Estimating Error Standard Deviation

Use --param "std_e" to estimate the error standard deviation (std_e) of the scheme.

The following commands estimate the error standard deviation for a binary secret distribution, target security levels (lambda), LWE dimensions, and various sizes for the ciphertext modulus:

python3 src/estimate.py --param "std_e" --lambda "192" --n "2048" --logq "64" --secret "binary"

Output Example

secret dist.   | lambda | lwe dim. | log q | output
---------------+--------+----------+-------+-------
Uniform (-1 0) | 192    | 2048     | 64    | 28.60

Show all estimations from formulas/numerical methods

When adding the option --table, the output shows the individual results for each of the formulas and numerical methods.

secret dist.   | lambda | lwe dim. | log q | log2(std_e) usvp  | log2(std_e) bdd    | output
---------------+--------+----------+-------+-------------------+--------------------+-------
Uniform (-1 0) | 192    | 2048     | 64    | 28.60             | 25.71              | 28.60

Compare results against the Lattice Estimator

Use option -v, to see the result (columns est ‘name of attack / num’) of running the Lattice Estimator with the given parameters and compare them with our formulas/numerical methods.

secret dist.   | lambda | lwe dim. | log q | log2(std_e) usvp   | est usvp | log2(std_e) bdd   | est bdd | output
---------------+--------+----------+-------+--------------------+----------+-------------------+---------+-------
Uniform (-1 0) | 192    | 2048     | 64    | 25.71              | 177      | 28.60             | 190     | 28.60