Title: Bravion - Strong Encryption Algorithm
Question: Is there more to encryption than XORing output from Random(256) with a chars from a string? Yes there's allot more to it.
Answer:
[ABOUT]
The name Bravion is pronnounced brave-ion. It is an alegory for molecules undergoing chemical reactions. A molecule is separeted into its ions, which then regroup with ions from a reactant to form new ions. In this algorithm, the ions change properties as well: protons, neutrons and electrons are reconfigured by the reactant and make the resulting molecules unpredictable without knowing the original reactant. Indeed it takes a brave ion to undergo such abuse :)
The routines here aren't very straight forward, even for one who has studied ciphers. I will try to keep it in lamens terms to the best of my ability. Bravion uses a 256bit key and a 128bit block size. It is an iterated (multiple rounds) substitution/permutation network. It is fast, but not nearly the fastest I've seen. I encrypt around 3MB/sec on my system.
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*************************** ALGORITHM ANALYSIS *****************************
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[GLOSSARY - read carefully]
block size:
Size in bits of the data to encrypt (fixed in all block
ciphers)
plaintext:
Data that has not yet been encrypted.
ciphertext:
Data that has been encrypted.
key:
Data used to modify plaintext into an incomprehensible sate.
entropy:
Unpredicatble data.
permutation:
Transformation of data by displacements (of individual or
grouped bits) or transformation of data by mathematical
functions. Dependent permutations require another source
of data, and once permutated, both data are required to
reverse the permutation.
dependency:
Data required to inverse a permutation.
key size:
Size in bits of the data used as a key (this can be
variable in *some* ciphers, but is limited to the
dependency imposed by the block size)
xor:
Bitwise exclusive OR. xor has an important property:
if A xor B = C, then C xor A = B, C xor B = A
xor works wonders for permutations.
mul:
Multiplication modulo 2^32 where a factor of 0 is
interpreted as 2^32+1.
add:
Addition modulo 2^32.
sub:
Subtraction modulo 2^32.
shr:
Bit-shift to the right covering the ENTIRE block of data
rather than individual integers.
shl:
Same as shr, but the bit shift is to the left.
substitution:
Exchanging one group of bits for another. The result of a
substitution depends on the bits that are being substituted.
This process is always reversable, using irreversable
substitution to change data is considered (by myself) a
permutation.
S-BOX:
An array of values that are used to replace on block of
data for another such as SBOX:array[0..255]of byte would
be used to replace a byte for another:
B:byte;
B:=SBOX[B];
To reverse the process S-BOXs can be structured such that
SBOX[SBOX[B]]=B or (preferably) a compliment of the X-BOX
can be created such that SBOX_1[SBOX_0[B]]=B
An S-BOX's array must be of suitable size to accept any
input data as an index (for a byte: 0..255, for a word:
0..65535). S-BOXs are very efficient substitution
mechanisms.
feistel network:
Data is divided into 2 halfs, one half is permutated
(and/or substituted) and the second half is a product
(usualy an xor) of the permuted first half and
itself. To reverse the process the inverse of the
product is obtained for to restore the second half
(in the case of an xor, another xor does the trick)
and the first half is then restored with the inserve
of the permutation applied to it.
round:
An intteration of a set of functions. Almost all ciphers
implement rounds. Some use as little as 8, others use as
many as 32. A general rule of thumb is the more rounds,
the harder it is to break the cipher (unless the rounds
are very simple). The number of rounds is usualy a little
bigger than the minimum needed to maintain a safe cihper.
It is a compromise between security and speed.
round keys:
Data that contains entropy from the key used in sequencial
order determined by the current round.
component:
A group of operations (permutations, substitutions etc..)
attacker:
Someone trying to decrypt ciphertext without the key.
satistical analysis:
Using probability theory to aid in *guessing* possible
plaintext from ciphertext.
brute force:
Decrypting ciphertext with every possible key until the
plaintext is found. If an attacker is unable to break a
cipher, the only option is brute force (holding a gun to
whomever knows the key's head is not considered brute
force, it's considered social engineering)
[ALGORITHM]
The encryption process can be broken down into 5 components.
BEFORE ITTERATING THROUGH THE ROUNDS[1] B[0]:=B[0] xor RK[PK[16],0]; //PK holds the path keys
B[1]:=B[1] xor RK[PK[17],1]; //that determine the round
B[2]:=B[2] xor RK[PK[18],2]; //keys to use
B[3]:=B[3] xor RK[PK[19],3];
A key-dependent permutation by XOR with round keys. Which
round keys are used depends on the original key. A set of
path keys is extrapolated from the key. Which round keys
are used is unknown to an attacker. This is done so that
in the event that portions of the round keys have been
recovered by an attacker, knowledge of the original key
is inherently required. The original key cannot be found
by solving all the round keys due to the initialization
mechanism (discussed later). This is done to the plaintext
before entering the first round and after finishing the
last round. This dissolves linearity of repetited
components (even though there should be none, I have taken
no chances with Bravion. I have not seen this sort of
permutation in any other algorithm, but I am confident that
this component seriously impairs an attacker's chances at
successful statistical analysis.
ROUND DESCRIPTION[2] CarryBit:=(B[0] and 2147483648) shr 31;
B[0]:=(B[0] shl 1) or ((B[1] and 2147483648) shr 31);
B[1]:=(B[1] shl 1) or ((B[2] and 2147483648) shr 31);
B[2]:=(B[2] shl 1) or ((B[3] and 2147483648) shr 31);
B[3]:=(B[3] shl 1) or CarryBit;
the data put through a shl and the last bit of the block
is put into the first bit. In most ciphers data is only
re-ordered in bytes, word, or longwords, and this leads to
statistical analysis of these groups of bits. Since each
bit is shifted 1 bit, every byte/word/longword recieves 1
bit from the previous. After itterating through 16 rounds,
each byte has been permuted with each bit twice. Their
order does not change however, so the same statistical
analysis can be accomplished. The solution to this problem
lies in [4]. The reverse is a shr and the first bit of the
block is put into the last bit.
[3] B[3]:=B[3] xor (B[2]-RK[i,3]);
B[2]:=B[2] xor Mul(B[1],RK[i,2]);
B[1]:=B[1] xor (B[0]+RK[i,1]);
B[0]:=B[0] xor RK[i,0];
Taking out all the components designed to reinforce
Bravion except [5], the heart of Bravion lies here. The
Theory employed here lies in 3 algebraic [is that how it's
spelt?] groups, add, mul, xor each having an etropy the
same size as its inputs (in this case 32bits). Using a
fixed parameter (the round key) and going through each
possible value with the second parameter will never result
in the same output with any of these 3 groups. The second
important property of this component is that all but one
longword of the block are dependent of the others. To
solve B[1] you must solve B[0], to solve B[2] you have to
have solved B[2] with B[0] and so on. Only B[0] is
independent of the other longwords of the block. xor is
used, because of the inefficiency (in speed) of calculating
the inverses of these algebraic groups.
[4] for i:=0 to 15 do T[i]:=B[P0[PK[i],0]]
Move(T,B,16);
//T,B:array[0..15]of byte
This is what I called a re-ordering matrix. Things get a
little akward in this component. Have a look at the square
matrix below:
P0:array[0..15,0..15]of longword = (
($A,$3,$B,$C,$5,$E,$9,$F,$0,$7,$4,$6,$1,$D,$2,$8),
($9,$5,$F,$3,$1,$0,$A,$4,$7,$B,$E,$8,$2,$6,$D,$C),
($6,$D,$A,$4,$3,$5,$2,$8,$B,$F,$9,$C,$0,$E,$7,$1),
($E,$7,$0,$D,$8,$B,$1,$3,$9,$6,$C,$4,$A,$2,$F,$5),
($C,$A,$2,$5,$F,$D,$7,$9,$4,$E,$6,$B,$8,$3,$1,$0),
($5,$9,$3,$8,$D,$6,$4,$C,$1,$0,$7,$2,$E,$B,$A,$F),
($0,$6,$4,$A,$7,$3,$B,$E,$2,$8,$5,$1,$D,$F,$C,$9),
($D,$F,$9,$0,$6,$2,$3,$1,$E,$C,$A,$5,$B,$8,$4,$7),
($1,$0,$C,$2,$9,$7,$6,$D,$3,$5,$8,$E,$F,$A,$B,$4),
($3,$8,$5,$7,$2,$C,$E,$B,$A,$9,$D,$F,$4,$1,$0,$6),
($F,$B,$D,$1,$C,$8,$0,$6,$5,$2,$3,$7,$9,$4,$E,$A),
($8,$E,$1,$9,$4,$F,$C,$5,$6,$D,$2,$A,$7,$0,$3,$B),
($4,$C,$7,$6,$E,$1,$5,$2,$F,$A,$B,$0,$3,$9,$8,$D),
($7,$2,$6,$B,$0,$4,$D,$A,$8,$1,$F,$3,$5,$C,$9,$E),
($2,$1,$8,$E,$B,$A,$F,$7,$D,$4,$0,$9,$C,$5,$6,$3),
($B,$4,$E,$F,$A,$9,$8,$0,$C,$3,$1,$D,$6,$7,$5,$2));
Pay attention to the values in each rown and each column.
In every row, values from 0 to 15 are assigned once, and in
every column, values from 0 to 15 are assigned once. Each
row represents an order to put the bytes of the block in.
To demonstrate I will use the following block of plaintext:
B=16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31
Using the first row for this demonstration value can be
assigned to a temporary block through indexing:
T[0]:=B[P0[0]]; //T[0]:=B[$A];
T[1]:=B[P0[1]]; //T[1]:=B[$3];
T[2]:=B[P0[2]]; //T[2]:=B[$B];
...and so on...
T[15]:=B[P0[15]]; //T[15]:=B[$8];
T=26,19,27,28,21,30,25,31,16,23,20,22,17,29,18,24
T now contains all bytes of B, but in the new order. T is
then copied into B and B has been re-ordered. There are 16
rows in all. A path key determines which row to use, hence
which order to put B in. To reverse the permutation I have
created a re-ordering matrix that is the inverse of this
one such that T[0]=B[P0[0]], B[0]=T[P1[0]. There are 16!
(=~2.09x10^13=~2^44) ways to re-order 16 bytes. This
subsitution occurs 16 times, and since no 2 rows will put
any byte in the same position (look at the columns), the
number of possible orders is increased by a factor of 16
each time, for a total of 16^16. This means that we cover
all the possible orders 4.2 million times in excess! This
is only the theoretical boundary, the true boundary is
still 16!, but we at least know that the resulting
ciphertext could be in ANY of these 16! arrangements. The
re-ordering matrix by itself helps, but does not do much
against statistical analysis because the bits are still in
8bit groups. Combined with the re-ordering matrix, the 1bit
shift, scatters bits independently from each-other in 16!
orders. I have read papers stating that idealy, blocks
should be permuted as one block and not sub-blocks, but
that because of the data size required to achieve such a
large permutation would be beyond the reach of our
technology. To put things into context, an S-BOX of 8bits
in 8bits out is 255bytes, 16bits-in 16bits-out is
131072bytes, 128bits-in 128bits-out would be
5.4x10^39bytes! Unfortunatly, this structure only allows
for 2^44 different block-sized permutations, but it's still
a great advantage.
[5] for i:=0 to 15 B[i]:=S0[B[i],j];
//B:array[0..15]of byte
This component substitutes each byte in B for another.
There are 16 of these S-BOXs and an inversed S-BOX for
each. One S-BOX is used for each round. I've added these
S-BOXs as a precaution. I used my random number generator
NoiseSpunge (http://www.delphi3000.com/article.asp?ID=2239)
to generate completly random S-BOXs. The result is the
outputs are drastic permutations on 8bit groups.
FINISHED ROUND
INITIALIZATION
Initialization is done in 3 steps.
[1] The key is divided into 32 bit groups. Each group serves as
as seed to a pseudo random number generator (PRNG). This
PRNG has a period of 2^32 implying that no 2 seeds will
generate the same sequence and that it will no show signs
of a pattern before ~4billion numbers have been output.
Each of the 8 seeds are used to generate 256bits which are
stored as the round keys.
[2] Path keys are extrapolated directly from the key by means
of this function:
for i:=0 to 15 do //SET 4BIT PATH KEYS
begin
PK[i]:=(Key[i] xor Key[i+16])and $F;
j:=16+(i mod 8);
PK[j]:=PK[j] xor (Key[i] xor Key[i+16])and $F0)shr 4;
end; //Key is interpreted as array[0..31]of byte
[3] The key is encrypted with the current round keys and the
resulting ciphertext is used to replace 2 sets of round
keys. This is repeated until each set of round keys has
been overwritten 128 times. This may seem like obsessive
paranoya, but that would be incorrect. This is a precaution
against brute force. If initialization requires encrypting
256 blocks, then for every key an attacker wants to test
will take the a little longer than it takes to decrypt 256
blocks! Of course to the end user this doesn't even put a
dent in his processor usage, but to an attacker trying to
test 2^256 keys, it will lengthen his search by a factor of
256. This is like adding 8bits of key data to his search.
I haven't seen this form of initialization used as a brute
force deterent before, but I'm certain I'm not the first to
think about it.
I strongly recomend you read this article: http://www.delphi3000.com/articles/article_2102.asp
as well use the unit included to produce the 256bit keys.
Below is the entire unit. Credit is as always well appreciated!
//BRAVION (C)Copyright DrMungkee 2001
unit Bravion;
interface
type
TBravionBlock8 = array[0..15]of byte;
TBravionBlock32 = array[0..3]of longword;
TBravionKey8 = array[0..31]of byte;
TBravionKey32 = array[0..7]of longword;
TBravionRoundKey32 = array[0..15]of TBravionBlock32;
TBravionPathKey8 = array[0..23]of longword;
TBravionContext = record
RK:TBravionRoundKey32;
PK:TBravionPathKey8;
end;
procedure BravionInit(var Context:TBravionContext;var Key:TBravionKey32);
procedure BravionDecrypt(var Context:TBravionContext;var B:TBravionBlock32);
procedure BravionEncrypt(var Context:TBravionContext;var B:TBravionBlock32);
implementation
const
//SUBSTITUTION BOXES FOR EACH ROUND
S0:array[0..15,0..255]of longword = ((
$68,$9D,$A8,$7C,$0D,$E1,$C1,$21,$BC,$97,$84,$A2,$DE,$EE,$45,$BD,
$17,$D8,$32,$D5,$A7,$1A,$64,$23,$1B,$B8,$07,$A1,$3B,$6E,$DF,$8D,
$24,$50,$F4,$73,$C4,$59,$B7,$38,$D3,$47,$10,$E7,$93,$DD,$0A,$3C,
$36,$AA,$9A,$B1,$75,$8E,$5B,$9B,$49,$33,$C8,$A4,$1C,$06,$20,$46,
$88,$FA,$FC,$CC,$2E,$AD,$05,$1D,$86,$EF,$04,$3F,$6D,$0F,$D2,$5C,
$DB,$5F,$0C,$71,$E3,$87,$A3,$8F,$AC,$9E,$0B,$AB,$EA,$5E,$AF,$16,
$44,$E6,$39,$FB,$2A,$43,$3A,$F9,$48,$7E,$11,$08,$4C,$CB,$ED,$8B,
$95,$C0,$01,$29,$4E,$B6,$63,$5D,$A9,$52,$56,$C5,$BB,$12,$81,$91,
$F7,$7F,$4F,$3E,$2C,$F1,$EB,$54,$B5,$00,$6C,$8A,$26,$FF,$1E,$CA,
$83,$9F,$D7,$EC,$77,$85,$B3,$F2,$CF,$28,$6B,$BF,$02,$96,$B0,$27,
$F8,$F6,$DC,$D6,$7B,$65,$78,$60,$70,$82,$B9,$98,$BA,$62,$30,$61,
$19,$B2,$09,$E9,$18,$79,$22,$14,$D9,$D1,$B4,$15,$E5,$F5,$92,$51,
$80,$6A,$53,$89,$D4,$E0,$0E,$31,$76,$55,$4D,$9C,$94,$E4,$A0,$FE,
$CD,$F3,$4A,$2F,$03,$1F,$69,$D0,$72,$F0,$AE,$8C,$E2,$41,$5A,$7D,
$13,$74,$35,$42,$A6,$90,$25,$C7,$58,$2B,$6F,$C2,$66,$99,$E8,$3D,
$C6,$C9,$57,$CE,$37,$67,$7A,$BE,$40,$2D,$34,$4B,$A5,$C3,$DA,$FD),(
$78,$8D,$66,$CD,$1A,$9C,$0A,$FB,$D8,$3B,$9E,$6B,$73,$54,$45,$75,
$15,$4C,$B5,$B1,$1B,$E0,$A3,$17,$2A,$57,$F0,$82,$07,$C5,$0C,$27,
$88,$12,$A5,$1F,$8F,$D2,$18,$7B,$D3,$D9,$56,$F9,$05,$5C,$06,$68,
$41,$6F,$94,$60,$C6,$C3,$6E,$E2,$D6,$11,$34,$19,$3D,$E5,$E1,$3E,
$47,$B2,$DB,$F4,$B6,$CF,$F5,$10,$4B,$FA,$AB,$7F,$1C,$37,$46,$EE,
$D7,$A6,$E9,$53,$FD,$CE,$EA,$8C,$84,$C7,$6C,$85,$9A,$D5,$28,$DC,
$2B,$FF,$32,$EB,$77,$F2,$24,$4E,$9D,$03,$20,$81,$59,$DE,$C4,$6A,
$A7,$89,$AE,$2E,$3A,$40,$86,$F8,$E4,$D1,$0B,$E8,$E7,$90,$D0,$08,
$02,$B0,$4F,$B3,$C0,$92,$1D,$97,$7D,$E6,$99,$21,$9B,$83,$70,$AC,
$C1,$80,$5E,$23,$5B,$4A,$65,$A8,$63,$61,$6D,$95,$16,$F1,$C2,$52,
$96,$7C,$FE,$3F,$BD,$0D,$B4,$44,$ED,$42,$A0,$2C,$35,$22,$04,$0E,
$D4,$51,$A2,$EC,$43,$AF,$B9,$EF,$39,$49,$2F,$69,$7E,$F3,$BF,$71,
$67,$25,$8B,$8A,$01,$2D,$76,$79,$5F,$E3,$87,$3C,$31,$5A,$36,$1E,
$9F,$98,$58,$CA,$A9,$BB,$DD,$AD,$A1,$50,$09,$33,$A4,$CB,$0F,$B8,
$13,$14,$26,$29,$30,$38,$62,$FC,$72,$64,$DF,$00,$F7,$C8,$8E,$4D,
$AA,$5D,$CC,$C9,$55,$74,$48,$DA,$91,$7A,$B7,$BC,$F6,$93,$BA,$BE),(
$74,$8B,$4E,$20,$AC,$E8,$7A,$EF,$E2,$D6,$80,$BE,$A7,$05,$AA,$55,
$C6,$DE,$1A,$5E,$1D,$30,$DA,$4B,$3D,$6D,$49,$4D,$5C,$9F,$77,$D1,
$0E,$B3,$A5,$28,$0A,$F6,$E0,$83,$63,$7D,$3A,$E7,$E1,$C4,$7C,$27,
$53,$54,$AD,$D3,$87,$F9,$FE,$A9,$1B,$F8,$99,$79,$43,$A1,$04,$46,
$B2,$B4,$67,$CD,$F5,$14,$64,$BA,$16,$4F,$AE,$6A,$5B,$02,$DD,$32,
$BF,$A4,$4C,$36,$2F,$10,$A6,$FA,$01,$8D,$ED,$FF,$7F,$93,$9A,$6F,
$1C,$A3,$92,$B0,$97,$2B,$AF,$6B,$2D,$41,$FB,$EB,$78,$22,$C1,$91,
$51,$15,$F1,$BC,$42,$6E,$70,$CB,$71,$C0,$25,$86,$8A,$18,$85,$98,
$39,$F4,$E5,$00,$D5,$0F,$17,$45,$C3,$5F,$58,$2E,$C5,$7B,$B9,$40,
$1F,$A0,$9C,$3E,$F2,$21,$31,$0B,$9B,$EA,$72,$5D,$76,$13,$3B,$52,
$C8,$61,$09,$D2,$96,$75,$11,$94,$CF,$D0,$29,$06,$CC,$DF,$CE,$33,
$62,$B5,$2C,$1E,$81,$88,$90,$A2,$26,$19,$84,$E3,$D8,$08,$3F,$F3,
$8F,$AB,$B1,$BD,$50,$60,$23,$FC,$3C,$65,$EC,$07,$FD,$A8,$03,$E9,
$DC,$95,$CA,$47,$35,$69,$0D,$38,$DB,$E4,$D4,$C9,$9D,$F0,$5A,$37,
$B8,$6C,$C7,$4A,$68,$82,$66,$24,$7E,$89,$0C,$12,$2A,$34,$44,$48,
$56,$57,$59,$73,$8C,$B6,$E6,$D7,$8E,$EE,$F7,$C2,$D9,$9E,$B7,$BB),(
$DE,$9A,$C5,$FB,$93,$3E,$4E,$99,$68,$CC,$2E,$34,$07,$4F,$D1,$AB,
$36,$50,$73,$19,$57,$F5,$16,$F8,$64,$D7,$37,$CA,$48,$62,$A9,$25,
$3C,$3F,$0C,$C3,$A0,$DF,$D3,$C0,$3D,$66,$B2,$52,$94,$5E,$0E,$4D,
$F0,$69,$8D,$AD,$EF,$4C,$29,$A1,$7C,$02,$23,$5D,$9E,$AC,$03,$97,
$B5,$D6,$6B,$BA,$DC,$83,$C6,$AF,$F6,$9F,$F2,$09,$75,$76,$54,$15,
$00,$DA,$8F,$71,$7B,$6F,$3A,$CE,$C1,$F1,$0F,$67,$B8,$C8,$ED,$45,
$32,$1A,$2B,$6E,$B1,$BE,$85,$C7,$28,$BB,$C2,$82,$5F,$FD,$B0,$5B,
$D5,$44,$61,$63,$7A,$0D,$1C,$E3,$F7,$A6,$8A,$98,$31,$7D,$11,$80,
$A7,$EB,$A8,$22,$51,$E2,$F4,$47,$74,$A3,$14,$FF,$E6,$33,$42,$DD,
$D8,$92,$01,$1D,$9C,$90,$EA,$BD,$8B,$B9,$E9,$24,$65,$7F,$D2,$6A,
$81,$30,$9B,$B7,$E4,$60,$B3,$4A,$8C,$18,$B6,$53,$5A,$41,$B4,$3B,
$D0,$F3,$2D,$87,$27,$26,$2A,$9D,$A4,$D4,$CF,$BC,$17,$72,$43,$46,
$2F,$08,$91,$E0,$1F,$13,$88,$6C,$89,$8E,$38,$A2,$40,$C4,$AE,$FA,
$FE,$E7,$EC,$78,$04,$84,$39,$E5,$77,$E8,$BF,$F9,$55,$59,$12,$21,
$10,$86,$1B,$C9,$05,$A5,$FC,$49,$EE,$CB,$E1,$79,$DB,$96,$5C,$CD,
$D9,$06,$0A,$0B,$1E,$20,$2C,$35,$4B,$56,$58,$6D,$70,$7E,$95,$AA),(
$AE,$02,$85,$29,$A7,$FB,$64,$1C,$77,$78,$69,$F4,$D7,$27,$0F,$41,
$54,$17,$A0,$03,$BB,$72,$E8,$3E,$C6,$3C,$65,$7D,$5E,$DD,$F7,$6B,
$E1,$E9,$2A,$EC,$B0,$34,$35,$73,$BA,$6D,$32,$7A,$50,$2E,$8A,$3D,
$12,$E6,$A6,$4A,$14,$8F,$31,$E2,$5D,$21,$CA,$8C,$48,$63,$8B,$92,
$87,$BC,$16,$61,$E3,$5B,$08,$A5,$E7,$DA,$93,$3B,$94,$13,$0D,$9E,
$07,$CE,$96,$38,$BE,$4F,$60,$66,$B3,$81,$F0,$B2,$36,$FE,$04,$FD,
$C4,$0A,$75,$BF,$A4,$2C,$1D,$83,$42,$C1,$BD,$49,$C9,$B5,$9C,$79,
$A1,$D8,$1B,$47,$D4,$74,$19,$24,$01,$51,$53,$EA,$ED,$1F,$67,$1E,
$71,$D0,$6A,$2F,$62,$3A,$11,$AF,$B1,$57,$26,$43,$9A,$CB,$1A,$70,
$C7,$7B,$39,$2B,$AB,$F2,$A9,$0B,$CC,$B9,$4B,$10,$DE,$E4,$FC,$D2,
$AC,$CD,$EE,$00,$20,$AD,$68,$56,$D3,$AA,$6F,$15,$30,$7C,$28,$E5,
$95,$25,$55,$5F,$0C,$D9,$C0,$A2,$59,$91,$C5,$82,$CF,$9B,$37,$A3,
$F9,$F5,$C2,$22,$A8,$23,$4D,$B7,$FA,$40,$C3,$FF,$D5,$0E,$05,$97,
$5C,$99,$18,$33,$D6,$F1,$B4,$DC,$B6,$D1,$09,$86,$8E,$F3,$52,$06,
$2D,$7E,$EB,$C8,$7F,$3F,$44,$45,$46,$4C,$4E,$58,$88,$DF,$80,$84,
$F8,$90,$9D,$9F,$F6,$8D,$B8,$89,$98,$EF,$5A,$DB,$E0,$6C,$6E,$76),(
$5E,$63,$73,$A1,$FE,$6A,$8E,$C1,$5C,$D8,$1F,$D7,$B1,$97,$FB,$91,
$78,$EB,$1C,$FA,$2C,$D5,$95,$B0,$40,$48,$89,$CE,$3C,$34,$43,$BF,
$4A,$32,$9C,$5B,$71,$AF,$FD,$D2,$29,$18,$C0,$20,$72,$2B,$45,$0E,
$C8,$55,$83,$15,$E5,$A7,$DB,$A5,$8D,$E7,$4F,$7D,$C3,$00,$D3,$85,
$B5,$B4,$C2,$D9,$04,$88,$B8,$AE,$80,$C4,$99,$BB,$61,$13,$0C,$60,
$6F,$9D,$AD,$56,$AA,$F1,$46,$8B,$F2,$8C,$F5,$F7,$51,$E4,$E6,$2F,
$37,$12,$82,$67,$CA,$DF,$A6,$B3,$0F,$AB,$53,$44,$7F,$E9,$10,$1A,
$7A,$9B,$92,$26,$81,$03,$DD,$C5,$11,$DA,$65,$BD,$4C,$42,$86,$E0,
$31,$50,$84,$1D,$B2,$B6,$27,$14,$CF,$49,$D1,$30,$23,$52,$9E,$7C,
$7E,$4B,$BA,$38,$BC,$3F,$EE,$6E,$02,$16,$74,$CB,$2A,$96,$E1,$E3,
$35,$58,$06,$3D,$09,$3E,$E2,$93,$E8,$9A,$8F,$D4,$94,$F4,$47,$CD,
$33,$3A,$A4,$05,$21,$66,$87,$22,$39,$70,$69,$1E,$F9,$75,$24,$79,
$1B,$2E,$5A,$A2,$C6,$C7,$6B,$A8,$54,$D6,$5F,$F6,$EA,$08,$57,$FF,
$28,$6D,$DC,$EF,$41,$BE,$0D,$FC,$7B,$DE,$76,$A9,$CC,$62,$01,$A3,
$EC,$25,$59,$3B,$F8,$07,$0A,$0B,$17,$19,$2D,$36,$A0,$ED,$4E,$B7,
$C9,$5D,$9F,$68,$AC,$64,$F3,$6C,$98,$4D,$D0,$8A,$77,$90,$F0,$B9),(
$4D,$B2,$3C,$E6,$96,$B9,$9D,$C3,$A3,$9E,$FE,$1B,$76,$ED,$46,$31,
$60,$C8,$3E,$98,$FF,$D0,$E2,$F8,$7D,$B8,$99,$FD,$64,$68,$BB,$40,
$8B,$25,$2A,$DE,$4F,$E5,$88,$DB,$2B,$44,$32,$EB,$15,$C5,$5E,$F1,
$3D,$01,$A4,$11,$BA,$5B,$8F,$0A,$37,$7F,$E0,$23,$7A,$2D,$EE,$1E,
$A6,$29,$F7,$F0,$35,$4C,$63,$8A,$93,$92,$34,$B4,$4A,$89,$C4,$F6,
$33,$9C,$FA,$0B,$38,$EA,$2F,$AD,$80,$E1,$1F,$BD,$91,$16,$5C,$9A,
$12,$0D,$26,$82,$6C,$DF,$19,$1A,$54,$45,$F3,$D8,$A1,$3A,$65,$86,
$77,$02,$B1,$74,$97,$BC,$6E,$CF,$F4,$7C,$B0,$8D,$50,$48,$FC,$41,
$09,$81,$95,$6A,$D5,$59,$0E,$E3,$05,$C0,$78,$51,$A8,$87,$84,$D6,
$C9,$E8,$C2,$14,$21,$49,$7E,$0C,$EC,$66,$13,$07,$C1,$10,$9B,$CD,
$C7,$E9,$94,$5F,$B7,$B3,$AB,$3B,$FB,$06,$0F,$F9,$D1,$39,$53,$08,
$6F,$CE,$D2,$61,$E7,$A0,$79,$55,$52,$30,$47,$B5,$04,$58,$75,$F5,
$DD,$73,$71,$67,$BE,$43,$D4,$D9,$1D,$AC,$20,$DA,$A5,$70,$6B,$BF,
$AF,$CC,$3F,$D3,$9F,$24,$DC,$28,$03,$17,$18,$1C,$22,$27,$85,$2E,
$83,$56,$C6,$A9,$2C,$5A,$62,$72,$36,$00,$69,$8E,$CB,$42,$4E,$AE,
$D7,$4B,$57,$A7,$A2,$EF,$E4,$CA,$5D,$6D,$F2,$7B,$8C,$90,$AA,$B6),(
$0C,$56,$BF,$EE,$4F,$AB,$7D,$3E,$73,$98,$A8,$85,$05,$F4,$95,$3D,
$C8,$D3,$67,$CA,$D2,$8C,$0D,$75,$47,$65,$CB,$63,$A2,$8F,$24,$C0,
$18,$5A,$3B,$FA,$16,$77,$31,$A5,$71,$34,$E4,$66,$42,$FC,$EF,$E3,
$DA,$D6,$92,$F1,$79,$EC,$C7,$4B,$99,$2D,$74,$12,$CD,$A9,$1B,$FF,
$B2,$7F,$8A,$1F,$F3,$D0,$B1,$09,$8B,$59,$22,$DB,$D5,$84,$91,$57,
$FE,$68,$C1,$C4,$6B,$87,$F0,$39,$17,$B7,$B0,$E8,$27,$1E,$9F,$2C,
$BE,$1D,$E0,$7B,$E2,$94,$69,$20,$03,$64,$02,$4D,$ED,$7E,$AF,$19,
$5D,$3C,$07,$6E,$36,$CC,$0E,$01,$51,$FD,$3F,$F5,$14,$DF,$0A,$93,
$60,$40,$CF,$26,$53,$81,$2B,$B3,$43,$A6,$C6,$B4,$DD,$52,$A4,$61,
$F6,$08,$28,$76,$7A,$46,$50,$7C,$C3,$A7,$9A,$13,$11,$4E,$04,$4A,
$4C,$33,$6A,$A1,$2E,$83,$BA,$B8,$49,$44,$6F,$E1,$29,$C5,$88,$E9,
$58,$90,$1A,$F7,$8D,$D8,$41,$15,$AC,$37,$F8,$E7,$89,$DC,$BC,$5B,
$E6,$8E,$D7,$23,$1C,$9B,$48,$38,$97,$B6,$55,$2F,$E5,$5F,$B9,$80,
$EA,$C9,$78,$6C,$30,$D1,$82,$AE,$D4,$9E,$00,$C2,$6D,$B5,$86,$DE,
$9D,$45,$54,$AA,$D9,$BD,$5C,$96,$FB,$35,$0F,$CE,$9C,$10,$72,$0B,
$70,$A3,$62,$A0,$25,$EB,$06,$21,$2A,$32,$3A,$5E,$AD,$BB,$F2,$F9),(
$9F,$7E,$36,$84,$96,$8F,$B9,$F9,$32,$71,$93,$A7,$CB,$FA,$8E,$BA,
$D3,$34,$7A,$6A,$E3,$B8,$90,$A5,$52,$A2,$48,$67,$CA,$02,$97,$E7,
$F6,$40,$7C,$BF,$9A,$CD,$DB,$27,$5B,$1B,$63,$AC,$0A,$F3,$B6,$31,
$C7,$80,$53,$4E,$ED,$C0,$CF,$19,$E1,$AA,$41,$E0,$07,$94,$57,$DD,
$9E,$EF,$1E,$25,$74,$FF,$30,$33,$EB,$D5,$FD,$06,$99,$B4,$EE,$98,
$1A,$47,$C1,$7D,$2C,$10,$51,$F0,$5D,$20,$38,$72,$EA,$43,$4D,$23,
$FE,$87,$DA,$0E,$15,$14,$BB,$01,$6C,$8A,$85,$56,$82,$05,$BE,$16,
$76,$2B,$EC,$D2,$44,$21,$61,$C8,$83,$49,$70,$F7,$F2,$AB,$37,$AF,
$9C,$60,$E8,$E5,$7B,$4F,$AE,$39,$04,$CE,$3A,$03,$D1,$54,$7F,$50,
$FB,$5E,$64,$24,$D7,$18,$86,$0D,$4B,$73,$A6,$3C,$69,$E6,$E4,$92,
$E9,$AD,$F4,$28,$6F,$91,$0B,$D8,$2D,$9B,$62,$45,$2A,$6E,$6D,$8C,
$59,$5C,$D9,$F8,$17,$66,$77,$A8,$8B,$DF,$78,$DE,$B3,$42,$79,$4C,
$A3,$89,$D0,$55,$1F,$A4,$C6,$00,$75,$A9,$09,$0C,$81,$B5,$3D,$B7,
$B2,$DC,$6B,$D6,$26,$9D,$3E,$95,$D4,$35,$3B,$E2,$65,$08,$4A,$13,
$1C,$2E,$FC,$0F,$F5,$88,$C9,$BC,$12,$F1,$22,$3F,$B1,$68,$C5,$B0,
$11,$1D,$29,$2F,$46,$58,$5A,$5F,$8D,$A0,$A1,$BD,$C3,$C4,$C2,$CC),(
$EF,$8D,$10,$2A,$79,$42,$8C,$85,$D9,$83,$24,$12,$E9,$9F,$38,$67,
$B2,$5C,$1A,$28,$36,$16,$B7,$11,$A5,$D2,$2E,$06,$1C,$FD,$E5,$41,
$4F,$F4,$20,$AF,$3F,$3B,$05,$35,$9C,$A1,$DA,$3E,$7A,$CD,$F2,$B1,
$FA,$7B,$E3,$F5,$5D,$FE,$ED,$1E,$26,$40,$F9,$BF,$46,$BE,$22,$4A,
$EE,$5F,$6E,$77,$DE,$E8,$D0,$7D,$F6,$31,$2B,$B9,$99,$F3,$9D,$93,
$A3,$A2,$7C,$68,$0A,$07,$6A,$C5,$03,$4C,$27,$C8,$3C,$0B,$4D,$56,
$54,$CF,$73,$72,$49,$A8,$B5,$BC,$F1,$C4,$53,$69,$14,$9B,$47,$C0,
$E0,$C2,$43,$13,$A6,$0C,$84,$E2,$29,$A7,$63,$D5,$2C,$74,$19,$0F,
$CE,$1F,$0D,$DF,$C1,$97,$BB,$65,$C3,$61,$01,$7F,$6F,$3D,$5B,$FC,
$87,$CA,$08,$B8,$09,$CC,$A9,$25,$86,$6D,$AE,$9A,$8A,$15,$66,$EA,
$C7,$37,$58,$BD,$DD,$DC,$60,$91,$B3,$95,$B4,$33,$EC,$D7,$A0,$64,
$2D,$98,$EB,$AD,$4B,$FB,$3A,$44,$71,$F8,$52,$A4,$9E,$E7,$89,$7E,
$39,$B0,$D3,$94,$8F,$45,$E6,$B6,$CB,$0E,$92,$18,$5E,$30,$57,$AA,
$02,$55,$D4,$48,$82,$6B,$E1,$D6,$8B,$21,$78,$75,$32,$90,$76,$70,
$6C,$DB,$C6,$88,$04,$17,$1B,$1D,$23,$2F,$34,$4E,$50,$FF,$8E,$AB,
$D8,$5A,$59,$AC,$00,$C9,$51,$BA,$F7,$D1,$62,$81,$80,$E4,$96,$F0),(
$88,$DF,$B7,$A7,$8A,$CE,$44,$6C,$4F,$4D,$FD,$92,$4A,$56,$A4,$4B,
$58,$D5,$FC,$E8,$F8,$F4,$3A,$43,$EF,$3E,$01,$AC,$36,$2E,$F2,$28,
$09,$C3,$67,$D3,$A1,$29,$DE,$50,$79,$14,$78,$97,$26,$9C,$24,$AD,
$15,$E9,$6B,$7B,$96,$87,$2D,$30,$9B,$8D,$89,$21,$4E,$20,$C8,$5A,
$6E,$71,$06,$33,$74,$E2,$9F,$85,$BD,$EB,$34,$DB,$BE,$B1,$A0,$1B,
$93,$CF,$1A,$E0,$5D,$59,$52,$46,$2C,$2B,$37,$CB,$FB,$38,$95,$9A,
$BC,$32,$AF,$8B,$DA,$11,$68,$B2,$5E,$23,$D8,$22,$7C,$91,$E4,$C2,
$41,$EE,$ED,$17,$05,$3D,$1C,$08,$83,$80,$4C,$D2,$5B,$9D,$3B,$02,
$C4,$C1,$7E,$F3,$BA,$12,$51,$72,$FE,$E5,$62,$70,$60,$EA,$35,$99,
$8C,$65,$BF,$45,$6D,$8E,$DD,$A9,$CA,$F0,$98,$53,$66,$D4,$AE,$B3,
$10,$5C,$F7,$0E,$18,$A8,$0F,$B0,$EC,$76,$AA,$A6,$F5,$3F,$D6,$F6,
$E7,$55,$82,$C9,$AB,$B6,$D0,$04,$C5,$7F,$86,$77,$07,$0C,$5F,$16,
$81,$63,$C7,$40,$31,$54,$B5,$49,$90,$FF,$27,$75,$7A,$CD,$48,$13,
$1D,$03,$D9,$D1,$E6,$0A,$84,$69,$C6,$B9,$B8,$C0,$A3,$B4,$94,$A2,
$D7,$F9,$9E,$6A,$1F,$1E,$0D,$DC,$E3,$CC,$3C,$0B,$6F,$2A,$00,$7D,
$39,$42,$BB,$19,$73,$61,$25,$2F,$47,$57,$64,$8F,$A5,$E1,$F1,$FA),(
$61,$C1,$70,$D5,$26,$07,$09,$EB,$8B,$5F,$28,$E5,$64,$91,$46,$32,
$E0,$72,$9A,$11,$C0,$45,$66,$99,$1D,$8D,$40,$62,$55,$EE,$BB,$5C,
$94,$E6,$1F,$00,$A2,$76,$1B,$34,$78,$0F,$2C,$F6,$97,$4D,$3F,$21,
$6E,$BA,$83,$8F,$B0,$9B,$9E,$2E,$F0,$C4,$FF,$71,$A4,$35,$D8,$69,
$88,$4C,$DB,$1A,$BD,$30,$C7,$47,$80,$90,$17,$A5,$50,$0A,$C3,$57,
$18,$03,$49,$37,$D4,$F8,$CE,$20,$CB,$65,$85,$02,$4A,$DA,$14,$24,
$75,$7A,$48,$A1,$CC,$98,$73,$FD,$C2,$FA,$E7,$68,$AB,$B3,$0C,$D2,
$FC,$53,$5A,$81,$2D,$63,$D3,$33,$DE,$95,$BC,$F2,$44,$4B,$B7,$5D,
$AE,$EC,$B4,$1E,$9C,$DC,$7E,$9D,$8A,$25,$B1,$A8,$22,$D9,$B8,$D0,
$82,$BF,$67,$6A,$01,$0D,$C9,$6B,$AA,$CA,$AC,$A9,$DD,$3C,$8E,$3B,
$F5,$F9,$C8,$23,$C5,$6F,$3A,$08,$51,$E4,$C6,$D6,$84,$87,$A6,$0E,
$FB,$A0,$0B,$E2,$8C,$1C,$15,$E1,$60,$B9,$10,$E8,$74,$5B,$9F,$ED,
$2B,$B2,$29,$7F,$E9,$F7,$36,$F4,$3D,$A3,$D1,$58,$38,$93,$04,$6D,
$B5,$AF,$05,$27,$31,$CF,$E3,$7B,$4F,$5E,$2F,$B6,$52,$7D,$42,$39,
$06,$12,$13,$59,$D7,$16,$CD,$3E,$4E,$BE,$92,$A7,$F3,$77,$EA,$79,
$89,$43,$AD,$86,$DF,$19,$41,$FE,$6C,$7C,$2A,$96,$54,$56,$EF,$F1),(
$99,$09,$EE,$E3,$4B,$6E,$04,$D0,$F6,$76,$8F,$EA,$A7,$2F,$EB,$D8,
$A9,$83,$96,$C8,$F7,$64,$B3,$54,$28,$9B,$B2,$9E,$41,$DF,$CD,$06,
$33,$65,$1F,$80,$4C,$E0,$0C,$B6,$39,$90,$7C,$50,$3C,$B8,$73,$91,
$92,$A2,$C5,$51,$C7,$1A,$4F,$21,$08,$A8,$36,$8B,$6A,$82,$86,$7E,
$59,$95,$D6,$B5,$FC,$37,$02,$B1,$16,$6C,$B0,$C9,$55,$B9,$DE,$F5,
$61,$98,$D4,$63,$C6,$FE,$BA,$C2,$24,$4A,$97,$5F,$67,$ED,$01,$2C,
$46,$9F,$3D,$A0,$23,$58,$62,$13,$2B,$34,$D2,$8E,$D1,$00,$70,$68,
$15,$2E,$31,$45,$A4,$EC,$81,$F4,$F3,$A3,$1C,$75,$07,$F0,$DA,$27,
$CB,$CE,$0F,$1B,$BB,$5B,$F2,$CF,$77,$D9,$18,$7B,$29,$EF,$FB,$D5,
$BE,$3F,$5E,$52,$8D,$26,$A1,$0E,$A5,$1D,$93,$43,$B7,$20,$F1,$38,
$57,$5C,$94,$A6,$79,$E9,$7D,$40,$F9,$0B,$DC,$25,$FD,$BC,$49,$BD,
$44,$AA,$6B,$12,$22,$4D,$0A,$53,$6D,$2D,$7A,$F8,$42,$C3,$4E,$7F,
$60,$E8,$19,$AF,$D7,$71,$78,$1E,$AD,$CA,$6F,$AC,$11,$0D,$8C,$C1,
$5A,$E7,$E2,$CC,$17,$30,$74,$3A,$BF,$3E,$88,$D3,$84,$66,$B4,$9A,
$87,$03,$05,$10,$14,$2A,$32,$69,$9C,$5D,$9D,$85,$E6,$AB,$48,$E1,
$FA,$3B,$72,$AE,$DD,$35,$89,$E5,$8A,$47,$C0,$56,$FF,$C4,$DB,$E4),(
$81,$13,$59,$92,$52,$E4,$BF,$02,$B7,$19,$FD,$87,$53,$2E,$F2,$80,
$CF,$12,$4F,$0A,$9B,$63,$9A,$E3,$68,$CB,$36,$EC,$C8,$2D,$34,$D3,
$31,$56,$F4,$62,$A4,$D4,$71,$ED,$DB,$B0,$B3,$8C,$5A,$D8,$2C,$8D,
$90,$B6,$91,$1C,$7D,$E7,$C5,$65,$F0,$21,$FA,$17,$57,$64,$B2,$75,
$38,$6D,$10,$16,$C9,$E5,$A2,$6A,$0B,$09,$94,$54,$C0,$BE,$42,$95,
$1A,$44,$66,$6B,$30,$73,$7C,$50,$99,$9D,$9E,$A9,$FB,$C4,$E2,$AD,
$6E,$A3,$9C,$55,$EE,$72,$84,$8A,$46,$D2,$28,$A6,$6F,$AE,$74,$F3,
$48,$BB,$35,$1F,$D7,$CC,$AC,$D1,$DD,$5D,$A7,$AA,$76,$3D,$8E,$D0,
$24,$2F,$EB,$DC,$41,$8F,$97,$0F,$3A,$DF,$B9,$DE,$D9,$BD,$7E,$47,
$5B,$14,$40,$FC,$4D,$58,$26,$C3,$29,$11,$4A,$43,$77,$EF,$33,$3B,
$A5,$3E,$88,$1E,$B5,$7F,$4E,$E0,$61,$F8,$DA,$E6,$7A,$03,$A0,$C1,
$BA,$78,$9F,$EA,$E8,$AB,$69,$07,$F9,$E9,$82,$93,$51,$D6,$F1,$FF,
$39,$89,$E1,$1D,$A1,$C7,$F7,$37,$CD,$96,$6C,$67,$D5,$B4,$BC,$60,
$B1,$70,$3F,$27,$85,$83,$7B,$C6,$20,$0C,$B8,$CE,$86,$F6,$0E,$AF,
$5F,$01,$04,$15,$23,$0D,$32,$F5,$22,$00,$18,$4B,$A8,$98,$FE,$2B,
$45,$8B,$5C,$5E,$79,$06,$25,$1B,$05,$CA,$49,$2A,$08,$3C,$C2,$4C),(
$41,$EB,$7F,$0F,$02,$6F,$C4,$47,$D9,$04,$37,$4C,$EF,$A3,$BC,$B6,
$17,$5B,$E4,$11,$1C,$18,$96,$6C,$AF,$58,$87,$50,$0A,$59,$E9,$3E,
$49,$90,$DF,$07,$F1,$D7,$CD,$AE,$82,$2A,$34,$C8,$E0,$7C,$19,$C0,
$9C,$D1,$BE,$31,$E7,$D6,$51,$AA,$EE,$F3,$28,$27,$8F,$A8,$05,$21,
$B7,$78,$E8,$33,$A6,$4D,$DE,$7D,$16,$2B,$9F,$67,$CF,$65,$3B,$BB,
$25,$C3,$6E,$72,$6A,$DD,$C2,$06,$C1,$10,$AD,$EC,$CE,$5F,$F6,$00,
$03,$EA,$29,$FF,$83,$A9,$92,$A7,$53,$71,$7E,$61,$35,$43,$5D,$B8,
$D4,$A4,$A2,$F2,$2D,$30,$DC,$1E,$5C,$88,$57,$24,$E2,$7A,$E1,$48,
$4A,$98,$38,$CA,$5E,$13,$62,$A0,$D5,$F9,$C7,$8B,$54,$80,$BA,$81,
$66,$A5,$F5,$1A,$CB,$6D,$D0,$E3,$F7,$C5,$09,$C6,$23,$20,$55,$94,
$B5,$74,$2C,$26,$1B,$01,$BF,$14,$93,$56,$42,$40,$D3,$B9,$39,$FE,
$8D,$E5,$12,$3A,$3F,$AB,$0B,$ED,$FC,$44,$85,$5A,$DB,$DA,$FB,$7B,
$B1,$63,$9D,$0C,$B3,$8E,$46,$45,$F8,$68,$BD,$77,$FA,$9B,$69,$75,
$76,$36,$99,$79,$FD,$91,$70,$3D,$08,$22,$95,$B0,$F4,$B4,$0E,$64,
$89,$F0,$C9,$2F,$97,$52,$86,$D8,$CC,$4E,$60,$8A,$8C,$4F,$B2,$4B,
$84,$2E,$AC,$A1,$32,$E6,$0D,$9A,$3C,$1D,$15,$1F,$6B,$73,$9E,$D2),(
$BE,$B5,$90,$5C,$C9,$3A,$23,$DF,$78,$00,$F1,$E7,$B8,$ED,$FB,$B3,
$1F,$F6,$6C,$12,$88,$32,$E8,$1C,$C8,$07,$5A,$C2,$25,$65,$B7,$CE,
$47,$CD,$70,$4B,$FC,$53,$DB,$93,$EF,$AB,$6A,$92,$39,$02,$56,$81,
$5E,$51,$1D,$30,$35,$7C,$5F,$A9,$BF,$29,$0A,$76,$DA,$DC,$67,$46,
$96,$19,$10,$0C,$9F,$C1,$43,$3F,$57,$74,$F3,$44,$79,$F7,$BA,$E4,
$6D,$F9,$4A,$34,$8D,$D5,$D8,$2A,$63,$05,$0B,$0E,$2D,$CC,$01,$18,
$D4,$EA,$E9,$31,$94,$15,$AA,$F8,$E1,$C3,$E6,$59,$91,$69,$48,$6E,
$20,$4D,$55,$45,$8A,$11,$66,$16,$F5,$1E,$03,$B1,$21,$9A,$38,$8B,
$D6,$CB,$F2,$D2,$B4,$4E,$3E,$D3,$2E,$EE,$24,$FE,$C5,$77,$33,$E2,
$54,$2C,$C6,$41,$BD,$17,$A0,$13,$D0,$40,$F0,$50,$A3,$EC,$CF,$FF,
$99,$DD,$D1,$09,$61,$AD,$1A,$AF,$89,$CA,$EB,$A5,$84,$8E,$3C,$3B,
$A4,$B0,$82,$8F,$83,$A1,$1B,$E5,$9C,$C0,$7A,$95,$3D,$52,$26,$9B,
$C4,$42,$7F,$F4,$9E,$08,$AC,$72,$D9,$0D,$AE,$FD,$FA,$49,$A7,$D7,
$B6,$62,$36,$68,$4F,$0F,$C7,$2F,$22,$BB,$9D,$04,$BC,$B2,$A8,$27,
$E3,$14,$A6,$7B,$06,$64,$28,$6B,$80,$A2,$97,$87,$73,$7D,$75,$8C,
$60,$85,$7E,$5D,$5B,$58,$37,$2B,$E0,$6F,$4C,$71,$86,$98,$B9,$DE));
//SUBSTITUTION BOXES' INVERSE FOR EACH ROUND
S1:array[0..15,0..255]of longword = ((
$89,$72,$9C,$D4,$4A,$46,$3D,$1A,$6B,$B2,$2E,$5A,$52,$04,$C6,$4D,
$2A,$6A,$7D,$E0,$B7,$BB,$5F,$10,$B4,$B0,$15,$18,$3C,$47,$8E,$D5,
$3E,$07,$B6,$17,$20,$E6,$8C,$9F,$99,$73,$64,$E9,$84,$F9,$44,$D3,
$AE,$C7,$12,$39,$FA,$E2,$30,$F4,$27,$62,$66,$1C,$2F,$EF,$83,$4B,
$F8,$DD,$E3,$65,$60,$0E,$3F,$29,$68,$38,$D2,$FB,$6C,$CA,$74,$82,
$21,$BF,$79,$C2,$87,$C9,$7A,$F2,$E8,$25,$DE,$36,$4F,$77,$5D,$51,
$A7,$AF,$AD,$76,$16,$A5,$EC,$F5,$00,$D6,$C1,$9A,$8A,$4C,$1D,$EA,
$A8,$53,$D8,$23,$E1,$34,$C8,$94,$A6,$B5,$F6,$A4,$03,$DF,$69,$81,
$C0,$7E,$A9,$90,$0A,$95,$48,$55,$40,$C3,$8B,$6F,$DB,$1F,$35,$57,
$E5,$7F,$BE,$2C,$CC,$70,$9D,$09,$AB,$ED,$32,$37,$CB,$01,$59,$91,
$CE,$1B,$0B,$56,$3B,$FC,$E4,$14,$02,$78,$31,$5B,$58,$45,$DA,$5E,
$9E,$33,$B1,$96,$BA,$88,$75,$26,$19,$AA,$AC,$7C,$08,$0F,$F7,$9B,
$71,$06,$EB,$FD,$24,$7B,$F0,$E7,$3A,$F1,$8F,$6D,$43,$D0,$F3,$98,
$D7,$B9,$4E,$28,$C4,$13,$A3,$92,$11,$B8,$FE,$50,$A2,$2D,$0C,$1E,
$C5,$05,$DC,$54,$CD,$BC,$61,$2B,$EE,$B3,$5C,$86,$93,$6E,$0D,$49,
$D9,$85,$97,$D1,$22,$BD,$A1,$80,$A0,$67,$41,$63,$42,$FF,$CF,$8D),(
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$FA,$CF,$57,$BD,$FD,$32,$54,$34,$13,$4B,$C9,$80,$D3,$1E,$81,$87,
$07,$6C,$6A,$DB,$52,$8F,$42,$C4,$0F,$89,$7E,$FE,$AA,$F4,$4E,$1D,
$25,$EF,$D2,$03,$FF,$F7,$EC,$D1,$C1,$A5,$0B,$0E,$75,$5D,$02,$8D,
$7D,$9E,$86,$78,$77,$4F,$08,$14,$BB,$A8,$F0,$8E,$44,$AC,$55,$FC),(
$E9,$E1,$07,$AD,$E2,$F8,$F5,$B7,$FC,$49,$13,$48,$D9,$E5,$DE,$87,
$42,$99,$11,$01,$91,$E3,$43,$3B,$EA,$09,$50,$F7,$33,$C3,$A3,$73,
$D8,$39,$E8,$E4,$80,$F6,$96,$D3,$6A,$98,$FB,$EF,$2E,$1D,$0D,$81,
$54,$20,$E6,$9E,$1E,$72,$1A,$C7,$40,$C0,$88,$9F,$FD,$7D,$A1,$D2,
$92,$84,$4E,$9B,$51,$F0,$68,$8F,$70,$FA,$9A,$EB,$FF,$94,$A6,$12,
$57,$BC,$04,$0C,$4B,$63,$21,$3C,$95,$02,$2C,$90,$F2,$79,$F3,$E0,
$CF,$A8,$23,$15,$3D,$37,$52,$CB,$18,$B6,$47,$53,$CA,$41,$60,$6C,
$D1,$26,$65,$55,$6E,$3F,$7C,$9C,$B1,$F4,$AC,$D6,$56,$34,$8E,$A5,
$0F,$00,$BA,$D5,$66,$D4,$DC,$0B,$A2,$C1,$67,$F1,$2B,$2F,$7E,$85,
$30,$32,$03,$BB,$4A,$4F,$C9,$86,$ED,$58,$16,$14,$62,$59,$5A,$B2,
$AE,$C4,$46,$61,$24,$A0,$6B,$7A,$EC,$5B,$7B,$B5,$76,$5F,$6D,$DF,
$29,$D0,$3E,$2A,$CD,$A4,$31,$08,$DA,$8A,$B0,$71,$CE,$8D,$4D,$06,
$4C,$AF,$FE,$97,$5D,$36,$D7,$C5,$1C,$44,$F9,$19,$75,$C8,$DB,$10,
$7F,$77,$69,$1F,$25,$CC,$BD,$74,$2D,$8C,$AA,$28,$83,$78,$8B,$89,
$A7,$C2,$5E,$17,$05,$45,$AB,$35,$B4,$B9,$B3,$82,$1B,$27,$64,$9D,
$38,$BE,$0E,$6F,$22,$E7,$DD,$C6,$A9,$B8,$3A,$5C,$93,$0A,$EE,$BF),(
$5F,$A5,$04,$60,$09,$3E,$57,$23,$D8,$9A,$1C,$B6,$C3,$F6,$DE,$03,
$59,$13,$B2,$85,$A7,$FA,$48,$10,$15,$2E,$93,$A4,$14,$F9,$77,$FB,
$9D,$3F,$D9,$9C,$7B,$50,$A3,$3B,$3A,$62,$29,$49,$A2,$74,$F1,$E3,
$75,$33,$F4,$43,$2A,$6C,$D1,$0A,$82,$AE,$B3,$4E,$F8,$D7,$1F,$B4,
$AB,$00,$AA,$6D,$B9,$C7,$C6,$07,$7F,$20,$80,$EF,$0B,$45,$E9,$ED,
$1B,$36,$E5,$68,$8C,$9E,$A9,$7A,$19,$1D,$BB,$11,$78,$6E,$84,$5D,
$EA,$6B,$86,$C1,$DF,$4D,$90,$4B,$C9,$CE,$54,$FC,$17,$95,$52,$05,
$D6,$69,$53,$FD,$A1,$CF,$D0,$CB,$41,$D3,$7D,$BF,$2D,$47,$6A,$02,
$8D,$8F,$28,$64,$F0,$BA,$E6,$1A,$79,$E0,$EB,$8B,$EC,$B0,$C5,$3C,
$21,$D5,$66,$A8,$9F,$DA,$16,$E4,$81,$D2,$F7,$CD,$30,$C2,$FE,$4A,
$87,$F3,$72,$0D,$71,$91,$44,$67,$3D,$65,$37,$B5,$F2,$5A,$27,$18,
$DB,$C0,$EE,$C4,$DD,$A0,$0F,$40,$6F,$AD,$8E,$4F,$0E,$CA,$32,$A6,
$2F,$58,$56,$51,$06,$99,$9B,$8A,$2B,$E2,$83,$94,$E8,$26,$5C,$4C,
$96,$31,$FF,$AC,$70,$88,$35,$25,$E7,$08,$BD,$BC,$76,$55,$46,$22,
$2C,$7E,$7C,$97,$12,$B1,$F5,$34,$42,$1E,$61,$01,$5B,$B7,$38,$0C,
$E1,$24,$73,$39,$DC,$92,$5E,$98,$C8,$89,$CC,$BE,$B8,$D4,$AF,$63),(
$09,$5E,$2D,$7A,$DB,$59,$E4,$19,$C5,$A3,$3A,$5A,$43,$C9,$5B,$D5,
$42,$75,$13,$97,$E1,$65,$77,$95,$5F,$41,$A6,$B6,$17,$32,$79,$10,
$70,$7C,$D8,$06,$8A,$1C,$BE,$DF,$E6,$39,$57,$F7,$91,$5C,$88,$D7,
$33,$63,$15,$8E,$53,$34,$D2,$F6,$7E,$2C,$05,$AF,$AE,$BC,$86,$47,
$99,$93,$C1,$46,$4B,$73,$3F,$20,$6E,$CD,$52,$23,$FA,$71,$85,$D4,
$9B,$31,$BD,$25,$90,$72,$2E,$48,$F5,$6B,$1A,$F4,$03,$F3,$30,$36,
$F0,$A4,$D1,$58,$E5,$1D,$76,$3E,$D3,$6D,$2A,$E7,$12,$50,$6F,$F9,
$22,$FB,$C7,$EC,$49,$EE,$3B,$8D,$08,$4C,$BA,$E3,$35,$ED,$F2,$C2,
$E8,$2F,$B2,$B4,$AC,$F1,$FC,$EB,$14,$A8,$74,$7F,$EF,$54,$AD,$B3,
$02,$6C,$2B,$27,$64,$BB,$40,$EA,$FD,$A0,$7D,$BF,$B8,$DA,$C4,$44,
$96,$B5,$E9,$9C,$B0,$AB,$E2,$CE,$DE,$37,$66,$29,$C6,$A5,$CA,$A7,
$B1,$7B,$DD,$0F,$84,$01,$D0,$1E,$0C,$FE,$4E,$D9,$DC,$94,$00,$38,
$B9,$45,$1B,$69,$C0,$8C,$92,$D6,$18,$04,$A9,$81,$5D,$21,$1F,$9E,
$98,$A2,$83,$87,$60,$55,$80,$CF,$56,$C8,$3C,$26,$3D,$A1,$FF,$07,
$F8,$68,$8F,$E0,$4F,$B7,$6A,$0B,$16,$62,$61,$AA,$9D,$0D,$89,$28,
$9A,$0A,$82,$4A,$C3,$78,$11,$4D,$67,$51,$CC,$0E,$24,$CB,$8B,$9F));
//RE-ORDERING MATRIX
P0:array[0..15,0..15]of longword = (
($A,$3,$B,$C,$5,$E,$9,$F,$0,$7,$4,$6,$1,$D,$2,$8),
($9,$5,$F,$3,$1,$0,$A,$4,$7,$B,$E,$8,$2,$6,$D,$C),
($6,$D,$A,$4,$3,$5,$2,$8,$B,$F,$9,$C,$0,$E,$7,$1),
($E,$7,$0,$D,$8,$B,$1,$3,$9,$6,$C,$4,$A,$2,$F,$5),
($C,$A,$2,$5,$F,$D,$7,$9,$4,$E,$6,$B,$8,$3,$1,$0),
($5,$9,$3,$8,$D,$6,$4,$C,$1,$0,$7,$2,$E,$B,$A,$F),
($0,$6,$4,$A,$7,$3,$B,$E,$2,$8,$5,$1,$D,$F,$C,$9),
($D,$F,$9,$0,$6,$2,$3,$1,$E,$C,$A,$5,$B,$8,$4,$7),
($1,$0,$C,$2,$9,$7,$6,$D,$3,$5,$8,$E,$F,$A,$B,$4),
($3,$8,$5,$7,$2,$C,$E,$B,$A,$9,$D,$F,$4,$1,$0,$6),
($F,$B,$D,$1,$C,$8,$0,$6,$5,$2,$3,$7,$9,$4,$E,$A),
($8,$E,$1,$9,$4,$F,$C,$5,$6,$D,$2,$A,$7,$0,$3,$B),
($4,$C,$7,$6,$E,$1,$5,$2,$F,$A,$B,$0,$3,$9,$8,$D),
($7,$2,$6,$B,$0,$4,$D,$A,$8,$1,$F,$3,$5,$C,$9,$E),
($2,$1,$8,$E,$B,$A,$F,$7,$D,$4,$0,$9,$C,$5,$6,$3),
($B,$4,$E,$F,$A,$9,$8,$0,$C,$3,$1,$D,$6,$7,$5,$2));
//RE-ORDERING MATRIX INVERSE
P1:array[0..15,0..15]of longword = (
($8,$C,$E,$1,$A,$4,$B,$9,$F,$6,$0,$2,$3,$D,$5,$7),
($5,$4,$C,$3,$7,$1,$D,$8,$B,$0,$6,$9,$F,$E,$A,$2),
($C,$F,$6,$4,$3,$5,$0,$E,$7,$A,$2,$8,$B,$1,$D,$9),
($2,$6,$D,$7,$B,$F,$9,$1,$4,$8,$C,$5,$A,$3,$0,$E),
($F,$E,$2,$D,$8,$3,$A,$6,$C,$7,$1,$B,$0,$5,$9,$4),
($9,$8,$B,$2,$6,$0,$5,$A,$3,$1,$E,$D,$7,$4,$C,$F),
($0,$B,$8,$5,$2,$A,$1,$4,$9,$F,$3,$6,$E,$C,$7,$D),
($3,$7,$5,$6,$E,$B,$4,$F,$D,$2,$A,$C,$9,$0,$8,$1),
($1,$0,$3,$8,$F,$9,$6,$5,$A,$4,$D,$E,$2,$7,$B,$C),
($E,$D,$4,$0,$C,$2,$F,$3,$1,$9,$8,$7,$5,$A,$6,$B),
($6,$3,$9,$A,$D,$8,$7,$B,$5,$C,$F,$1,$4,$2,$E,$0),
($D,$2,$A,$E,$4,$7,$8,$C,$0,$3,$B,$F,$6,$9,$1,$5),
($B,$5,$7,$C,$0,$6,$3,$2,$E,$D,$9,$A,$1,$F,$4,$8),
($4,$9,$1,$B,$5,$C,$2,$0,$8,$E,$7,$3,$D,$6,$F,$A),
($A,$1,$0,$F,$9,$D,$E,$7,$2,$B,$5,$4,$C,$8,$3,$6),
($7,$A,$F,$9,$1,$E,$C,$D,$6,$5,$4,$0,$8,$B,$2,$3));
function Mul(const Factor1,Factor2:longword):longword;
var Product:Int64;
Lhalf,Rhalf:longword;
begin
Product:=Factor1*Factor2;
if Product=0 then Result:=1-Factor1-Factor2 else
begin
Lhalf:=Product shr 32;
Rhalf:=Product and $FFFFFFFF;
Result:=Rhalf-Lhalf;
if Rhalf end;
end;
procedure BravionEncrypt(var Context:TBravionContext;var B:TBravionBlock32);
var Temp:array[0..15]of longword;
pB:^TBravionBlock8;
CarryBit:longword;
i:integer;
begin
pB:=@B;
with Context do
begin
//ALGORITHM PERMUTATION
B[0]:=B[0] xor RK[PK[16],0];
B[1]:=B[1] xor RK[PK[17],1];
B[2]:=B[2] xor RK[PK[18],2];
B[3]:=B[3] xor RK[PK[19],3];
for i:=0 to 15 do //16 ROUNDS
begin
//IRRATIONALIZE 8BIT GROUPS
CarryBit:=(B[0] and 2147483648) shr 31;
B[0]:=(B[0] shl 1) or ((B[1] and 2147483648) shr 31);
B[1]:=(B[1] shl 1) or ((B[2] and 2147483648) shr 31);
B[2]:=(B[2] shl 1) or ((B[3] and 2147483648) shr 31);
B[3]:=(B[3] shl 1) or CarryBit;
//PERMUTATION
B[3]:=B[3] xor (B[2]-RK[i,3]);
B[2]:=B[2] xor Mul(B[1],RK[i,2]);
B[1]:=B[1] xor (B[0]+RK[i,1]);
B[0]:=B[0] xor RK[i,0];
//SUBSTITUTION
{if anyone can optimize the following 20 lines please post it as a comment.
Bellow may seem slow, but it's MUCH faster than using Temp as a byte array
and Move(Temp,B,16). This is probably because the compiler is optimized for 32bit integers. An assembly version would be VERY fast.}
Temp[0]:=S0[i,pB^[P0[PK[i],0]]];
Temp[1]:=S0[i,pB^[P0[PK[i],1]]];
Temp[2]:=S0[i,pB^[P0[PK[i],2]]];
Temp[3]:=S0[i,pB^[P0[PK[i],3]]];
Temp[4]:=S0[i,pB^[P0[PK[i],4]]];
Temp[5]:=S0[i,pB^[P0[PK[i],5]]];
Temp[6]:=S0[i,pB^[P0[PK[i],6]]];
Temp[7]:=S0[i,pB^[P0[PK[i],7]]];
Temp[8]:=S0[i,pB^[P0[PK[i],8]]];
Temp[9]:=S0[i,pB^[P0[PK[i],9]]];
Temp[10]:=S0[i,pB^[P0[PK[i],10]]];
Temp[11]:=S0[i,pB^[P0[PK[i],11]]];
Temp[12]:=S0[i,pB^[P0[PK[i],12]]];
Temp[13]:=S0[i,pB^[P0[PK[i],13]]];
Temp[14]:=S0[i,pB^[P0[PK[i],14]]];
Temp[15]:=S0[i,pB^[P0[PK[i],15]]];
B[0]:=(Temp[3]shl 24)or(Temp[2]shl 16)or(Temp[1]shl 8)or Temp[0];
B[1]:=(Temp[7]shl 24)or(Temp[6]shl 16)or(Temp[5]shl 8)or Temp[4];
B[2]:=(Temp[11]shl 24)or(Temp[10]shl 16)or(Temp[9]shl 8)or Temp[8];
B[3]:=(Temp[15]shl 24)or(Temp[14]shl 16)or(Temp[13]shl 8)or Temp[12];
end;
//ALGORITHM PERMUTATION
B[0]:=B[0] xor RK[PK[20],0];
B[1]:=B[1] xor RK[PK[21],1];
B[2]:=B[2] xor RK[PK[22],2];
B[3]:=B[3] xor RK[PK[23],3];
end;
end;
procedure BravionDecrypt(var Context:TBravionContext;var B:TBravionBlock32);
var Temp:array[0..15]of longword;
pB:^TBravionBlock8;
CarryBit:longword;
i:integer;
begin
pB:=@B;
with Context do
begin
B[3]:=B[3] xor RK[PK[23],3];
B[2]:=B[2] xor RK[PK[22],2];
B[1]:=B[1] xor RK[PK[21],1];
B[0]:=B[0] xor RK[PK[20],0];
for i:=15 downto 0 do
begin
Temp[0]:=S1[i,pB^[P1[PK[i],0]]];
Temp[1]:=S1[i,pB^[P1[PK[i],1]]];
Temp[2]:=S1[i,pB^[P1[PK[i],2]]];
Temp[3]:=S1[i,pB^[P1[PK[i],3]]];
Temp[4]:=S1[i,pB^[P1[PK[i],4]]];
Temp[5]:=S1[i,pB^[P1[PK[i],5]]];
Temp[6]:=S1[i,pB^[P1[PK[i],6]]];
Temp[7]:=S1[i,pB^[P1[PK[i],7]]];
Temp[8]:=S1[i,pB^[P1[PK[i],8]]];
Temp[9]:=S1[i,pB^[P1[PK[i],9]]];
Temp[10]:=S1[i,pB^[P1[PK[i],10]]];
Temp[11]:=S1[i,pB^[P1[PK[i],11]]];
Temp[12]:=S1[i,pB^[P1[PK[i],12]]];
Temp[13]:=S1[i,pB^[P1[PK[i],13]]];
Temp[14]:=S1[i,pB^[P1[PK[i],14]]];
Temp[15]:=S1[i,pB^[P1[PK[i],15]]];
B[0]:=(Temp[3]shl 24)or(Temp[2]shl 16)or(Temp[1]shl 8)or Temp[0];
B[1]:=(Temp[7]shl 24)or(Temp[6]shl 16)or(Temp[5]shl 8)or Temp[4];
B[2]:=(Temp[11]shl 24)or(Temp[10]shl 16)or(Temp[9]shl 8)or Temp[8];
B[3]:=(Temp[15]shl 24)or(Temp[14]shl 16)or(Temp[13]shl 8)or Temp[12];
B[0]:=B[0] xor RK[i,0];
B[1]:=B[1] xor (B[0]+RK[i,1]);
B[2]:=B[2] xor Mul(B[1],RK[i,2]);
B[3]:=B[3] xor (B[2]-RK[i,3]);
CarryBit:=(B[3] and 1) shl 31;
B[3]:=(B[3] shr 1) or((B[2] and 1) shl 31);
B[2]:=(B[2] shr 1) or((B[1] and 1) shl 31);
B[1]:=(B[1] shr 1) or((B[0] and 1) shl 31);
B[0]:=(B[0] shr 1) or CarryBit;
end;
B[3]:=B[3] xor RK[PK[19],3];
B[2]:=B[2] xor RK[PK[18],2];
B[1]:=B[1] xor RK[PK[17],1];
B[0]:=B[0] xor RK[PK[16],0];
end;
end;
procedure BravionInit(var Context:TBravionContext;var Key:TBravionKey32);
const M1=longword(259200);
M2=longword(134456);
M3=longword(243000);
I1=longword(7141);
I2=longword(8121);
I3=longword(4561);
C1=longword(54773);
C2=longword(28411);
C3=longword(51349);
var X1,X2,X3:longword;
R:array[1..97]of real;
Temp:TBravionBlock32;
i,j,k:integer;
begin
with Context do
begin
FillChar(PK,Sizeof(TBravionPathKey8),0);
FillChar(RK,Sizeof(TBravionRoundKey32),0);
i:=0;
repeat //KEY EXPANSION
{I'm actualy using a PRNG with 2^32 period for the expansion}
X1:=(Key[i]+C1)mod M1;
X1:=(X1*I1+C1)mod M1;
X2:=X1 mod M2;
X1:=(X1*I1+C1)mod M1;
X3:=X1 mod M3;
for j:=1 to 97 do
begin
X1:=(X1*I1+C1)mod M1;
X2:=(X2*I2+C2)mod M2;
R[j]:=(X1+X2/M2)/M1;
end;
for j:=0 to 3 do
begin
X1:=(X1*I1+C1)mod M1;
X2:=(X2*I2+C2)mod M2;
X3:=(X3*I3+C3)mod M3;
k:=1+(97*X3)div M3;
RK[i*2,j]:=trunc($FFFFFFFF*R[k]);
R[k]:=(X1+X2/M2)/M1;
X1:=(X1*I1+C1)mod M1;
X2:=(X2*I2+C2)mod M2;
X3:=(X3*I3+C3)mod M3;
k:=1+(97*X3)div M3;
RK[(i*2)+1,j]:=trunc($FFFFFFFF*r[k]);
R[k]:=(X1+X2/M2)/M1;
end;
Inc(i,1);
until i=8;
for i:=0 to 15 do //SET 4BIT PATH KEYS
begin
PK[i]:=(TBravionKey8(Key)[i] xor TBravionKey8(Key)[i+16])and $F;
j:=16+(i and 7);
PK[j]:=PK[j] xor ((TBravionKey8(Key)[i] xor TBravionKey8(Key)[i+16])and $F0)shr 4;
end;
end;
for i:=0 to 127 do //PERMUTE ROUND KEYS
begin
j:=0;
repeat
Move(Key[0],Temp,Sizeof(TBravionBlock32));
BravionEncrypt(Context,Temp);
Move(Temp,Context.RK[j],Sizeof(TBravionBlock32));
Move(Key[4],Temp,Sizeof(TBravionBlock32));
BravionEncrypt(Context,Temp);
Move(Temp,Context.RK[j+1],Sizeof(TBravionBlock32));
Inc(j,2);
until j=16;
end;
end;
end.