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Stream Ciphers

Stream Ciphers. Day 18. 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. Problem: Random string of bits. Linear Feedback Shift Register.

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Stream Ciphers

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  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 9654-10,346 range • FIPS 140-1 (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

  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.

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