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Bouillaguet Charles
pcg
Commits
1a3d4db5
Commit
1a3d4db5
authored
Apr 13, 2020
by
Bouillaguet Charles
Browse files
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READY !
parent
3dbab27b
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4 changed files
Cunknown/Find_full_S.py
+199
-0
199 additions, 0 deletions
Cunknown/Find_full_S.py
Cunknown/step2.py
+4
-4
4 additions, 4 deletions
Cunknown/step2.py
Cunknown/step3.py
+171
-0
171 additions, 0 deletions
Cunknown/step3.py
challenges/pcg64s-challenge.c
+3
-2
3 additions, 2 deletions
challenges/pcg64s-challenge.c
with
377 additions
and
6 deletions
Cunknown/Find_full_S.py
0 → 100644
+
199
−
0
View file @
1a3d4db5
import
time
import
fpylll
import
os
from
itertools
import
product
from
math
import
log
import
random
k
=
64
known_up
=
6
known_low
=
13
a
=
2549297995355413924
*
2
**
64
+
4865540595714422341
nbiter
=
5
nboutput
=
40
N
=
2
**
128
K
=
2
**
64
LOW
=
2
**
known_low
polA
=
[
0
];
powA
=
[
1
];
for
i
in
range
(
1
,
nboutput
):
polA
.
append
((
polA
[
i
-
1
]
+
powA
[
i
-
1
])
%
N
)
powA
.
append
((
powA
[
i
-
1
]
*
a
)
%
N
)
def
sortiesGenerateur
(
k
):
#OK !
c
=
random
.
randrange
(
N
)
|
1
S
=
[
random
.
randrange
(
N
)]
for
i
in
range
(
k
-
1
):
S
.
append
((
S
[
i
]
*
a
+
c
)
%
N
)
X
=
[]
for
i
in
range
(
k
):
x
=
(
S
[
i
]
%
K
)
^
(
S
[
i
]
>>
64
)
rot
=
S
[
i
]
>>
122
X
.
append
((
x
>>
rot
)
|
((
x
<<
(
64
-
rot
))
%
K
))
return
X
,
S
,
c
## Unrotate
def
rotateX
(
X
,
rot
,
k
):
#OK !
rX
=
[];
for
i
in
range
(
k
):
rX
.
append
((
X
[
i
]
>>
rot
[
i
])
+
((
X
[
i
]
<<
(
64
-
rot
[
i
]))
%
K
))
return
rX
def
unrotateX
(
X
,
rot
,
k
):
#OK !
rot2
=
[]
for
i
in
range
(
k
):
rot2
.
append
(
64
-
rot
[
i
])
return
rotateX
(
X
,
rot2
,
k
)
def
to_bits
(
x
,
k
):
r
=
[]
for
_
in
range
(
k
):
r
.
append
(
x
&
1
)
x
>>=
1
return
r
def
carries
(
x
,
y
):
"""
Renvoie les retenues générées lors du calcul de x + y.
C
'
est ce qu
'
il faut XORer sur x^y pour obtenir x+y
"""
return
(
x
+
y
)
^
(
x
^
y
)
def
MAJ
(
a
,
b
,
c
):
return
(
a
and
b
)
or
(
a
and
c
)
or
(
b
and
c
)
if
__name__
==
'
__main__
'
:
# teste la proba de succès des algorithmes
n
=
1000
success
=
0
X
,
S
,
c
=
sortiesGenerateur
(
nboutput
)
# génère ce qu'on est pas censé connaître, et que le gros calcul doit retrouver
W0
=
S
[
0
]
%
LOW
WC
=
c
%
LOW
rot
=
[]
for
i
in
range
(
nboutput
):
rot
.
append
(
S
[
i
]
>>
122
)
uX
=
unrotateX
(
X
,
rot
,
nboutput
)
start_DS
=
(
S
[
1
]
-
S
[
0
])
%
N
DS
=
[(
polA
[
i
]
*
start_DS
)
%
N
for
i
in
range
(
nboutput
)]
Carry
=
[
carries
(
S
[
0
],
DS
[
i
])
%
N
for
i
in
range
(
nboutput
)]
for
i
in
range
(
1
,
nboutput
):
assert
S
[
i
]
==
(
S
[
0
]
+
DS
[
i
])
%
N
assert
S
[
i
]
==
S
[
0
]
^
DS
[
i
]
^
Carry
[
i
]
# Goal : récupérer S[1] et S[0]
S0
=
S
[
0
]
S1
=
S
[
1
]
S
=
[
to_bits
(
x
,
128
)
for
x
in
S
]
DS
=
[
to_bits
(
x
,
128
)
for
x
in
DS
]
X
=
[
to_bits
(
x
,
64
)
for
x
in
uX
]
Carry
=
[
to_bits
(
x
,
128
)
for
x
in
Carry
]
rot
=
[
to_bits
(
x
,
6
)
for
x
in
rot
]
for
i
in
range
(
nboutput
):
# the rotations give 6 bits
for
j
in
range
(
6
):
assert
S
[
i
][
122
+
j
]
==
rot
[
i
][
j
]
assert
S
[
i
][
58
+
j
]
==
S
[
i
][
122
+
j
]
^
X
[
i
][
58
+
j
]
for
j
in
range
(
128
):
assert
S
[
i
][
j
]
==
S
[
0
][
j
]
^
DS
[
i
][
j
]
^
Carry
[
i
][
j
]
# pas de retenue sur le bit de poids faible
assert
Carry
[
i
][
0
]
==
0
for
j
in
range
(
64
):
# ceci permet de passer de carry[i][j] à Carry[i][j+64] et vice-versa
assert
(
X
[
i
][
j
]
^
X
[
0
][
j
])
^
(
DS
[
i
][
j
]
^
DS
[
i
][
j
+
64
])
==
Carry
[
i
][
j
]
^
Carry
[
i
][
j
+
64
]
# en particulier
assert
(
X
[
i
][
0
]
^
X
[
0
][
0
])
^
(
DS
[
i
][
0
]
^
DS
[
i
][
64
])
==
Carry
[
i
][
64
]
for
j
in
range
(
1
,
128
):
# ceci permet de passer de Carry[i][j-1] et S[0][j-1] à Carry[i][j]
assert
Carry
[
i
][
j
]
==
MAJ
(
S
[
0
][
j
-
1
],
DS
[
i
][
j
-
1
],
Carry
[
i
][
j
-
1
])
assert
S
[
i
][
1
]
==
S
[
0
][
1
]
^
DS
[
i
][
1
]
^
Carry
[
i
][
1
]
assert
S
[
i
][
1
]
==
S
[
0
][
1
]
^
DS
[
i
][
1
]
^
MAJ
(
S
[
0
][
0
],
DS
[
i
][
0
],
Carry
[
i
][
0
])
assert
S
[
i
][
1
]
==
S
[
0
][
1
]
^
DS
[
i
][
1
]
^
(
S
[
0
][
0
]
and
DS
[
i
][
0
])
for
j
in
range
(
1
,
64
):
assert
S
[
i
][
64
+
j
]
==
S
[
0
][
64
+
j
]
^
DS
[
i
][
64
+
j
]
^
MAJ
(
S
[
0
][
63
+
j
],
DS
[
i
][
63
+
j
],
Carry
[
i
][
63
+
j
])
# l'équation VRAIMENT utile est la suivante :
assert
(
X
[
i
][
j
]
^
X
[
0
][
j
])
^
DS
[
i
][
64
+
j
]
^
DS
[
i
][
j
]
==
MAJ
(
S
[
0
][
j
-
1
],
DS
[
i
][
j
-
1
],
Carry
[
i
][
j
-
1
])
^
MAJ
(
S
[
0
][
63
+
j
],
DS
[
i
][
63
+
j
],
Carry
[
i
][
63
+
j
])
# bonnes conditions: DS[i][0] == 1, DS[i][64] == Carry[i][64].
######################################################################################################""
known_S
=
[
-
1
]
*
128
known_Carry
=
[]
for
_
in
range
(
nboutput
):
known_Carry
.
append
([
-
1
]
*
128
)
for
j
in
range
(
6
):
known_S
[
122
+
j
]
=
rot
[
0
][
j
]
known_S
[
58
+
j
]
=
known_S
[
122
+
j
]
^
X
[
0
][
58
+
j
]
for
k
in
range
(
122
,
128
):
assert
known_S
[
k
]
==
S
[
0
][
k
]
for
k
in
range
(
58
,
64
):
assert
known_S
[
k
]
==
S
[
0
][
k
]
for
i
in
range
(
nboutput
):
known_Carry
[
i
][
0
]
=
0
known_Carry
[
i
][
64
]
=
(
X
[
i
][
0
]
^
X
[
0
][
0
])
^
(
DS
[
i
][
0
]
^
DS
[
i
][
64
])
for
j
in
range
(
58
):
print
(
"
j = {}
"
.
format
(
j
))
# on connaît S[0][0:j], Carry[*][0:j+1], S[0][64:64+j], Carry[*][64:64+j+1]
# vérifie que tous les précédents sont OK
for
k
in
range
(
j
):
assert
known_S
[
k
]
!=
-
1
assert
known_S
[
k
]
==
S
[
0
][
k
]
for
k
in
range
(
j
+
1
):
for
i
in
range
(
nboutput
):
assert
known_Carry
[
i
][
k
]
!=
-
1
assert
known_Carry
[
i
][
k
]
==
Carry
[
i
][
k
]
# trouve i>0 tq DS[i][j-1] != Carry[i][j-1], DS[i][64] == Carry[i][64]
# ça marcherait aussi en échangeant == et !=
i
=
None
for
k
in
range
(
1
,
nboutput
):
if
DS
[
k
][
j
]
!=
known_Carry
[
k
][
j
]
and
DS
[
k
][
64
+
j
]
==
known_Carry
[
k
][
64
+
j
]:
i
=
k
break
if
i
is
None
:
raise
ValueError
(
"
no i matching conditions
"
)
print
(
"
OK with i = {}
"
.
format
(
i
))
# assert MAJ(S[0][j], DS[i][j], Carry[i][j]) == S[0][j]
# assert MAJ(S[0][64+j], DS[i][64+j], Carry[i][64+j]) == DS[i][64+j]
# assert (X[i][j+1] ^ X[0][j+1]) ^ DS[i][65+j] ^ DS[i][j+1] ^ DS[i][64+j] == S[0][j]
known_S
[
j
]
=
(
X
[
i
][
j
+
1
]
^
X
[
0
][
j
+
1
])
^
DS
[
i
][
65
+
j
]
^
DS
[
i
][
j
+
1
]
^
DS
[
i
][
64
+
j
]
known_S
[
j
+
64
]
=
X
[
0
][
j
]
^
known_S
[
j
]
for
i
in
range
(
nboutput
):
known_Carry
[
i
][
j
+
1
]
=
MAJ
(
known_S
[
j
],
DS
[
i
][
j
],
known_Carry
[
i
][
j
])
known_Carry
[
i
][
j
+
65
]
=
MAJ
(
known_S
[
64
+
j
],
DS
[
i
][
64
+
j
],
known_Carry
[
i
][
64
+
j
])
found_S0
=
0
for
i
in
range
(
128
):
found_S0
+=
known_S
[
i
]
<<
i
assert
found_S0
==
S0
print
(
"
{:032x}
"
.
format
(
found_S0
))
found_S1
=
(
found_S0
+
start_DS
)
%
N
assert
found_S1
==
S1
assert
(
found_S1
-
a
*
found_S0
)
%
N
==
c
\ No newline at end of file
This diff is collapsed.
Click to expand it.
Cunknown/step2.py
+
4
−
4
View file @
1a3d4db5
...
...
@@ -233,10 +233,10 @@ def full_DS(X, W0, WC, rots):
output
=
set
()
# vérifie qu'on a bien trouvé un des bon DS complet.
listDS
=
[
findDS
(
rot
,
W0
,
WC
)
for
rot
in
listrot
]
listDS
=
[
(
findDS
(
rot
,
W0
,
WC
)
,
rot
)
for
rot
in
listrot
]
output
.
update
(
listDS
)
listDS
=
[
findDSdebug
(
rot
,
W0
,
WC
)
for
rot
in
listrot
]
listDS
=
[
(
findDSdebug
(
rot
,
W0
,
WC
)
,
rot
)
for
rot
in
listrot
]
output
.
update
(
listDS
)
return
output
...
...
@@ -313,8 +313,8 @@ if __name__ == '__main__':
try
:
listDS
=
full_DS
(
X
,
W0
,
WC
,
rot
)
for
DS
in
listDS
:
for
DS
,
rot
in
listDS
:
true_DS
=
((
DS
[
0
]
<<
known_low
)
+
(
a
-
1
)
*
W0
+
WC
)
%
N
print
(
"
Got W_0
= {:04x},
W_c =
{:04x},
DS =
{:032x}
"
.
format
(
W0
,
WC
,
true_DS
))
print
(
"
W_0, W_c, DS, rot
= {:04x}, {:04x}, {:032x}
, {}
"
.
format
(
W0
,
WC
,
true_DS
,
rot
))
except
ValueError
as
e
:
pass
This diff is collapsed.
Click to expand it.
Cunknown/step3.py
0 → 100644
+
171
−
0
View file @
1a3d4db5
import
time
import
fpylll
import
os
from
itertools
import
product
from
math
import
log
import
random
k
=
64
known_up
=
6
known_low
=
13
a
=
2549297995355413924
*
2
**
64
+
4865540595714422341
nbiter
=
5
nboutput
=
40
N
=
2
**
128
K
=
2
**
64
LOW
=
2
**
known_low
polA
=
[
0
];
powA
=
[
1
];
for
i
in
range
(
1
,
nboutput
):
polA
.
append
((
polA
[
i
-
1
]
+
powA
[
i
-
1
])
%
N
)
powA
.
append
((
powA
[
i
-
1
]
*
a
)
%
N
)
## Unrotate
def
rotateX
(
X
,
rot
,
k
):
#OK !
rX
=
[];
for
i
in
range
(
k
):
rX
.
append
((
X
[
i
]
>>
rot
[
i
])
+
((
X
[
i
]
<<
(
64
-
rot
[
i
]))
%
K
))
return
rX
def
unrotateX
(
X
,
rot
,
k
):
#OK !
rot2
=
[]
for
i
in
range
(
k
):
rot2
.
append
(
64
-
rot
[
i
])
return
rotateX
(
X
,
rot2
,
k
)
def
to_bits
(
x
,
k
):
r
=
[]
for
_
in
range
(
k
):
r
.
append
(
x
&
1
)
x
>>=
1
return
r
def
carries
(
x
,
y
):
"""
Renvoie les retenues générées lors du calcul de x + y.
C
'
est ce qu
'
il faut XORer sur x^y pour obtenir x+y
"""
return
(
x
+
y
)
^
(
x
^
y
)
def
MAJ
(
a
,
b
,
c
):
return
(
a
and
b
)
or
(
a
and
c
)
or
(
b
and
c
)
def
sortiesGenerateur
(
S0
,
c
,
k
):
S
=
[
S0
]
for
i
in
range
(
k
-
1
):
S
.
append
((
S
[
i
]
*
a
+
c
)
%
N
)
X
=
[]
for
i
in
range
(
k
):
x
=
(
S
[
i
]
%
K
)
^
(
S
[
i
]
>>
64
)
rot
=
S
[
i
]
>>
122
X
.
append
((
x
>>
rot
)
|
((
x
<<
(
64
-
rot
))
%
K
))
return
X
if
__name__
==
'
__main__
'
:
X
=
[
0
]
*
48
X
[
1
]
=
0xd4166f4c3e02d10a
;
X
[
2
]
=
0x1d1ceb21e7737101
;
X
[
3
]
=
0xf8b90f473a5426d3
;
X
[
4
]
=
0xe3a3b7babb2ad9ca
;
X
[
5
]
=
0x0077f2c80987dd13
;
X
[
6
]
=
0xf8ddaf2431548a13
;
X
[
7
]
=
0x80935e041bbab85a
;
X
[
8
]
=
0xbe0fde3939201c50
;
X
[
9
]
=
0xe9604fdf6b2177b7
;
X
[
10
]
=
0x95d9cf24a229cedf
;
X
[
11
]
=
0x0434a85418759293
;
X
[
12
]
=
0x04d230c1debe7999
;
X
[
13
]
=
0x83a3cd257d4d04b0
;
X
[
14
]
=
0x13990a23037c13c4
;
X
[
15
]
=
0xfbfaea2e50411202
;
X
[
16
]
=
0x421a394a36baebf8
;
X
[
17
]
=
0x5a878c4594ea7221
;
X
[
18
]
=
0xbd37307bdd522b9c
;
X
[
19
]
=
0x39af06b3e9b3ae10
;
X
[
20
]
=
0x1d21f1cee77b8e2e
;
X
[
21
]
=
0xe4bddad0aacaf420
;
X
[
22
]
=
0x1009ed344cd7f2f4
;
X
[
23
]
=
0xff287c5797cceb71
;
X
[
24
]
=
0x85e8968b0d8ab49b
;
X
[
25
]
=
0x69a9b821830862cc
;
X
[
26
]
=
0xf9fe65ed23740aea
;
X
[
27
]
=
0x47669184bc43d948
;
X
[
28
]
=
0xe3f19b31915ae6d3
;
X
[
29
]
=
0x5f3945718b6dac44
;
X
[
30
]
=
0x49bfacfe8056b33c
;
X
[
31
]
=
0xf2b358ceb722628f
;
X
[
32
]
=
0xb4d1bf17f2c57b71
;
X
[
33
]
=
0xb4300000ad802deb
;
X
[
34
]
=
0xe3125e8022de888d
;
X
[
35
]
=
0x2c7f6d404196ed4d
;
X
[
36
]
=
0xb10490274ecbe897
;
X
[
37
]
=
0xb04da8a406da3814
;
X
[
38
]
=
0xbc70124be9a196c9
;
X
[
39
]
=
0xf81a244f765141e6
;
X
[
40
]
=
0x20413cda8442a149
;
X
[
41
]
=
0xf654f8084029c557
;
X
[
42
]
=
0xa1677f2f18f8484c
;
X
[
43
]
=
0x3ef4f6e355c53e70
;
X
[
44
]
=
0x30cceccd8f73c567
;
X
[
45
]
=
0xf22a193ded925cb6
;
X
[
46
]
=
0xa9c0cba2f6abbd89
;
X
[
47
]
=
0xf26c7311f52ededb
;
del
X
[
0
]
original_X
=
X
W_0
,
W_c
,
start_DS
,
rot
=
0x01d0
,
0x035b
,
0x65cca9e25d817ee1460ae35556d5069b
,
(
28
,
53
,
44
,
7
,
47
,
22
,
2
,
10
,
60
,
27
,
46
,
27
,
28
,
2
,
44
,
10
,
36
,
10
,
62
,
42
,
20
,
40
,
15
,
14
,
7
,
59
,
44
,
46
,
59
,
9
,
46
,
10
,
61
,
5
,
28
,
53
,
19
,
32
,
18
,
55
)
# W_0, W_c, start_DS, rot = 0x01d0, 0x035b, 0x65cca9e25d817ee1460ae35556d5069b, (28, 53, 44, 7, 47, 22, 2, 10, 60, 27, 46, 27, 28, 2, 44, 10, 36, 10, 62, 33, 20, 40, 15, 14, 7, 59, 44, 46, 59, 9, 46, 10, 61, 5, 28, 53, 19, 32, 18, 55)
# W_0, W_c, start_DS, rot = 0x05d0, 0x035b, 0x65cca9e25d817ee1460ae35556d5069b, (28, 53, 44, 7, 47, 22, 2, 10, 60, 27, 46, 27, 28, 2, 44, 10, 36, 10, 62, 42, 20, 40, 15, 14, 7, 59, 44, 46, 59, 9, 46, 10, 61, 5, 28, 53, 19, 32, 18, 55)
# W_0, W_c, start_DS, rot = 0x05d0, 0x035b, 0x65cca9e25d817ee1460ae35556d5069b, (28, 53, 44, 7, 47, 22, 2, 10, 60, 27, 46, 27, 28, 2, 44, 10, 36, 10, 62, 33, 20, 40, 15, 14, 7, 59, 44, 46, 59, 9, 46, 10, 61, 5, 28, 53, 19, 32, 18, 55)
uX
=
unrotateX
(
X
,
rot
,
nboutput
)
DS
=
[(
polA
[
i
]
*
start_DS
)
%
N
for
i
in
range
(
nboutput
)]
DS
=
[
to_bits
(
x
,
128
)
for
x
in
DS
]
X
=
[
to_bits
(
x
,
64
)
for
x
in
uX
]
rot
=
[
to_bits
(
x
,
6
)
for
x
in
rot
]
known_S
=
[
-
1
]
*
128
known_Carry
=
[]
for
_
in
range
(
nboutput
):
known_Carry
.
append
([
-
1
]
*
128
)
for
j
in
range
(
6
):
known_S
[
122
+
j
]
=
rot
[
0
][
j
]
known_S
[
58
+
j
]
=
known_S
[
122
+
j
]
^
X
[
0
][
58
+
j
]
for
i
in
range
(
nboutput
):
known_Carry
[
i
][
0
]
=
0
known_Carry
[
i
][
64
]
=
(
X
[
i
][
0
]
^
X
[
0
][
0
])
^
(
DS
[
i
][
0
]
^
DS
[
i
][
64
])
for
j
in
range
(
58
):
# on connaît S[0][0:j], Carry[*][0:j+1], S[0][64:64+j], Carry[*][64:64+j+1]
# trouve i>0 tq DS[i][j-1] != Carry[i][j-1], DS[i][64] == Carry[i][64]
# ça marcherait aussi en échangeant == et !=
i
=
None
for
k
in
range
(
1
,
nboutput
):
if
DS
[
k
][
j
]
!=
known_Carry
[
k
][
j
]
and
DS
[
k
][
64
+
j
]
==
known_Carry
[
k
][
64
+
j
]:
i
=
k
break
if
i
is
None
:
raise
ValueError
(
"
no i matching conditions
"
)
print
(
"
OK with i = {}
"
.
format
(
i
))
known_S
[
j
]
=
(
X
[
i
][
j
+
1
]
^
X
[
0
][
j
+
1
])
^
DS
[
i
][
65
+
j
]
^
DS
[
i
][
j
+
1
]
^
DS
[
i
][
64
+
j
]
known_S
[
j
+
64
]
=
X
[
0
][
j
]
^
known_S
[
j
]
for
i
in
range
(
nboutput
):
known_Carry
[
i
][
j
+
1
]
=
MAJ
(
known_S
[
j
],
DS
[
i
][
j
],
known_Carry
[
i
][
j
])
known_Carry
[
i
][
j
+
65
]
=
MAJ
(
known_S
[
64
+
j
],
DS
[
i
][
64
+
j
],
known_Carry
[
i
][
64
+
j
])
found_S0
=
0
for
i
in
range
(
128
):
found_S0
+=
known_S
[
i
]
<<
i
found_S1
=
(
found_S0
+
start_DS
)
%
N
found_c
=
(
found_S1
-
a
*
found_S0
)
%
N
XX
=
sortiesGenerateur
(
found_S0
,
found_c
,
64
)
for
i
,
x
in
enumerate
(
XX
):
print
(
"
X[{:2d}] = 0x{:016x};
"
.
format
(
i
,
x
))
This diff is collapsed.
Click to expand it.
challenges/pcg64s-challenge.c
+
3
−
2
View file @
1a3d4db5
...
...
@@ -24,11 +24,12 @@ int main()
printf
(
"Predictor input:
\n
"
);
for
(
int
i
=
0
;
i
<
3
;
i
++
)
printf
(
"X[%2d] = 0x%016"
PRIx64
"
\n
"
,
i
,
pcg64s_random_r
(
&
rng
));
printf
(
"X[%2d] = 0x%016"
PRIx64
"
;
\n
"
,
i
,
pcg64s_random_r
(
&
rng
));
printf
(
"
\n
"
);
printf
(
"Remaining of the sequence (predictor output, in principle):
\n
"
);
for
(
int
i
=
3
;
i
<
10
;
i
++
)
printf
(
"X[%2d] = 0x%016"
PRIx64
"
\n
"
,
i
,
pcg64s_random_r
(
&
rng
));
printf
(
"X[%2d] = 0x%016"
PRIx64
"
;
\n
"
,
i
,
pcg64s_random_r
(
&
rng
));
return
EXIT_SUCCESS
;
}
\ No newline at end of file
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