# Poseidon Hasher

**goal**: implement a specific version of Poseidon Hasher and generate its constants

**1. Run [calc_round_numbers script](https://github.com/daira/pasta-hadeshash/blob/master/code/calc_round_numbers.py)**

Input parameters:

- `alpha = 5` (3 or 5 are the most common choices for alpha)
- `p = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001` (254 bits) [prime number from bn256](https://github.com/privacy-scaling-explorations/halo2curves/blob/main/src/bn256/fr.rs#L19)
- `t = 5` is the required width of the hasher (rate + 1)

Output:

--- x^5 WITH security margin for bn256---
  t = 5
  M = 128
  alpha = 5
  security_margin = True
  R_F = 8
  R_P = 56
  min_sbox_cost = 96
  min_size_cost = 24384

**2. Run [generate parameters grain sage script](https://github.com/daira/pasta-hadeshash/blob/master/code/generate_parameters_grain.sage)**

$ sage generate_parameters_grain.sage 1 0 254 5 8 60 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001 --rust

where:
- `1` means "prime field"
- `0` means "non-negative sbox"
- `254` is the bitsize of the bn256 field
- `5` is the Poseidon width (rate + 1) `t`
- `8` is the number of full round `R_F` from previous step
- `60` is the number of partial rounds `R_P` from previous step (note: as mentioned [here](https://github.com/daira/pasta-hadeshash/blob/master/code/generate_parameters_grain.sage#L6) `R_P` has to be increased to closest multiple of `t`)
- `0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001` is the prime field for bn256

Output:

Number of round constants: 340
Round constants for GF(p):
    [
        pallas::Base::from_raw([
            0x4f3c_2bd8_1a6d_a891,
            0xd889_bb4e_bd47_c386,
            0x7f53_e29c_cac9_8ed7,
            0x0eb5_44fe_e281_5dda,
        ]),
        pallas::Base::from_raw([
            0xba73_3f28_4751_28cb,
            0xa197_aeb1_2ea6_4713,
            0xf02f_dba7_dd73_7fbc,
            0x0554_d736_315b_8662,
        ]),
        pallas::Base::from_raw([
            0xf508_7c58_d5e8_c2d4,
            0x5490_7df0_c0fb_0035,
            0xbcd7_4805_6307_c377,
            0x2f83_b9df_259b_2b68,
        ]),
    ...