Estimating LWE Dimension

Use --param "n" to estimate the LWE dimension (n) of the scheme.

The following commands estimate the LWE dimension for a binary secret distribution, error distribution as a discrete Gaussian with standard deviation of 3.19, target security levels (lambda), and various sizes for the ciphertext modulus:

python3 src/estimate.py --param "n" --lambda "128" --logq "27;37;45;54" --secret "binary" --error "gaussian" --std "3.19"

Output Example

secret dist.   | lambda | log q | output | pow
---------------+--------+-------+--------+-----
Uniform (-1 0) | 128    | 27    | 1063   | 1024
Uniform (-1 0) | 128    | 37    | 1442   | 1024
Uniform (-1 0) | 128    | 45    | 1746   | 2048
Uniform (-1 0) | 128    | 54    | 2090   | 2048

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 | log q | usvp | usvp_s | usvp num | bdd  | bdd_s | bdd num | output | pow
---------------+--------+-------+------+--------+----------+------+-------+---------+--------+-----
Uniform (-1 0) | 128    | 27    | 1045 | 1043   | 1032     | 1062 | 1063  | 1029    | 1063   | 1024
Uniform (-1 0) | 128    | 37    | 1424 | 1425   | 1416     | 1442 | 1442  | 1411    | 1442   | 1024
Uniform (-1 0) | 128    | 45    | 1727 | 1730   | 1723     | 1746 | 1746  | 1715    | 1746   | 2048
Uniform (-1 0) | 128    | 54    | 2069 | 2072   | 2068     | 2088 | 2090  | 2057    | 2090   | 2048

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 | log q | usvp | est usvp | usvp_s | est usvp_s | usvp num | est num | bdd  | est bdd | bdd_s | est bdd_s | bdd num | output | pow
---------------+--------+-------+------+----------+--------+------------+----------+---------+------+---------+-------+-----------+---------+--------+-----
Uniform (-1 0) | 128    | 27    | 1045 | 130      | 1043   | 130        | 1032     | 126     | 1062 | 130     | 1063  | 130       | 1029    | 1063   | 1024
Uniform (-1 0) | 128    | 37    | 1424 | 129      | 1425   | 129        | 1416     | 126     | 1442 | 129     | 1442  | 129       | 1411    | 1442   | 1024
Uniform (-1 0) | 128    | 45    | 1727 | 129      | 1730   | 129        | 1723     | 127     | 1746 | 129     | 1746  | 129       | 1715    | 1746   | 2048
Uniform (-1 0) | 128    | 54    | 2069 | 129      | 2072   | 129        | 2068     | 127     | 2088 | 129     | 2090  | 129       | 2057    | 2090   | 2048