# Cryptographic Parameters

## Default parameters

The TFHE cryptographic scheme relies on a variant of Regev cryptosystem, and is based on a problem so hard to solve that it is even post-quantum resistant.

In practice, you need to tune some cryptographic parameters in order to ensure both the correctness of the result and the security of the computation.

To make it simpler, we provide two sets of parameters, which ensure correct computations for a certain probability with the standard security of 128 bits. There exists an error probability due to the probabilistic nature of the encryption, which requires adding randomness (called noise) following a Gaussian distribution. If this noise is too large, the decryption will not give a correct result. There is a trade-off between efficiency and correctness: generally, using a less efficient parameter set (in terms of computation time) leads to a smaller risk of having an error during homomorphic evaluation.

In the two proposed sets of parameters, the only difference lies in this probability error. The default parameter set ensures a probability error of at most $2^{-40}$ when computing a programmable bootstrapping (i.e., any gates but the not). The other one is closer to the error probability claimed into the original TFHE paper, namely $2^{-165}$, but it is up-to-date regarding security requirements.

The following array summarizes this:

Parameter setError probability

DEFAULT_PARAMETERS

$2^{-40}$

TFHE_LIB_PARAMETERS

$2^{-165}$

## User-defined parameters

Note that, if you desire, you can also create your own set of parameters. This is an unsafe operation as failing to properly fix the parameters will potentially result in an incorrect and/or insecure computation:

use tfhe::boolean::prelude::*;

fn main() {
// WARNING: might be insecure and/or incorrect
// You can create your own set of parameters
let parameters = unsafe {
BooleanParameters::new(
LweDimension(586),
GlweDimension(2),
PolynomialSize(512),
StandardDev(0.00008976167396834998),
StandardDev(0.00000002989040792967434),
DecompositionBaseLog(8),
DecompositionLevelCount(2),
DecompositionBaseLog(2),
DecompositionLevelCount(5),
)
};
}

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