Classy Group

The Group of unknown order that is used to sample our Class groups of imaginary quadratic order

Class groups of binary quadratic forms omits the trusted setup that RSA needs. The order of the class group of a negative prime discriminant d, where |d| ≡ 3 mod 4, is believed to be difficult to compute when |d| is sufficiently large, making the order of the class group effectively unknown. Therefore, a suitable discriminant — and its associated class group — can be chosen without the need for a trusted setup, which is a major advantage for using class groups in applications requiring groups of unknown order.

group_class_op time: [1.7747 us 1.7954 us 1.8216 us]
Found 5 outliers among 100 measurements (5.00%) 3 (3.00%) high mild 2 (2.00%) high severe

group_class_exp time: [15.983 ms 16.357 ms 16.712 ms]
Found 3 outliers among 100 measurements (3.00%) 2 (2.00%) high mild 1 (1.00%) high severe

group_class_square time: [762.11 ns 775.93 ns 791.58 ns]
Found 11 outliers among 100 measurements (11.00%) 7 (7.00%) high mild 4 (4.00%) high severe

group_class_op time: [1.5665 us 1.5763 us 1.5880 us]
Found 6 outliers among 100 measurements (6.00%) 2 (2.00%) high mild 4 (4.00%) high severe

Benchmarking group_class_exp: Warming up for 3.0000 s Warning: Unable to complete 100 samples in 5.0s. You may wish to increase target time to 70.6s or reduce sample count to 10 group_class_exp time: [13.789 ms 13.830 ms 13.875 ms]
Found 9 outliers among 100 measurements (9.00%) 3 (3.00%) high mild 6 (6.00%) high severe

group_class_square time: [578.73 ns 582.13 ns 586.30 ns]
Found 15 outliers among 100 measurements (15.00%) 3 (3.00%) low mild 5 (5.00%) high mild 7 (7.00%) high severe

blake2 time: [121.22 ns 121.72 ns 122.33 ns]
Found 11 outliers among 100 measurements (11.00%) 1 (1.00%) low severe 3 (3.00%) low mild 4 (4.00%) high mild 3 (3.00%) high severe

hash_to_prime time: [303.36 us 306.26 us 309.21 us]
Found 1 outliers among 100 measurements (1.00%) 1 (1.00%) high severe

• https://github.com/Chia-Network/vdf-competition/blob/master/classgroups.pdf