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Mush is a mutual shrinking generator. It™s easy to explain [1590]. Take two addi-
tive generators: A and B. If the carry bit of A is set, clock B. If the carry bit of B is
set, clock A. Clock A, and set the carry bit if there is a carry. Clock B, and set the
carry bit if there is a carry. The final output is the XOR of the output of A and B.
The easiest generators to use are the ones from Fish:
32
Ai=(Ai-55+Al-24)mod2
Bi = (Bi - 52+ Bi - 19)mod 232
On the average, three generator iterations are required to produce one output
word. And if the coefficients of the additive generators are chosen correctly and are
relatively prime, the output sequence will be maximal length. I know of no suc-
cessful attacks, but remember that this algorithm is very new.


16.10 GIFFORD
David Gifford invented a stream cipher and used it to encrypt news wire reports in
the Boston area from 1984 until 1988 [608,607,609]. The algorithm has a single
g-byte register: bo, hi, . . . , b,. The key is the initial state of the register. The algorithm
works in OFB; the plaintext does not affect the algorithm at all. (SeeFigure 16.17).
To generate a key byte k,, concatenate b. and bz and concatenate b4 and b7. Multi-
ply the two together to get a 32-bit number. The third byte from the left is ki.
To update the register, take b, and sticky right shift it 1 bit. This means the left-
most bit is both shifted and also remains in place. Take b, and shift it 1 bit to the
left; there should be a 0 in the right-most bit position. Take the XOR of the modified
bl, the modified b7, and bo. Shift the original register 1 byte to the right and put this
byte in the left-most position.
This algorithm remained secure throughout its life, but was broken in 1994 [287].
It turns out that the feedback polynomial isn™t primitive and can be attacked that
way-oops.
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Figure 16.17 Gifford.


16.11 M
ALGORITHM
The name is from Knuth [863]. It™s a method for combining multiple pseudo-random
streams that increases their security. One generator™s output is used to select a
delayed output from the other generator [996,1003]. In C:
#define ARR-SIZE (8192) /* for example - the larger the better
*/

static unsigned char delayI: ARR-SIZE 1;

unsigned char prngA( void );
long prngB( void ) ;

void init-algM( void )

long i ;

for ( i = 0 ; i < ARR-SIZE ; i++ 1
delayCi1 = prngA0 ;

1 /* init-algM */

unsigned char algM( void 1
(
long j,v ;
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CHAPTER 16 Pseudo-Random-Sequence Generators


/* get the delay[l index */
j = prngB0 % ARRKSIZE ;
/* get the value to return */
v = delay[jl ;
/* replace it */
delay[jl = prngA0 ;

return (v);
I I* algM *I

This has strength in that if prngA were truly random, one could not learn any-
thing about prngB (and could therefore not cryptanalyze it). If prngA were of the
form that it could be cryptanalyzed only if its output were available in order (i.e.,
only if prngB were cryptanalyzed first) and otherwise it was effectively truly ran-
dom, then the combination would be secure.

16.12 PKZIP
Roger Schlafly designed the encryption algorithm built into the PKZIP data com-
pression program. It™s a stream cipher that encrypts data one byte at a time. At least,
this is the algorithm in version 2.04g. I can™t speak for later versions, but unless
there is some announcement you can probably assume that they are identical.
The algorithm uses three 32-bit variables, initialized as follows:
KO= 305419896
K1= 591751049
Kz = 878082192
It has an g-bit key, K3, derived from Kz. Here is the algorithm (all symbols are stan-
dard C notation):
Ci = Pi h KS
Ko = crc32 (Ko, Pi)
K1 = K1 + (K,, & OxOOOOOOff)
K1 = K1 134775813 + 1
l


Kz = crc32 (K,, K1 >> 24)
K3 = ((Kz I 2) ((Kz I 2) A 1)) >> 8
l



The function crc32 takes the previous value and a byte, XORs them, and calcu-
lates the next value by the CRC polynomial denoted by Oxedb88320. In practice, a
256-entry table can be precomputed and the crc32 calculation becomes:
crc32 (a, b) = (a >> 8) h table [(a & Oxff) 0 b]
The table is precomputed by the original definition of crc32:
table [i] = crc32 (i, 0)
To encrypt a plaintext stream, first loop the key bytes through the encryption
algorithm to update the keys. Ignore the ciphertext output in this step. Then
encrypt the plaintext, one byte at a time. Twelve random bytes are prepended to the
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16.12 PKZIP


plaintext, but that™s not really important. Decryption is similar to encryption,
except that Ci is used in the second step of the algorithm instead of Pi.
of PKZlP
Security
Unfortunately, it™s not that great. An attack requires 40 to 200 bytes of known
plaintext and has a time complexity of about 2” [166]. You can do it in a few hours
on your personal computer. If the compressed file has any standard headers, getting
the known plaintext is no problem. Don™t use the built-in encryption in PKZII?

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