Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  it is shown that given a sufficient number of (noisy) random binary linear equations, the Learning from Parity with Noise (LPN) problem can be solved in essentially cube root time in the number of unknowns. The techniques used to recover the solution are known from fast correlation attacks on stream ciphers. As in fast correlation attacks, the performance of the algorithm depends on the number of equations given. It is shown that if this number exceeds a certain bound, and the bias of the noisy equations is polynomial in number of unknowns n, the running time of the algorithm is reduced to 2 n 3 +o(n) compared to the brute force checking of all 2 n possible solutions. The mentioned bound is explicitly given and it is further shown that when this bound is exceeded, the complexity of the approach can even be further reduced.
['Urs Wagner']
I am writing a research paper on a idea Solving the LPN problem in cube-root time
[{"from": "human", "value": "I am writing a research paper on a idea Solving the LPN problem in cube-root time"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  it is shown that given a sufficient number of (noisy) random binary linear equations, the Learning from Parity with Noise (LPN) problem can be solved in essentially cube root time in the number of unknowns. The techniques used to recover the solution are known from fast correlation attacks on stream ciphers. As in fast correlation attacks, the performance of the algorithm depends on the number of equations given. It is shown that if this number exceeds a certain bound, and the bias of the noisy equations is polynomial in number of unknowns n, the running time of the algorithm is reduced to 2 n 3 +o(n) compared to the brute force checking of all 2 n possible solutions. The mentioned bound is explicitly given and it is further shown that when this bound is exceeded, the complexity of the approach can even be further reduced."}]