signitc/parameters.py at main · kahrens-code/signitc · GitHub

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"""
Parameter sets for SIGNITC stored as dictionaries to be imported into setup.py.

p_M127: Mersenne prime 2^127 - 1.
p_2D: A prime for two dimensional IdealToIsogeny from "Ideal-to-isogeny algorithm using 2-dimensional isogenies and its application to SQIsign" (ePrint 2024/778)
p_1973: A prime for NIST level I from the SQIsign Specs.
p_6983: The prime from the SQISign paper.
p_M521: Mersenne prime 2^521 - 1.

Parameter set is decided by setting `params` on the last lines.
"""

# Sage imports
from sage.all import ZZ

p_M127 = {
    "kappa": 127,
    "p": ZZ(2**127 - 1),
    "d_s": 2**127,
    "d_T": 77158673929, #tested ~20 min of sequential delay
    "N_M": 2**59,
}

p_2D = {
    "kappa": 250,
    "p": ZZ(5 * 2**248 - 1),
    "d_s": 2**248 * 5,
    "d_T": 39857517021631, #expected several days of sequential delay
    "N_M": 2**121,
}

p_1973 = {
    "kappa": 252,
    "p": ZZ(23920667128620486487914848107166358953830561597426178123910317653495243603967),
    "d_s": 2**75* 3**36 * 23**2 * 59**2 * 101**2 * 109**2 * 197**2 * 7**4 * 11 * 13 * 37 * 89 * 97 * 107 * 131 * 137,
    #or "d_s": 2**75* 3**36 * 23**2 * 59**2 * 101**2 * 109**2 * 197**2 * 491**2 * 743**2 * 1913**2 and "kappa": 253
    "d_T": 275446333, #tested ~1 min of sequential delay
    "N_M": 2**122,
}

p_6983 = {
    "kappa": 255,
    "p": ZZ(73743043621499797449074820543863456997944695372324032511999999999999999999999),
    "d_s": 2**33 * 5**21 * 7**2 * 11 * 31 * 83 * 107 * 137 * 3**53 * 43 * 103**2 * 109 * 199 * 227 * 419 * 569,
    #"d_T": 517434778561, #expected several hours of sequential delay
    "d_T": 26602537156291, #expected several days of sequential delay
    "N_M": 2**123,
}

p_M521 = {
    "kappa": 521,
    "p": ZZ(2**521 - 1),
    "d_s": 2**521,
    #"d_T": 34110701, #tested ~40s of sequential delay
    #"d_T": 308761441, #tested ~2 min of sequential delay
    #"d_T": 2400573761, #tested ~7 min of sequential delay
    "d_T": 65427463921, #tested ~45 min of sequential delay
    #"d_T": 108140989558681, #expected several months of sequential delay
    #"d_T": 145295143558111, #expected several months of sequential delay
    "N_M": 2**59,
}

# ************************* #
# Pick parameter dictionary #
# ************************* #

# params = p_M127
# params = p_2D
params = p_1973
# params = p_6983
# params = p_M521