Introduction to Cryptography with Open-Source Software

Random numbers and stream ciphers 343

however c ryptographically very weak. The shrinking generator [22] uses the

results of two LFSRs, called A and S. The output bits are generated by the

A sequence, and their output is controlled by the S sequence. At each stage

new bits a

k

and s

k

are obtained. If s

k

is one, then a

k

is output as the next

generated bit; if s

k

is z e ro, new bits of the A and S sequences are produced.

Suppo se A is produced by x

4

+ x + 1 and seeded with [0, 0, 1, 1], and S by

x

5

+ x

2

+ 1 seeded with [0, 0, 0, 1, 1]. Then:

S : 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0

A : 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0

output: 1 0 0 1 1 1 0 1

The output ...