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# Implementation of the Lilliput-AE tweakable block cipher.
#
# Authors, hereby denoted as "the implementer":
# Kévin Le Gouguec,
# Léo Reynaud
# 2019.
#
# For more information, feedback or questions, refer to our website:
# https://paclido.fr/lilliput-ae
#
# To the extent possible under law, the implementer has waived all copyright
# and related or neighboring rights to the source code in this file.
# http://creativecommons.org/publicdomain/zero/1.0/
"""Multiplications for Lilliput-TBC's tweakey schedule.
This module provides a list of functions implementing lane multiplications,
from ALPHAS[0] = α₀ = I to ALPHAS[6] = α₆ = M_R³.
"""
from functools import reduce
from operator import xor
def _Sl(n):
return lambda xi: (xi<<n) & 0xff
def _Sr(n):
return lambda xi: xi>>n
def _Id(xi):
return xi
def _0(xi):
return 0
def _M1(xi):
return (xi<<3 ^ xi>>3) & 0xff
def _M2(xi):
return (xi<<6 ^ (xi&0b11111000) ^ xi>>6) & 0xff
M = (
( _0, _Id, _0, _0, _0, _0, _0, _0),
( _0, _0, _Id, _0, _0, _0, _0, _0),
( _0, _0, _Sl(3), _Id, _0, _0, _0, _0),
( _0, _0, _0, _Sr(3), _Id, _0, _0, _0),
( _0, _0, _0, _0, _0, _Id, _0, _0),
( _0, _Sl(2), _0, _0, _0, _0, _Id, _0),
( _0, _0, _0, _0, _0, _0, _0, _Id),
(_Id, _0, _0, _0, _0, _0, _0, _0),
)
M2 = (
( _0, _0, _Id, _0, _0, _0, _0, _0),
( _0, _0, _Sl(3), _Id, _0, _0, _0, _0),
( _0, _0, _Sl(6), _M1, _Id, _0, _0, _0),
( _0, _0, _0, _Sr(6), _Sr(3), _Id, _0, _0),
( _0, _Sl(2), _0, _0, _0, _0, _Id, _0),
( _0, _0, _Sl(2), _0, _0, _0, _0, _Id),
(_Id, _0, _0, _0, _0, _0, _0, _0),
( _0, _Id, _0, _0, _0, _0, _0, _0),
)
M3 = (
( _0, _0, _Sl(3), _Id, _0, _0, _0, _0),
( _0, _0, _Sl(6), _M1, _Id, _0, _0, _0),
( _0, _0, _0, _M2, _M1, _Id, _0, _0),
( _0, _Sl(2), _0, _0, _Sr(6), _Sr(3), _Id, _0),
( _0, _0, _Sl(2), _0, _0, _0, _0, _Id),
(_Id, _0, _Sl(5), _Sl(2), _0, _0, _0, _0),
( _0, _Id, _0, _0, _0, _0, _0, _0),
( _0, _0, _Id, _0, _0, _0, _0, _0),
)
def _multiplication(m):
def _multiply(x):
return list(reversed([
reduce(xor, (mj[i](xi) for i, xi in enumerate(reversed(x))))
for mj in m
]))
return _multiply
def _multiply_MR(lane):
multiplied_lane = [lane[(byte+1) % 8] for byte in range(0, 8)]
multiplied_lane[2] ^= ((lane[4] >> 3) & 0xff)
multiplied_lane[4] ^= ((lane[6] << 3) & 0xff)
multiplied_lane[5] ^= ((lane[3] << 2) & 0xff)
return multiplied_lane
def _multiply_MR2(lane):
multiplied_lane = [lane[(byte+2) % 8] for byte in range(0, 8)]
multiplied_lane[1] ^= ((lane[4] >> 3) & 0xff)
multiplied_lane[2] ^= ((lane[5] >> 3) & 0xff)
multiplied_lane[3] ^= ((lane[6] << 3) & 0xff)
multiplied_lane[4] ^= ((lane[3] << 2) & 0xff) ^ ((lane[7] << 3) & 0xff)
multiplied_lane[5] ^= ((lane[4] << 2) & 0xff)
# binary matrix m3
multi_mat_l6_m3 = 0
l6 = lane[6]
multi_mat_l6_m3 ^= (l6 & 0x1)
multi_mat_l6_m3 ^= (l6 & 0x2)
multi_mat_l6_m3 ^= (l6 & 0x4)
multi_mat_l6_m3 ^= (l6 & 0x8)
multi_mat_l6_m3 ^= (l6 & 0x10)
multiplied_lane[2] ^= multi_mat_l6_m3
return multiplied_lane
def _multiply_MR3(lane):
multiplied_lane = [lane[(byte+3) % 8] for byte in range(0, 8)]
multiplied_lane[0] ^= ((lane[4] >> 3) & 0xff)
multiplied_lane[1] ^= ((lane[5] >> 3) & 0xff)
multiplied_lane[3] ^= ((lane[3] << 2) & 0xff) ^ ((lane[7] << 3) & 0xff)
multiplied_lane[4] ^= ((lane[0] << 3) & 0xff) ^ ((lane[4] << 2) & 0xff)
multiplied_lane[5] ^= ((lane[5] << 2) & 0xff) ^ ((lane[6] << 5) & 0xff)
# binary matrix m3
multi_mat_l6_m3 = 0
l6 = lane[6]
multi_mat_l6_m3 ^= (l6 & 0x1)
multi_mat_l6_m3 ^= (l6 & 0x2)
multi_mat_l6_m3 ^= (l6 & 0x4)
multi_mat_l6_m3 ^= (l6 & 0x8)
multi_mat_l6_m3 ^= (l6 & 0x10)
# binary matrix m3
multi_mat_l7_m3 = 0
l7 = lane[7]
multi_mat_l7_m3 ^= (l7 & 0x1)
multi_mat_l7_m3 ^= (l7 & 0x2)
multi_mat_l7_m3 ^= (l7 & 0x4)
multi_mat_l7_m3 ^= (l7 & 0x8)
multi_mat_l7_m3 ^= (l7 & 0x10)
# binary matrix m4
multi_mat_l3_m4 = 0
l3 = lane[3]
multi_mat_l3_m4 ^= ((l3 & 0x2) >> 1)
multi_mat_l3_m4 ^= ((l3 & 0x4) >> 1)
multi_mat_l3_m4 ^= ((l3 & 0x8) >> 1)
multi_mat_l3_m4 ^= ((l3 & 0x10) >> 1)
multi_mat_l3_m4 ^= ((l3 & 0x20) >> 1)
# binary matrix m1 for MR
multi_mat_l6_m1 = 0
l6 = lane[6]
multi_mat_l6_m1 ^= ((l6 & 0x8) >> 3)
multi_mat_l6_m1 ^= ((l6 & 0x10) >> 3)
multi_mat_l6_m1 ^= ((l6 & 0x20) >> 3)
multi_mat_l6_m1 ^= ((l6 & 0x40) >> 3) ^ ((l6 & 0x1) << 3)
multi_mat_l6_m1 ^= ((l6 & 0x80) >> 3) ^ ((l6 & 0x2) << 3)
multi_mat_l6_m1 ^= ((l6 & 0x4) << 3)
multi_mat_l6_m1 ^= ((l6 & 0x8) << 3)
multi_mat_l6_m1 ^= ((l6 & 0x10) << 3)
multiplied_lane[1] ^= multi_mat_l6_m3
multiplied_lane[2] ^= multi_mat_l3_m4 ^ multi_mat_l6_m1 ^ multi_mat_l7_m3
return multiplied_lane
ALPHAS = (
list, # Identity.
_multiplication(M),
_multiplication(M2),
_multiplication(M3),
_multiply_MR,
_multiply_MR2,
_multiply_MR3
)
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