Pseudo-random number generation based on periodic sampling of one or more linear feedback shift registers
Disclosed are various embodiments for generating pseudo-random numbers. One such embodiment is an apparatus comprising digital hardware configured to generate pseudo-random numbers. The apparatus uses a linear feedback shift register in which the correlation between successive pseudo-random numbers is reduced.
1. An apparatus comprising:
digital circuitry configured to:
periodically switch between a first plurality of iterative outputs generated by at least a first linear feedback shift register and a second plurality of iterative outputs generated by at least a second linear feedback shift register to generate a plurality of pseudo-random numbers in which a correlation between successive ones of the plurality of pseudo-random numbers is reduced.
2. The apparatus of claim 1 , wherein said digital circuitry comprises a plurality of flip-flops and a plurality of gates.
3. The apparatus of claim 1 , wherein said digital circuitry comprises at least one nonlinear operator electrically coupled to a tap from the linear feedback shift register.
4. The apparatus of claim 1 , wherein the plurality of pseudo-random numbers are generated with a period equal to a sum of periods of the first linear feedback shift register and the second linear feedback shift register.
5. The apparatus of claim 1 , wherein the digital circuitry is further configured to encrypt the plurality of pseudo-random numbers by employing a hashing function that varies an initial value of the hashing function over time by way of a function operating on one or more variables.
6. The apparatus of claim 1 , wherein the LFSR is configured to generate a three bit output.
7. The apparatus of claim 1 , wherein the digital circuitry is further configured to preprocess the first plurality of bits to append an extra plurality of bits on the first plurality of bits to attain a predefined bit length.
8. An apparatus comprising:
a linear feedback shift register (LFSR) in a computing device configured to produce a plurality of bits at each of a plurality of successive iterations; and
an output configured to periodically sample the plurality of bits produced by the LFSR using a specified sampling period, wherein the specified sampling period is greater than a successive iteration.
9. The apparatus of claim 8 , wherein the specified sampling period is equal to a number of the plurality of bits produced by the LFSR.
10. The apparatus of claim 8 , wherein n is a number of the plurality of bits produced by the LFSR and the specified sampling period is equal to 2n−1.
11. The apparatus of claim 8 , wherein the plurality of bits generated by the LFSR corresponds to a maximal length sequence.
12. The apparatus of claim 11 , wherein n is a number of the plurality of bits produced by the LFSR and the maximal length sequence has outputs characterized by periodicity 2n−1.
13. The apparatus of claim 8 , wherein the LFSR is configured to generate a three bit output.
14. An apparatus comprising:
a linear feedback shift register (LFSR) configured to output a first plurality of bits; and
a nonlinear operator configured to output a second plurality of bits by performing a nonlinear operation on the first plurality of bits from the LFSR using at least an operand having a value specific to the LFSR.
15. The apparatus of claim 14 , wherein the nonlinear operator comprises an XOR operator.
16. The apparatus of claim 14 , wherein the operand comprises a unique bit sequence associated with the LFSR.
17. The apparatus of claim 14 , wherein the plurality of bits generated by the LFSR corresponds to a maximal length sequence.
18. The apparatus of claim 14 , wherein the apparatus further comprises a preprocessor configured to preprocess the first plurality of bits to append an extra plurality of bits on the first plurality of bits to attain a predefined bit length.
19. The apparatus of claim 14 , wherein the LFSR is configured to generate a three bit output.
20. The apparatus of claim 14 , wherein the apparatus is further comprises a preprocessor configured to preprocess the first plurality of bits to append an extra plurality of bits on the first plurality of bits to attain a predefined bit length.