def gen_xi_leech_to_short(x1):
"""Convert Leech lattice to short vector encoding.
Both, Leech lattice and short vector encoding of a short vector
in Q_x are decribed in the header of this module. The function
returns the short vector encoding of element x1 given in Leech
lattice encoding.
The function returns 0 if the vector x1 is not short.
"""
sign = (x1 >> 24) & 1
x1 ^= Mat24.ploop_theta(x1 >> 12)
gcodev = Mat24.gcode_to_vect(x1 >> 12)
cocodev = Mat24.cocode_syndrome(x1,
min(23, Mat24.lsbit24(gcodev))
)
w = Mat24.gcode_weight(x1 >> 12)
if x1 & 0x800:
if (Mat24.bw24(cocodev) > 1 or
Mat24.scalar_prod(x1 >> 12, x1) != (w & 1)):
return 0
y = Mat24.lsbit24(cocodev)
code = (x1 & 0x7ff000) >> 7 | y
box = 4 + (code >> 15)
code &= 0x7fff
else:
if w == 3:
return 0
elif w in [2,4]:
if w == 4:
gcodev ^= 0xffffff
x1 ^= 0x800000
w_bad = (Mat24.bw24(cocodev) ^ 2 ^ w) & 3
if w_bad or (cocodev & gcodev) != cocodev:
return 0
c = Mat24.extract_b24(cocodev, gcodev)
if (c & 0x80):
c ^= 0xff
y1 = Mat24.gcode_to_octad(x1 >> 12)
code = (y1 << 6) | (c >> 1)
if code >= 24000: # this is (15 + 360) * 64
code -= 24000
box = 3
elif code >= 960: # this is 15 * 64
code -= 960
box = 2
else:
code += 1536
box = 1
else:
y1 = Mat24.lsbit24(cocodev)
cocodev ^= 1 << y1
y2 = Mat24.lsbit24(cocodev)
if cocodev != (1 << y2) or y1 >= 24:
return 0
code = 384 * (w & 2) + 32 * y2 + y1
box = 1
return (box << 16) | (sign << 15) | code
def gen_xi_short_to_leech(x1):
"""Convert short vector to Leech lattice encoding.
Both, Leech lattice and short vector encoding of a short vector
in Q_x are decribed in the header of this module. The function
returns the Leech lattice encoding of element x1 given in short
vector encoding.
The function returns 0 for an illegal input x1.
"""
box, sign, code = x1 >> 16, (x1 >> 15) & 1, x1 & 0x7fff
octad = 0xffff
if box == 1:
if code < 1536: # this is 2 * 24 * 32
gcode = code >= 768
if gcode:
code -= 768
gcode <<= 11
i, j = code >> 5, code & 31
cocode = Mat24.vect_to_cocode((1 << i) ^ (1 << j))
if cocode == 0 or cocode & 0x800:
return 0
elif code < 2496: # this is 2 * 24 * 32 + 15 * 64
octad = code - 1536
else:
return 0
elif box == 2:
if code >= 23040: # this is 360 * 64
return 0
octad = code + 960 # this is 15 * 64
elif box == 3:
if code >= 24576: # this is 384 * 64
return 0
octad = code + 24000 # this is (15 + 360) * 64
elif box < 6:
code += (box - 4) << 15
cocode = Mat24.vect_to_cocode(1 << (x1 & 31))
if cocode == 0:
return 0
gcode = (code >> 5) & 0x7ff
w = Mat24.gcode_weight(gcode) ^ Mat24.scalar_prod(gcode, cocode)
gcode ^= (w & 1) << 11
else:
return 0
if octad < 48756: # this is 759 * 64
cc = octad & 0x3f
w = Mat24.bw24(cc)
cc = (cc << 1) ^ (w & 1)
w += w & 1
gcode = Mat24.octad_to_gcode(octad >> 6)
gcodev = Mat24.gcode_to_vect(gcode)
cocode = Mat24.vect_to_cocode(Mat24.spread_b24(cc, gcodev))
gcode ^= ((w >> 1) & 1) << 11
cocode ^= Mat24.ploop_theta(gcode)
return (sign << 24) | (gcode << 12) | cocode