning With Errors with Binary Secrets
WebMar 18, 2024 · Significant innovation has been made in the development of public-key cryptography that is able to withstand quantum attacks, known as post-quantum cryptography (PQC). This paper focuses on the development of an efficient PQC hardware implementation. Specifically, an implementation of the binary Ring-learning-with-errors … WebOct 2, 2024 · Further, this LWE has been converted to binary strings, and mathematical circuits such as modulo adder, multiplier, and a noise generator are conceptualized to map the LWE scheme in the FPGA architecture. In Sect. 3, LWE-based homomorphic encryption scheme is explained. In Sect. 4, the design architecture for the FPGA-based … WebJun 5, 2024 · Binary error LWE is the particular case of the learning with errors (LWE) problem in which errors are chosen in { 0, 1 }. It has various cryptographic applications, … how to sell old gold jewelry