#!/usr/bin/env python2
# -*- coding: utf-8 -*-
'''
sha3sum – SHA-3 (Keccak) checksum calculator
Copyright © 2013 Mattias Andrée (maandree@member.fsf.org)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
'''
class SHA3:
'''
SHA-3/Keccak hash algorithm implementation
@author Mattias Andrée (maandree@member.fsf.org)
'''
def __init__(self):
'''
Constructor
'''
self.RC = [0x0000000000000001, 0x0000000000008082, 0x800000000000808A, 0x8000000080008000,
0x000000000000808B, 0x0000000080000001, 0x8000000080008081, 0x8000000000008009,
0x000000000000008A, 0x0000000000000088, 0x0000000080008009, 0x000000008000000A,
0x000000008000808B, 0x800000000000008B, 0x8000000000008089, 0x8000000000008003,
0x8000000000008002, 0x8000000000000080, 0x000000000000800A, 0x800000008000000A,
0x8000000080008081, 0x8000000000008080, 0x0000000080000001, 0x8000000080008008]
'''
:list<int> Round contants
'''
self.B = [0] * 25
'''
:list<int> Keccak-f round temporary
'''
self.C = [0] * 5
'''
:list<int> Keccak-f round temporary
'''
(self.r, self.c, self.n, self.b, self.w, self.wmod, self.l, self.nr) = (0, 0, 0, 0, 0, 0, 0, 0)
'''
r:int The bitrate
c:int The capacity
n:int The output size
b:int The state size
w:int The word size
wmod:int The word mask
l:int ℓ, the binary logarithm of the word size
nr:int 12 + 2ℓ, the number of rounds
'''
self.S = None
'''
:list<int> The current state
'''
self.M = None
'''
:bytes Left over water to fill the sponge with at next update
'''
def rotate(self, x, n):
'''
Rotate a word
@param x:int The value to rotate
@param n:int Rotation steps
@return :int The value rotated
'''
m = n % self.w
return ((x >> (self.w - m)) + (x << m)) & self.wmod
def rotate64(self, x, n):
'''
Rotate a 64-bit word
@param x:int The value to rotate
@param n:int Rotation steps
@return :int The value rotated
'''
return ((x >> (64 - n)) + (x << n)) & 0xFFFFFFFFFFFFFFFF
def lb(self, x):
'''
Binary logarithm
@param x:int The value of which to calculate the binary logarithm
@return :int The binary logarithm
'''
rc = 0
if (x & 0xFF00) != 0: rc += 8 ; x >>= 8
if (x & 0x00F0) != 0: rc += 4 ; x >>= 4
if (x & 0x000C) != 0: rc += 2 ; x >>= 2
if (x & 0x0002) != 0: rc += 1
return rc
def keccakFRound(self, A, rc):
'''
Perform one round of computation
@param A:list<int> The current state
@param rc:int Round constant
'''
if self.w == 64:
# θ step (step 1 and 2 of 3)
self.C[0] = (A[0] ^ A[1]) ^ (A[2] ^ A[3]) ^ A[4]
self.C[2] = (A[10] ^ A[11]) ^ (A[12] ^ A[13]) ^ A[14]
db = self.C[0] ^ self.rotate64(self.C[2], 1)
self.C[4] = (A[20] ^ A[21]) ^ (A[22] ^ A[23]) ^ A[24]
dd = self.C[2] ^ self.rotate64(self.C[4], 1)
self.C[1] = (A[5] ^ A[6]) ^ (A[7] ^ A[8]) ^ A[9]
da = self.C[4] ^ self.rotate64(self.C[1], 1)
self.C[3] = (A[15] ^ A[16]) ^ (A[17] ^ A[18]) ^ A[19]
dc = self.C[1] ^ self.rotate64(self.C[3], 1)
de = self.C[3] ^ self.rotate64(self.C[0], 1)
# ρ and π steps, with last part of θ
self.B[0] = self.rotate64(A[0] ^ da, 0)
self.B[1] = self.rotate64(A[15] ^ dd, 28)
self.B[2] = self.rotate64(A[5] ^ db, 1)
self.B[3] = self.rotate64(A[20] ^ de, 27)
self.B[4] = self.rotate64(A[10] ^ dc, 62)
self.B[5] = self.rotate64(A[6] ^ db, 44)
self.B[6] = self.rotate64(A[21] ^ de, 20)
self.B[7] = self.rotate64(A[11] ^ dc, 6)
self.B[8] = self.rotate64(A[1] ^ da, 36)
self.B[9] = self.rotate64(A[16] ^ dd, 55)
self.B[10] = self.rotate64(A[12] ^ dc, 43)
self.B[11] = self.rotate64(A[2] ^ da, 3)
self.B[12] = self.rotate64(A[17] ^ dd, 25)
self.B[13] = self.rotate64(A[7] ^ db, 10)
self.B[14] = self.rotate64(A[22] ^ de, 39)
self.B[15] = self.rotate64(A[18] ^ dd, 21)
self.B[16] = self.rotate64(A[8] ^ db, 45)
self.B[17] = self.rotate64(A[23] ^ de, 8)
self.B[18] = self.rotate64(A[13] ^ dc, 15)
self.B[19] = self.rotate64(A[3] ^ da, 41)
self.B[20] = self.rotate64(A[24] ^ de, 14)
self.B[21] = self.rotate64(A[14] ^ dc, 61)
self.B[22] = self.rotate64(A[4] ^ da, 18)
self.B[23] = self.rotate64(A[19] ^ dd, 56)
self.B[24] = self.rotate64(A[9] ^ db, 2)
else:
# θ step (step 1 and 2 of 3)
self.C[0] = (A[0] ^ A[1]) ^ (A[2] ^ A[3]) ^ A[4]
self.C[2] = (A[10] ^ A[11]) ^ (A[12] ^ A[13]) ^ A[14]
db = self.C[0] ^ self.rotate(self.C[2], 1)
self.C[4] = (A[20] ^ A[21]) ^ (A[22] ^ A[23]) ^ A[24]
dd = self.C[2] ^ self.rotate(self.C[4], 1)
self.C[1] = (A[5] ^ A[6]) ^ (A[7] ^ A[8]) ^ A[9]
da = self.C[4] ^ self.rotate(self.C[1], 1)
self.C[3] = (A[15] ^ A[16]) ^ (A[17] ^ A[18]) ^ A[19]
dc = self.C[1] ^ self.rotate(self.C[3], 1)
de = self.C[3] ^ self.rotate(self.C[0], 1)
# ρ and π steps, with last part of θ
self.B[0] = self.rotate(A[0] ^ da, 0)
self.B[1] = self.rotate(A[15] ^ dd, 28)
self.B[2] = self.rotate(A[5] ^ db, 1)
self.B[3] = self.rotate(A[20] ^ de, 27)
self.B[4] = self.rotate(A[10] ^ dc, 62)
self.B[5] = self.rotate(A[6] ^ db, 44)
self.B[6] = self.rotate(A[21] ^ de, 20)
self.B[7] = self.rotate(A[11] ^ dc, 6)
self.B[8] = self.rotate(A[1] ^ da, 36)
self.B[9] = self.rotate(A[16] ^ dd, 55)
self.B[10] = self.rotate(A[12] ^ dc, 43)
self.B[11] = self.rotate(A[2] ^ da, 3)
self.B[12] = self.rotate(A[17] ^ dd, 25)
self.B[13] = self.rotate(A[7] ^ db, 10)
self.B[14] = self.rotate(A[22] ^ de, 39)
self.B[15] = self.rotate(A[18] ^ dd, 21)
self.B[16] = self.rotate(A[8] ^ db, 45)
self.B[17] = self.rotate(A[23] ^ de, 8)
self.B[18] = self.rotate(A[13] ^ dc, 15)
self.B[19] = self.rotate(A[3] ^ da, 41)
self.B[20] = self.rotate(A[24] ^ de, 14)
self.B[21] = self.rotate(A[14] ^ dc, 61)
self.B[22] = self.rotate(A[4] ^ da, 18)
self.B[23] = self.rotate(A[19] ^ dd, 56)
self.B[24] = self.rotate(A[9] ^ db, 2)
# ξ step
A[0] = self.B[0] ^ ((~(self.B[5])) & self.B[10])
A[1] = self.B[1] ^ ((~(self.B[6])) & self.B[11])
A[2] = self.B[2] ^ ((~(self.B[7])) & self.B[12])
A[3] = self.B[3] ^ ((~(self.B[8])) & self.B[13])
A[4] = self.B[4] ^ ((~(self.B[9])) & self.B[14])
A[5] = self.B[5] ^ ((~(self.B[10])) & self.B[15])
A[6] = self.B[6] ^ ((~(self.B[11])) & self.B[16])
A[7] = self.B[7] ^ ((~(self.B[12])) & self.B[17])
A[8] = self.B[8] ^ ((~(self.B[13])) & self.B[18])
A[9] = self.B[9] ^ ((~(self.B[14])) & self.B[19])
A[10] = self.B[10] ^ ((~(self.B[15])) & self.B[20])
A[11] = self.B[11] ^ ((~(self.B[16])) & self.B[21])
A[12] = self.B[12] ^ ((~(self.B[17])) & self.B[22])
A[13] = self.B[13] ^ ((~(self.B[18])) & self.B[23])
A[14] = self.B[14] ^ ((~(self.B[19])) & self.B[24])
A[15] = self.B[15] ^ ((~(self.B[20])) & self.B[0])
A[16] = self.B[16] ^ ((~(self.B[21])) & self.B[1])
A[17] = self.B[17] ^ ((~(self.B[22])) & self.B[2])
A[18] = self.B[18] ^ ((~(self.B[23])) & self.B[3])
A[19] = self.B[19] ^ ((~(self.B[24])) & self.B[4])
A[20] = self.B[20] ^ ((~(self.B[0])) & self.B[5])
A[21] = self.B[21] ^ ((~(self.B[1])) & self.B[6])
A[22] = self.B[22] ^ ((~(self.B[2])) & self.B[7])
A[23] = self.B[23] ^ ((~(self.B[3])) & self.B[8])
A[24] = self.B[24] ^ ((~(self.B[4])) & self.B[9])
# ι step
A[0] ^= rc
def keccakF(self, A):
'''
Perform Keccak-f function
@param A:list<int> The current state
'''
if (self.nr == 24):
self.keccakFRound(A, 0x0000000000000001)
self.keccakFRound(A, 0x0000000000008082)
self.keccakFRound(A, 0x800000000000808A)
self.keccakFRound(A, 0x8000000080008000)
self.keccakFRound(A, 0x000000000000808B)
self.keccakFRound(A, 0x0000000080000001)
self.keccakFRound(A, 0x8000000080008081)
self.keccakFRound(A, 0x8000000000008009)
self.keccakFRound(A, 0x000000000000008A)
self.keccakFRound(A, 0x0000000000000088)
self.keccakFRound(A, 0x0000000080008009)
self.keccakFRound(A, 0x000000008000000A)
self.keccakFRound(A, 0x000000008000808B)
self.keccakFRound(A, 0x800000000000008B)
self.keccakFRound(A, 0x8000000000008089)
self.keccakFRound(A, 0x8000000000008003)
self.keccakFRound(A, 0x8000000000008002)
self.keccakFRound(A, 0x8000000000000080)
self.keccakFRound(A, 0x000000000000800A)
self.keccakFRound(A, 0x800000008000000A)
self.keccakFRound(A, 0x8000000080008081)
self.keccakFRound(A, 0x8000000000008080)
self.keccakFRound(A, 0x0000000080000001)
self.keccakFRound(A, 0x8000000080008008)
else:
for i in range(self.nr):
self.keccakFRound(A, self.RC[i] & self.wmod)
def toLane(self, message, n, ww, off):
'''
Convert a chunk of byte:s to a word
@param message:bytes The message
@param n:int `min(len(message), rr)`
rr:int Bitrate in bytes
@param ww:int Word size in bytes
@param off:int The offset in the message
@return :int Lane
'''
rc = 0
i = off + ww - 1
while i >= off:
rc = (rc << 8) | (message[i] if (i < n) else 0)
i -= 1
return rc
def toLane64(self, message, n, off):
'''
Convert a chunk of byte:s to a 64-bit word
@param message:bytes The message
@param n:int `min(len(message), rr)`
rr:int Bitrate in bytes
@param off:int The offset in the message
@return :int Lane
'''
return ((message[off + 7] << 56) if (off + 7 < n) else 0) | \
((message[off + 6] << 48) if (off + 6 < n) else 0) | \
((message[off + 5] << 40) if (off + 5 < n) else 0) | \
((message[off + 4] << 32) if (off + 4 < n) else 0) | \
((message[off + 3] << 24) if (off + 3 < n) else 0) | \
((message[off + 2] << 16) if (off + 2 < n) else 0) | \
((message[off + 1] << 8) if (off + 1 < n) else 0) | \
((message[off]) if (off < n) else 0)
def pad10star1(self, msg, r):
'''
pad 10*1
@param msg:bytes The message to pad
@param r:int The bitrate
@return :bytes The message padded
'''
nnn = len(msg) << 3
nrf = nnn >> 3
nbrf = nnn & 7
ll = nnn % r
bbbb = 1 if nbrf == 0 else ((msg[nrf] >> (8 - nbrf)) | (1 << nbrf))
message = None
if ((r - 8 <= ll) and (ll <= r - 2)):
message = [bbbb ^ 128]
else:
nnn = (nrf + 1) << 3
nnn = ((nnn - (nnn % r) + (r - 8)) >> 3) + 1
message = [0] * (nnn - nrf)
message[0] = bbbb
nnn -= nrf
message[nnn - 1] = 0x80
return msg[:nrf] + message
def initialise(self, r, c, n):
'''
Initialise Keccak sponge
@param r:int The bitrate
@param c:int The capacity
@param n:int The output size
'''
self.r = r
self.c = c
self.n = n
self.b = r + c
self.w = self.b // 25
self.l = self.lb(self.w)
self.nr = 12 + (self.l << 1)
self.wmod = (1 << self.w) - 1
self.S = [0] * 25
self.M = []
def update(self, msg, msglen = None):
'''
Absorb the more of the message message to the Keccak sponge
@param msg:bytes The partial message
@param msglen:int The length of the partial message
'''
if msglen is not None:
msg = msg[:msglen]
rr = self.r >> 3
ww = self.w >> 3
self.M += msg
nnn = len(self.M)
nnn -= nnn % ((self.r * self.b) >> 3)
message = self.M[:nnn]
self.M = self.M[nnn:]
# Absorbing phase
if ww == 8:
for i in range(0, nnn, rr):
n = min(len(message), rr)
self.S[ 0] ^= self.toLane64(message, n, 0)
self.S[ 5] ^= self.toLane64(message, n, 8)
self.S[10] ^= self.toLane64(message, n, 16)
self.S[15] ^= self.toLane64(message, n, 24)
self.S[20] ^= self.toLane64(message, n, 32)
self.S[ 1] ^= self.toLane64(message, n, 40)
self.S[ 6] ^= self.toLane64(message, n, 48)
self.S[11] ^= self.toLane64(message, n, 56)
self.S[16] ^= self.toLane64(message, n, 64)
self.S[21] ^= self.toLane64(message, n, 72)
self.S[ 2] ^= self.toLane64(message, n, 80)
self.S[ 7] ^= self.toLane64(message, n, 88)
self.S[12] ^= self.toLane64(message, n, 96)
self.S[17] ^= self.toLane64(message, n, 104)
self.S[22] ^= self.toLane64(message, n, 112)
self.S[ 3] ^= self.toLane64(message, n, 120)
self.S[ 8] ^= self.toLane64(message, n, 128)
self.S[13] ^= self.toLane64(message, n, 136)
self.S[18] ^= self.toLane64(message, n, 144)
self.S[23] ^= self.toLane64(message, n, 152)
self.S[ 4] ^= self.toLane64(message, n, 160)
self.S[ 9] ^= self.toLane64(message, n, 168)
self.S[14] ^= self.toLane64(message, n, 176)
self.S[19] ^= self.toLane64(message, n, 184)
self.S[24] ^= self.toLane64(message, n, 192)
self.keccakF(self.S)
message = message[rr:]
else:
for i in range(0, nnn, rr):
n = min(len(message), rr)
self.S[ 0] ^= self.toLane(message, n, ww, 0)
self.S[ 5] ^= self.toLane(message, n, ww, ww)
self.S[10] ^= self.toLane(message, n, ww, 2 * ww)
self.S[15] ^= self.toLane(message, n, ww, 3 * ww)
self.S[20] ^= self.toLane(message, n, ww, 4 * ww)
self.S[ 1] ^= self.toLane(message, n, ww, 5 * ww)
self.S[ 6] ^= self.toLane(message, n, ww, 6 * ww)
self.S[11] ^= self.toLane(message, n, ww, 7 * ww)
self.S[16] ^= self.toLane(message, n, ww, 8 * ww)
self.S[21] ^= self.toLane(message, n, ww, 9 * ww)
self.S[ 2] ^= self.toLane(message, n, ww, 10 * ww)
self.S[ 7] ^= self.toLane(message, n, ww, 11 * ww)
self.S[12] ^= self.toLane(message, n, ww, 12 * ww)
self.S[17] ^= self.toLane(message, n, ww, 13 * ww)
self.S[22] ^= self.toLane(message, n, ww, 14 * ww)
self.S[ 3] ^= self.toLane(message, n, ww, 15 * ww)
self.S[ 8] ^= self.toLane(message, n, ww, 16 * ww)
self.S[13] ^= self.toLane(message, n, ww, 17 * ww)
self.S[18] ^= self.toLane(message, n, ww, 18 * ww)
self.S[23] ^= self.toLane(message, n, ww, 19 * ww)
self.S[ 4] ^= self.toLane(message, n, ww, 20 * ww)
self.S[ 9] ^= self.toLane(message, n, ww, 21 * ww)
self.S[14] ^= self.toLane(message, n, ww, 22 * ww)
self.S[19] ^= self.toLane(message, n, ww, 23 * ww)
self.S[24] ^= self.toLane(message, n, ww, 24 * ww)
self.keccakF(self.S)
message = message[rr:]
def digest(self, msg = None, msglen = None, withReturn = None):
'''
Absorb the last part of the message and squeeze the Keccak sponge
@param msg:bytes? The rest of the message
@param msglen:int The length of the partial message
@param withReturn:bool Whether to return the hash instead of just do a quick squeeze phrase and return `None`
@return :bytes? The hash sum, or `None` if `withReturn` is `False`
'''
if (msg is not None) and isinstance(msg, bool):
(msg, withReturn) = (withReturn, msg)
elif (msglen is not None) and isinstance(msglen, bool):
(msglen, withReturn) = (withReturn, msglen)
if msg is None:
msg = []
elif msglen is not None:
msg = msg[:msglen]
message = self.pad10star1(self.M + msg, self.r)
self.M = None
nnn = len(message)
rr = self.r >> 3
nn = (self.n + 7) >> 3
ww = self.w >> 3
# Absorbing phase
if ww == 8:
for i in range(0, nnn, rr):
n = min(len(message), rr)
self.S[ 0] ^= self.toLane64(message, n, 0)
self.S[ 5] ^= self.toLane64(message, n, 8)
self.S[10] ^= self.toLane64(message, n, 16)
self.S[15] ^= self.toLane64(message, n, 24)
self.S[20] ^= self.toLane64(message, n, 32)
self.S[ 1] ^= self.toLane64(message, n, 40)
self.S[ 6] ^= self.toLane64(message, n, 48)
self.S[11] ^= self.toLane64(message, n, 56)
self.S[16] ^= self.toLane64(message, n, 64)
self.S[21] ^= self.toLane64(message, n, 72)
self.S[ 2] ^= self.toLane64(message, n, 80)
self.S[ 7] ^= self.toLane64(message, n, 88)
self.S[12] ^= self.toLane64(message, n, 96)
self.S[17] ^= self.toLane64(message, n, 104)
self.S[22] ^= self.toLane64(message, n, 112)
self.S[ 3] ^= self.toLane64(message, n, 120)
self.S[ 8] ^= self.toLane64(message, n, 128)
self.S[13] ^= self.toLane64(message, n, 136)
self.S[18] ^= self.toLane64(message, n, 144)
self.S[23] ^= self.toLane64(message, n, 152)
self.S[ 4] ^= self.toLane64(message, n, 160)
self.S[ 9] ^= self.toLane64(message, n, 168)
self.S[14] ^= self.toLane64(message, n, 176)
self.S[19] ^= self.toLane64(message, n, 184)
self.S[24] ^= self.toLane64(message, n, 192)
self.keccakF(self.S)
message = message[rr:]
else:
for i in range(0, nnn, rr):
n = min(len(message), rr)
self.S[ 0] ^= self.toLane(message, n, ww, 0)
self.S[ 5] ^= self.toLane(message, n, ww, ww)
self.S[10] ^= self.toLane(message, n, ww, 2 * ww)
self.S[15] ^= self.toLane(message, n, ww, 3 * ww)
self.S[20] ^= self.toLane(message, n, ww, 4 * ww)
self.S[ 1] ^= self.toLane(message, n, ww, 5 * ww)
self.S[ 6] ^= self.toLane(message, n, ww, 6 * ww)
self.S[11] ^= self.toLane(message, n, ww, 7 * ww)
self.S[16] ^= self.toLane(message, n, ww, 8 * ww)
self.S[21] ^= self.toLane(message, n, ww, 9 * ww)
self.S[ 2] ^= self.toLane(message, n, ww, 10 * ww)
self.S[ 7] ^= self.toLane(message, n, ww, 11 * ww)
self.S[12] ^= self.toLane(message, n, ww, 12 * ww)
self.S[17] ^= self.toLane(message, n, ww, 13 * ww)
self.S[22] ^= self.toLane(message, n, ww, 14 * ww)
self.S[ 3] ^= self.toLane(message, n, ww, 15 * ww)
self.S[ 8] ^= self.toLane(message, n, ww, 16 * ww)
self.S[13] ^= self.toLane(message, n, ww, 17 * ww)
self.S[18] ^= self.toLane(message, n, ww, 18 * ww)
self.S[23] ^= self.toLane(message, n, ww, 19 * ww)
self.S[ 4] ^= self.toLane(message, n, ww, 20 * ww)
self.S[ 9] ^= self.toLane(message, n, ww, 21 * ww)
self.S[14] ^= self.toLane(message, n, ww, 22 * ww)
self.S[19] ^= self.toLane(message, n, ww, 23 * ww)
self.S[24] ^= self.toLane(message, n, ww, 24 * ww)
self.keccakF(self.S)
message = message[rr:]
# Squeezing phase
if withReturn:
rc = [0] * ((self.n + 7) >> 3)
ptr = 0
olen = self.n
j = 0
ni = min(25, rr)
while olen > 0:
i = 0
while (i < ni) and (j < nn):
v = self.S[(i % 5) * 5 + i // 5]
for _ in range(ww):
if j < nn:
rc[ptr] = v & 255
ptr += 1
v >>= 8
j += 1
i += 1
olen -= self.r
if olen > 0:
self.keccakF(self.S)
if (self.n & 7) != 0:
rc[len(rc) - 1] &= (1 << (self.n & 7)) - 1
return rc
olen = self.n
while olen > self.r:
olen -= self.r
self.keccakF(self.S)
return None
def simpleSqueeze(self, times = 1):
'''
Force some rounds of Keccak-f
@param times:int The number of rounds
'''
for i in range(times):
self.keccakF(self.S)
def fastSqueeze(self, times = 1):
'''
Squeeze as much as is needed to get a digest a number of times
@param times:int The number of digests
'''
for i in range(times):
self.keccakF(self.S) # Last squeeze did not do a ending squeeze
olen = self.n
while olen > self.r:
olen -= self.r
self.keccakF(self.S)
def squeeze(self):
'''
Squeeze out another digest
@return :bytes The hash sum
'''
self.keccakF(self.S) # Last squeeze did not do a ending squeeze
nn = (self.n + 7) >> 3
ww = self.w >> 3
rc = [0] * nn
olen = self.n
j = 0
ptr = 0
ni = min(25, self.r >> 3)
while olen > 0:
i = 0
while (i < ni) and (j < nn):
v = self.S[(i % 5) * 5 + i // 5]
for _ in range(ww):
if j < nn:
rc[ptr] = v
ptr += 1
v >>= 8
j += 1
i += 1
olen -= self.r
if olen > 0:
self.keccakF(self.S)
if (self.n & 7) != 0:
rc[len(rc) - 1] &= (1 << (self.n & 7)) - 1
return rc