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Definition 1 (LPN oracle) An LPN oracle LPN for an unkown vector x 2 f0; 1gk with 2 (0; 1 2) returns pairs of the form. g $ f0; 1gk; hx; gi + e ; where e. Ber . Here, hx; gi denotes the scalar product of vectors x and g. We also write hx; gi as x gT, where gT is the transpose of the row vector g.
The fastest known algorithms for solving LPN runs in sub-exponential time in the general case and in contrast to most of the number-theoretic problems in cryptography, there is no available quantum algorithms that could solve LPN in. a signi cantly faster time than the classical ones.
7 lip 2008 · We present a probabilistic private-key encryption scheme named LPN-C whose security can be reduced to the hardness of the Learning from Parity with Noise (LPN) problem. The proposed protocol...
In this paper, we propose faster algorithms for solving LPN based on an op-timal precise embedding of cascaded perfect codes with the parameters found by integer linear programming to efficiently reduce the dimension of the secret infor-mation.
We provide a complete picture of the hardness of LPN over integer rings by showing: 1) the equivalence between its search and decisional versions; 2) an eficient reduction from LPN over F2 to LPN over Z2λ; and 3) generalization of our results to any integer ring.
28 kwi 2016 · The best published algorithm for solving it at Asiacrypt 2014 improved the classical BKW algorithm by using covering codes, which claimed to marginally compromise the 80-bit security of HB variants, LPN-C and Lapin.
We present a new algorithm for solving the LPN problem. The algorithm has a similar form as some previous methods, but includes a new key step that makes use of approximations of random words to a nearest codeword in a linear code. It outperforms previous methods for many parameter choices.
