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At CRYPTO 2017, Rosca et al. introduce a new variant of the Learning With Errors (LWE) problem, called the Middle-Product LWE (MP-LWE). The hardness of this new assumption is based on the hardness of ...
A Nonstandard Variant of Learning with Rounding with Polynomial Modulus and Unbounded Samples
Lattices LWE Learning with Rounding
2018/1/30
The learning with rounding problem (LWR) has become a popular cryptographic assumption to study recently due to its determinism and resistance to known quantum attacks. Unfortunately, LWR is only know...
Rounding and Chaining LLL: Finding Faster Small Roots of Univariate Polynomial Congruences
Coppersmith's Algorithm Small Roots of Polynomial Equations LLL
2016/1/9
In a seminal work at EUROCRYPT '96, Coppersmith showed how to find all small roots of a univariate polynomial congruence in polynomial time: this has found many applications in public-key cryptanalysi...
Lattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of...
We show the following reductions from the learning with errors problem (LWE) to the learning with rounding problem (LWR): (1) Learning the secret and (2) distinguishing samples from random strings is ...
Rounding LLL: Finding Faster Small Roots of Univariate Polynomial Congruences
Coppersmith's Algorithm Small Roots of Polynomial Equations
2014/3/10
In a seminal work at EUROCRYPT '96, Coppersmith showed how to find all small roots of a univariate polynomial congruence in polynomial time: this has found many applications in public-key cryptanalysi...
Learning with Rounding, Revisited: New Reduction, Properties and Applications
Learning with Errors Learning with Rounding Lossy Trapdoor Functions
2013/4/18
The learning with rounding (LWR) problem, introduced by Banerjee, Peikert and Rosen [BPR12] at EUROCRYPT '12, is a variant of learning with errors (LWE), where one replaces random errors with determin...