This is an implementation of various algorithms designed to analyze and calculate the bit security of the Learning Parity with Noise (LPN) problem, as well as its dual problem Syndrome Decoding. The application supports analysis under exact or regular noise mode, and considers attacks including:

• Plain Gauss Elimination
  
• Statistical Decoding and its 2.0
• Information Set Decoding (including standard and BJMM variants)
• The algebraic attack in this paper

It allows users to compute the complexity of various decoding strategies, providing insights about how secure their parameters are against several attacks.

Here is the parameters need for the LPN sample you want to analyze:

• k: the length of the secret
• N: the number of samples
• t: the hamming weight of the noise

And here are the parameters needed for the dual LPN, i.e., Syndrome Decoding sample you want to analyze:

• n: the number of correlations used in the dual LPN problem, another scale of the parity check matrix

From the view of Syndrome Decoding problem, e.g. He^T = s, n is the length of the syndrome vector s, N is the length of the solution vector e, and the parameter t is the Hamming weight bound of the solution, i.e. |e| ≤ t.

You can also put your sample on larger fields for more algebraic structures and specify the field with:

• q: the size of the field if you want to use finite field 𝔽_q
• λ: the logarithm size of the ring if you want to use ring ℤ_2^λ