Random number generators

1. A method of generating a parameter for a random-number generator, comprising:

(1) generating a value;

(2) using the value to select a prime number;

(3) generating the parameter based on the selected prime number and a second prime number; and

(4) outputting the parameter for use with the random-number generator.

2. The method of claim 1 , wherein step 4 comprises:

using the parameter for a linear congruential random-number generator.

3. The method of claim 2 , further comprising:

(5) passing an output of the linear congruential random-number generator through a block encryptor.

4. The method of claim 1 , further comprising:

(5) using an output of the random number generator to establish a pseudo-randomly selected network address that is used to transmit a digital computer message.

5. The method of claim 3 , further comprising:

(6) using an output of the random number generator to establish a pseudo-randomly selected network address that is used to transmit a digital computer message.

6. The method of claim 1 , wherein the second prime number comprises a previously selected prime number.

7. The method of claim 6 , wherein step (3) comprises generating the parameter by multiplying the selected prime number by the second prime number.

8. The method of claim 7 , further comprising repeating steps (1) through (3) a plurality of times while the parameter is less than a predetermined value, wherein the parameter generated during each iteration of steps (1) through (3) is a product of a most recently selected one of the selected prime numbers and previously selected prime numbers.

9. The method of claim 1 , wherein step (2) comprises mapping the generated value to the prime number based on a nonlinear distribution function.

10. The method of claim 1 , wherein step 2 comprises:

searching through an ordered table of entries, each of the entries including a prime number and a weight, a respective prime number from one of the entries being selected based on the parameter and a corresponding one of the weights.

11. The method of claim 1 , wherein step (1) comprises generating a random value.

12. The method of claim 1 , further comprising repeating steps (1)–(4) for a plurality of random number generators.

13. A method of generating a parameter for a random-number generator, comprising:

(1) generating a first value;

(2) using the first value to select a first prime number P;

(3) generating a second value;

(4) using the second value to select a number K such that PK is at most equal to a predetermined maximum number;

(5) generating the parameter as a function of PK; and

(6) outputting the parameter for use with the random-number generator.

14. The method of claim 13 , further comprising:

(7) generating a third value;

(8) using the third value to select a second prime number;

(9) generating a second parameter by multiplying the selected second prime number by at least one previously selected prime number; and

(10) using the parameter and the second parameter as parameters for the random-number generator.

15. The method of claim 14 , wherein the random-number generator is a linear-congruential random-number generator.

16. The method of claim 15 , further comprising:

(11) passing an output of the linear congruential random-number generator through a block encryptor.

17. The method of claim 16 , further comprising:

(12) using an output of the linear congruential random-number generator to establish a pseudo-randomly selected network address that is used to transmit a digital computer message.

18. The method of claim 14 , further comprising repeating acts (7) through (9) a plurality of times while the second parameter is less than a predetermined value, wherein the second parameter generated during each iteration of acts (7) through (9) is a product of a most recently selected one of the selected prime numbers and previously selected prime numbers.

19. The method of claim 14 , wherein step (7) comprises generating a random value.

20. The method of claim 13 , wherein act 6 comprises:

using the parameter for a linear congruential random-number generator.

21. The method of claim 20 , further comprising:

(7) passing an output of the linear congruential random-number generator through a block encryptor.

22. The method of claim 21 , further comprising:

(8) using an output of the linear congruential random-number generator to establish a pseudo-randomly selected network address that is used to transmit a digital computer message.

23. The method of claim 13 , wherein step 2 comprises:

searching through an ordered table of entries, each of the entries including a prime number and a weight, a respective prime number from one of the entries being selected based on the first parameter and a corresponding one of the weights.

24. The method of claim 13 , wherein step (1) comprises generating a random value.

25. The method of claim 13 , wherein step (3) comprises generating a random value.

26. An apparatus for generating a parameter for a random-number generator, the apparatus comprising:

means for mapping a random value to a prime number P; and

means for generating the parameter by multiplying the prime number P by at least one previously selected prime number.

27. The apparatus of claim 26 , wherein the means for generating produces the parameter for a linear congruential random-number generator.

28. The apparatus of claim 27 , further comprising:

a block encryptor, wherein an output of the linear congruential random-number generator is arranged to be passed through the block encryptor.

29. The apparatus of claim 26 , wherein the prime number mapper is arranged to search through an ordered table of entries, each of the entries including a prime number and a weight, a respective prime number from one of the entries being selected based on the random value and a corresponding one of the weights.

30. An apparatus for generating a parameter for a random-number generator, the apparatus comprising:

first means for mapping a random value to a prime number P;

second means for mapping a second random value to a number K such that PK is at most equal to a predetermined maximum number; and

means for generating a parameter as a function of PK, wherein the second means for mapping is included within the means for generating.

31. The apparatus of claim 30 , wherein the means for generating produces the parameter for a linear congruential random-number generator.

32. The apparatus of claim 30 , further comprising:

a block encryptor, wherein an output of the linear congruential random-number generator is arranged to be passed through the block encryptor.

33. The apparatus of claim 30 , wherein the prime number mapper is arranged to search through an ordered table of entries, each of the entries including a prime number and a weight, a respective prime number from one of the entries being selected based on the random value and a corresponding one of the weights.

34. A machine-readable medium having information including instructions for a processor recorded thereon, the instructions comprising:

(1) generating a random value;

(2) using the random value to select a prime number;

(3) generating a parameter based on the selected prime number and a second prime number; and

(4) outputting the parameter for use as a parameter for a random number generator.

35. The machine-readable medium of claim 34 , wherein step 4 comprises:

using the parameter for a linear congruential random-number generator.

36. The machine-readable medium of claim 35 , further having instructions comprising:

(5) passing an output of the linear congruential random-number generator through a block encryptor.

37. The machine-readable medium of claim 36 , further having instructions comprising:

(6) using an output of the linear congruential random-number generator to establish a pseudo-randomly selected network address that is used to transmit a digital computer message.

38. The machine-readable medium of claim 34 further having instructions comprising:

(5) using an output of the random-number generator to establish a pseudo-randomly selected network address that is used to transmit a digital computer message.

39. The machine-readable medium of claim 38 , further having instructions comprising repeating steps (1) through (3) a plurality of times while the parameter is less than a predetermined value, wherein the parameter generated during each iteration of steps (1) through (3) is a product of a most recently selected one of the selected prime numbers and previously selected prime numbers.

40. The machine-readable medium of claim 34 , wherein step 2 comprises:

searching through an ordered table of entries, each of the entries including a prime number and a weight, a respective prime number from one of the entries being selected based on the random value and a corresponding one of the weights.

41. The machine-readable medium of claim 34 , wherein the second prime number comprises a previously selected prime number.

42. The machine-readable medium of claim 41 , wherein step (3) comprises generating the parameter by multiplying the selected prime number by the second prime number.

43. A machine-readable medium having instructions recorded thereon for a processor to generate a parameter for a random-number generator, the instructions comprising:

(1) generating a first value;

(2) using the first value to select a first prime number P;

(3) generating a second value;

(4) using the second value to select a number K such that PK is at most equal to a predetermined maximum number; and

(5) generating the parameter as a function of PK.

44. The machine-readable medium of claim 43 , further having instructions comprising:

(6) generating a third value;

(7) using the third value to select a second prime number; and

(8) generating a second parameter by multiplying the selected second prime number by at least one previously selected prime number.

45. The machine-readable medium of claim 44 , further having instructions comprising:

(9) using the parameter and the second parameter as the parameter of a linear congruential random-number generator.

46. The machine-readable medium of claim 45 , further having instructions comprising:

(10) passing an output of the linear congruential random-number generator through a block encryptor.

47. The machine-readable medium of claim 46 , further having instructions comprising:

(11) using an output of the linear congruential random-number generator to establish a pseudo-randomly selected network address that is used to transmit a digital computer message.

48. The machine-readable medium of claim 44 , further having instructions comprising repeating acts (6) through (8) a plurality of times while the second parameter is less than a predetermined value, wherein the second parameter generated during each iteration of acts (6) through (8) is a product of a most recently selected one of the selected prime numbers and previously selected prime numbers.

49. The machine-readable medium of claim 43 , further having instructions comprising:

(6) using the parameter as the parameter of a linear congruential random-number generator.

50. The machine-readable medium of claim 49 , further having instructions comprising:

(7) passing an output of the linear congruential random-number generator through a block encryptor.

51. The machine-readable medium of claim 50 , further having instructions comprising:

(8) using an output of the linear congruential random-number generator to establish a pseudo-randomly selected network address that is used to transmit a digital computer message.

52. The machine-readable medium of claim 43 , further having instructions comprising:

using the parameter as the parameter for the random-number generator, wherein

an output of the random-number generator is used to establish a pseudo-randomly selected network address that is used to transmit a digital computer message.

53. The machine-readable medium of claim 43 , wherein step 2 comprises:

searching through an ordered table of entries, each of the entries including a prime number and a weight, a respective prime number from one of the entries being selected based on the first value and a corresponding one of the weights.