1. Stream Ciphers
Day 18

2. Objectives Students will be able to…
…to create a pseudo-random number with a linear feedback shift register.
…understand some of the methods for checking to a set of bits for randomness.

3. Problem: Random string of bits

4. Linear Feedback Shift Register

5. Primitive polynomials
Example: p(x) = x3 + x + 1
Length until repeating is 2n - 1

6. Example 1: Find a list of primitive polynomials.
Generate a list of random bits.

7. Example 2: Generate a list of 20000 random bits. 20-bit register
You will need…
a coin for the initial 20-bit register
Excel program from the SMA website.

8. Test or randomness Create 20,000 bits
Count the number of 1’s: Must be in the ,346 range
FIPS (Poker test)
Divide into 4-bit segments and convert to decimal numbers
Count and store the number of occurrences
1.03 < x < 57.4

9. Test or randomness The Runs test Length of Run Required Interval 1
2,267-2,733 2 1, 3 4 5
90-223 6+

10. Test or randomness The long run test Run of length 34 or more
On the sample of 20,000 bits, the test is passed if there are NO long runs

11. Example 3:
Test your 20,000 “random” bits for randomness using the 4 tests.