Enciphering/deciphering apparatus and method incorporating random variable and keystream generation

• US 6,014,445 A
• Filed: 10/22/1996
• Issued: 01/11/2000
• Est. Priority Date: 10/23/1995
• Status: Expired due to Term

• Current Assignee: Tohru Kohda, Kabushiki Kaisha Toshiba (Toshiba Corporation)
• Original Assignee: Kabushiki Kaisha Toshiba (Toshiba Corporation)
• Inventors: Tsuneda, Akio, Kohda, Tohru
• Primary Examiner(s): Swann, Tod R.
• Assistant Examiner(s): Darrow, Justin T.
• Application Number:
  US08/734,919
• Time in Patent Office: 1,176 Days
• Field of Search: 380/28, 380/42, 380/43, 364/717.01
• US Class Current: 380/28
• CPC Class Codes: H04L 2209/08 Randomization, e.g. dummy operations or using noise
• CPC Class Codes: H04L 9/001 using chaotic signals
• CPC Class Codes: H04L 9/065 Encryption by serially and continuously modifying data stream elements, e.g. stream cipher systems, RC4, SEAL or A5/3

Abstract

An enciphering apparatus embodying this invention comprises chaos generation means for generating a real-valued sequence along a chaotic orbit in accordance with a predetermined number of first common keys and a predetermined nonlinear map, bit generation means for performing predetermined binarization on each real value in the generated real-valued sequence based on a predetermined number of second common keys to generate a binary sequence, and logic operation means for executing a predetermined logic operation on a binary sequence of an input plaintext and the generated keystream sequence bit by bit to generate a binary sequence of a ciphertext. For example, the first common keys are an initial seed of a nonlinear map and a value of a parameter k, and the bit generation means acquires plural pieces of binary data for each real value in the real-valued sequence using values indicated by a plurality of second keys as thresholds and obtains exclusive OR of those binary data.

Claims

1. An enciphering apparatus comprising:

chaos generation means for generating a real-valued sequence along a chaotic orbit in accordance with a predetermined number of first common keys and a predetermined nonlinear map;

bit generation means for normalizing individual real values in said real-valued sequence over a predetermined interval and for binarizing said normalized real values using values indicated by a predetermined number of second common keys as thresholds to generate a binary sequence; and

logic operation means for executing a predetermined logic operation on a binary sequence of an input plaintext and said generated keystream sequence bit by bit to generate a binary sequence of ciphertext.

2. The enciphering apparatus according to claim 1, wherein said first common keys are an initial seed of said predetermined nonlinear map, or an initial seed of said predetermined nonlinear map and a value of a parameter of said nonlinear map;

and

said second common keys represent a predetermined number of different thresholds based on said predetermined binarization.

3. The enciphering apparatus according to claim 2, wherein said initial seed of said predetermined nonlinear map and said value of said parameter of said nonlinear map are real values.

4. The enciphering apparatus according to claim 1, wherein said predetermined nonlinear map is a Chebyshev map of degree k (k:

being a real value equal to or greater than

     2) given by a differential equation ω

_n+1 =cos (k cos^-1 ω

_n); and

said first common keys are an initial seed ω

₀ of said Chebyshev map where -1<

ω

₀ <

1, and a value of said parameter k.

5. The enciphering apparatus according to claim 1, wherein said logic operation means performs an exclusive OR operation or an exclusive AND operation.

6. The enciphering apparatus according to claim 1, wherein said bit generation means binarizes individual real values in said real-valued sequence using values indicated by said second common keys as thresholds.

7. The enciphering apparatus according to claim 1, wherein said bit generation means acquires absolute values of individual real values in said real-valued sequence and binarizes said absolute values of said real values using values indicated by said second common keys as thresholds.

8. The enciphering apparatus according to claim 1, wherein said second common keys are bit numbers indicating bit positions of real values in a binary representation;

and

said bit generation means selects values of individual real values in said real-valued sequence in a binary representation, at bit positions indicated by said second common keys, to binarize said real values.

9. The enciphering apparatus according to claim 1, wherein said second common keys are bit numbers indicating bit positions of real values in a binary representation;

and

said bit generation means selects values of normalized values of said real values in said real-valued sequence in a binary representation, at bit positions indicated by said second common keys, to binarize said real values.

10. The enciphering apparatus according to claim 1, wherein said bit generation means acquires plural pieces of binary data of individual real values in said real-valued sequence using values indicated by said plurality of second common keys as thresholds, and performs predetermined nonlinear coupling process on said plural pieces of binary data.

11. The enciphering apparatus according to claim 1, wherein said second common keys are bit numbers indicating bit positions of real values in a binary representation;

and

said bit generation means selects values of individual real values in said real-valued sequence or values obtained by performing a predetermined process on said real values, in a binary representation, at bit positions indicated by said second common keys, and performs predetermined nonlinear coupling on said selected values to binarize said real values.

12. The enciphering apparatus according to claim 10, wherein said logic operation means performs an exclusive OR operation or an exclusive AND operation.

13. The enciphering apparatus according to claim 11, wherein said logic operation means performs an exclusive OR operation or an exclusive AND operation.

14. The enciphering apparatus according to claim 1, wherein said chaos generation means executes a program described in a predetermined language by using a floating-point computing device to generate a sequence of values of said predetermined nonlinear map.

15. A keystream generating method for a keystream generating apparatus for use in a stream enciphering apparatus or a stream deciphering apparatus for performing a logic operation on a binary sequence of a plaintext or a ciphertext and a keystream sequence generated based on a predetermined common key to generate a ciphertext or an original plaintext, said keystream generating method comprising the steps of:

generating a real-valued sequence along a chaotic orbit in accordance with a predetermined number of first common keys and a Chebyshev map of degree k (k;

being a real value equal to or greater than

     2) given by a differential equation ω

_n+1 =cos (k cos^-1 ω

_n), the first common keys being an initial seed ω

₀ of the Chebyshev map where -1<

ω

₀ <

1, and a value of the parameter k; and

performing predetermined binarization on each real value in said generated real-valued sequence based on a predetermined number of second common keys to generate a binary sequence.

16. The keystream generating method according to claim 15, wherein the first common keys are an initial seed of the predetermined nonlinear map, or an initial seed of the predetermined nonlinear map and a value of a parameter of the nonlinear map;

and the second common keys represent a predetermined number of different thresholds based on the predetermined binarization.

17. A random variable generating method in a stream enciphering system based on a chaotic binary sequence comprising the steps of:

generating a real-valued sequence along a chaotic orbit in accordance with a predetermined number of first common keys and a predetermined nonlinear map;

normalizing individual real values in said real-valued sequence over a predetermined interval and binarizing said normalized real values using values indicated by a predetermined number of second common keys as thresholds to generate a binary sequence; and

executing a predetermined logic operation on a binary sequence of an input plaintext and said generated keystream sequence bit by bit to generate a random variable.

18. The random variable generating method according to claim 17, wherein the initial seed of the predetermined nonlinear map and the value of the parameter of the nonlinear map are real values.

19. The method according to claim 17, wherein said random variable generating step includes:

sequentially delaying said generated real-valued sequence in accordance with given m types of delay amounts (m being an integer equal to or greater than

     1);

performing predetermined binarization on said real-value sequence undelayed and on each of said m real-valued sequences to produce m+1 binary sequences; and

executing a predetermined logic operation based on said generated m+1 binary sequences to generate random variables.

20. The random variable generating method according to claim 19, wherein based on a plurality of random variables generated by said method according to claim 19, a predetermined logic operation is performed to generate random variables to be output.

21. A random variable generating method comprising the steps of:

generating a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map with a given real value as an initial seed;

performing binarization on each real value in said generated real-valued sequence with given 2M+1 (M being an integer equal to or greater than

     1) values as thresholds to generate 2M+1 binary sequences, said 2M+1 thresholds t_r (r=0 to 2M) satisfying relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take; and

executing a predetermined logic operation based on said generated 2M+1 binary sequences to generate random variables.

22. The random variable generating method according to claim 21, wherein said logic operation is an exclusive OR.

23. The random variable generating method according to claim 22, wherein said 2M+1 thresholds t_r (r=0 to 2M) satisfy relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take.

24. The random variable generating method according to claim 21, wherein said nonlinear map has an equidistributivity of the invariant measure, symmetric property of the invariant measure and symmetric property of the map.

25. The random variable generating method according to claim 22, wherein said nonlinear map has an equidistributivity of the invariant measure, symmetric property of the invariant measure and symmetric property of the map.

26. The random variable generating method according to claim 21, wherein ideal random variables are produced by using, as said nonlinear map, one having an equidistributivity of the invariant measure, symmetric property of the invariant measure and symmetric property of the map, and permitting said 2M+1 thresholds t_r (r=0 to 2M) to satisfy relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take.

27. The random variable generating method according to claim 22, wherein ideal random variables are produced by using, as said nonlinear map, one having an equidistributivity of the invariant measure, symmetric property of the invariant measure and symmetric property of the map, and permitting said 2M+1 thresholds t_r (r=0 to 2M) to satisfy relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take.

28. An enciphering apparatus comprising:

real-valued sequence generation means for generating a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map using a real value, indicated by a first common key, as an initial seed;

binarization means for performing binarization on each real value in said generated real-value sequence with 2M+1 (M being an integer equal to or greater than

     1) values indicated by a second common key as thresholds to generate 2M+1 binary sequence, said 2M+1 thresholds t_r (r=0 to 2M) satisfying relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take;

first logic operation means for executing a predetermined first logic operation based on said generated 2M +1 binary sequences to generate a keystream sequence; and

second logic operation means for executing a predetermined second logic operation based on a binary sequence of a plaintext and said keystream sequence to generate a binary sequence of a ciphertext.

29. The enciphering apparatus according to claim 28, wherein said first logic operation and said second logic operation are both exclusive ORs.

30. The enciphering apparatus according to claim 28, wherein said nonlinear map has an equidistributivity of the invariant measure, symmetric property of the invariant measure and symmetric property of the map.

31. The enciphering apparatus according to claim 28, wherein ideal random variables are produced by using, as said nonlinear map, one having an equidistributivity of the invariant measure, symmetric property of the invariant measure and symmetric property of the map, and permitting said 2M+1 thresholds t_r (r=0 to 2M) to satisfy relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take.

33. The enciphering apparatus according to one of claim 28, wherein when said nonlinear map has a predetermined number of parameters, at least one of said parameters is used as a common key.

34. The enciphering apparatus according to one of claim 29, wherein when said nonlinear map has a predetermined number of parameters, at least one of said parameters is used as a common key.

35. The enciphering apparatus according to one of claim 28, wherein when said nonlinear map has a predetermined number of parameters, at least one of said parameters is used as a common key.

36. The enciphering apparatus according to one of claim 30, wherein when said nonlinear map has a predetermined number of parameters, at least one of said parameters is used as a common key.

37. The enciphering apparatus according to one of claim 31, wherein when said nonlinear map has a predetermined number of parameters, at least one of said parameters is used as a common key.

39. The enciphering apparatus according to one of claim 28, wherein said nonlinear map is a Chebyshev map expressed by a differential equation ω

_n+1 =cos (k cos^-1 ω

_n) where k is a real number equal to or greater than 2; and

said first common key is information indicative of an initial seed ω

₀ of said Chebyshev map (-1<

ω

₀ <

1) and said parameter k.

40. The enciphering apparatus according to one of claim 29, wherein said nonlinear map is a Chebyshev map expressed by a differential equation ω

_n+1 =cos (k cos^-1 ω

_n) where k is a real number equal to or greater than 2; and

said first common key is information indicative of an initial seed ω

_n of said Chebyshev map (-1<

ω

₀ <

1) and said parameter k.

41. The enciphering apparatus according to one of claim 28, wherein said nonlinear map is a Chebyshev map expressed by a differential equation ω

_n+1 =cos (k cos^-1 ω

_n) where k is a real number equal to or greater than 2; and

said first common key is information indicative of an initial seed ω

₀ of said Chebyshev map (-1<

ω

₀ <

1) and said parameter k.

42. The enciphering apparatus according to one of claim 30, wherein said nonlinear map is a Chebyshev map expressed by a differential equation ω

_n+1 =cos (k cos^-1 ω

_n) where k is a real number equal to or greater than 2; and

said first common key is information indicative of an initial seed ω

₀ of said Chebyshev map (-1<

ω

₀ <

1) and said parameter k.

43. The enciphering apparatus according to one of claim 31, wherein said nonlinear map is a Chebyshev map expressed by a differential equation ω

_n+1 =cos (k cos^-1 ω

_n) where k is a real number equal to or greater than 2; and

said first common key is information indicative of an initial seed ω

₀ of said Chebyshev map (-1<

ω

₀ <

1) and said parameter k.

45. The enciphering apparatus according to claim 39, wherein said parameter k takes an even-numbered value.

46. The enciphering apparatus according to claim 40, wherein said parameter k takes an even-numbered value.

47. The enciphering apparatus according to claim 41, wherein said parameter k takes an even-numbered value.

48. The enciphering apparatus according to claim 42, wherein said parameter k takes an even-numbered value.

49. The enciphering apparatus according to claim 43, wherein said parameter k takes an even-numbered value.

51. The enciphering apparatus according to one of claims 28, wherein said real-valued sequence generation means executes a program described in a predetermined language by using a floating-point computing device to generate a sequence of values of said nonlinear map.

52. The enciphering apparatus according to one of claims 29, wherein said real-valued sequence generation means executes a program described in a predetermined language by using a floating-point computing device to generate a sequence of values of said nonlinear map.

53. The enciphering apparatus according to one of claims 28, wherein said real-valued sequence generation means executes a program described in a predetermined language by using a floating-point computing device to generate a sequence of values of said nonlinear map.

54. The enciphering apparatus according to one of claims 30, wherein said real-valued sequence generation means executes a program described in a predetermined language by using a floating-point computing device to generate a sequence of values of said nonlinear map.

55. The enciphering apparatus according to one of claims 31, wherein said real-valued sequence generation means executes a program described in a predetermined language by using a floating-point computing device to generate a sequence of values of said nonlinear map.

57. The apparatus according to claim 28, wherein said binarization means includes:

delay means for sequentially delaying said generated real-valued sequences in association with one or plural kinds of delay amounts indicated by a second common key; and

a plurality of binarization means, provided in association with said real-valued sequence output from said real-valued sequence generation means and one or a plurality of real-valued sequences delayed by a predetermined amount and output by said delay means, for performing predetermined binarizations on individual real values in the associated real-valued sequences based on associated third common keys.

58. The enciphering apparatus according to claim 57, wherein said real-valued sequence generation means, said delay means, said plurality of binarization means and said first logic operation means are provided for each of a plurality of systems;

and

wherein said apparatus further comprises fourth logic operation means for performing a predetermined fourth logic operation based on a binary sequence output from said first logic operation means in each system to generate a keystream sequence,

whereby based on a binary sequence of a plaintext and said keystream sequence, said second logic operation means performs said second predetermined logic operation to generate a binary sequence of a ciphertext.

59. The enciphering apparatus according to claim 57, wherein each of said plurality of binarization means includes binarization means for performing predetermined binarization on individual real values in the associated real-valued sequence using a plurality of values, indicated by that one of said third common keys which is associated with said binarization means, as thresholds to generate a plurality of binary sequences, and third logic operation means for performing predetermined third logic operation based on said plurality of generated binary sequences to generate said binary sequences to be given to said first logic operation means.

60. The enciphering apparatus according to claim 58, wherein each of said plurality of binarization means includes binarization means for performing predetermined binarization on individual real values in the associated real-valued sequence using a plurality of values, indicated by that one of said third common keys which is associated with said binarization means, as thresholds to generate a plurality of binary sequences, and third logic operation means for performing predetermined third logic operation based on said plurality of generated binary sequences to generate said binary sequences to be given to said first logic operation means.

61. The enciphering apparatus according to claim 57, wherein each of said plurality of binarization means binarizes individual real values in the associated real-valued sequence using a value, indicated by that one of said third common keys which is associated with said binarization means, as a threshold.

62. The enciphering apparatus according to claim 58, wherein each of said plurality of binarization means binarizes individual real values in the associated real-valued sequence using a value, indicated by that one of said third common keys which is associated with said binarization means, as a threshold.

63. The enciphering apparatus according to claim 57, wherein each of said plurality of binarization means binarizes individual real values in the associated real-valued sequence by selecting values at bit positions of values in binary representation, acquired by normalizing said real values in a predetermined range.

64. The enciphering apparatus according to claim 58, wherein each of said plurality of binarization means binarizes individual real values in the associated real-valued sequence by selecting values at bit positions of values in binary representation, acquired by normalizing said real values in a predetermined range.

32. An enciphering apparatus comprising:

real-valued sequence generation means for generating a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map having an equidistributivity of the invariant measure, symmetric property of the invariant measure and symmetric property of the map, using a real value, indicated by a first common key, as an initial seed;

binarization means for performing binarization on each real value in said generated real-valued sequence with 2M+1 (M being an integer equal to or greater than

     1) values indicated by a second common key as thresholds to generate 2M+1 binary sequences;

first exclusive OR means for performing an exclusive OR of said generated 2M+1 binary sequences to generate a keystream sequence; and

second exclusive OR means for performing an exclusive OR of a binary sequence of a plaintext and said keystream sequence to generate a binary sequence of a ciphertext,

whereby a binary sequence of ideal random variables is generated by using, as said nonlinear map, one having an equidistributivity of the invariant measure, symmetric property of the invariant measure and symmetric property of the map, and permitting said 2M+1 thresholds t_r (r=0 to 2M) to satisfy relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take.

38. The enciphering apparatus according to one of claim 32, wherein when said nonlinear map has a predetermined number of parameters, at least one of said parameters is used as a common key.

44. The enciphering apparatus according to one of claim 32, wherein said nonlinear map is a Chebyshev map expressed by a differential equation ω

_n+1 =cos (k cos^-1 ω

_n) where k is a real number equal to or greater than 2; and

said first common key is information indicative of an initial seed ω

₀ of said Chebyshev map (-1<

ω

₀ <

1) and said parameter k.

50. The enciphering apparatus according to claim 44, wherein said parameter k takes an even-numbered value.

56. The enciphering apparatus according to one of claims 32, wherein said real-valued sequence generation means executes a program described in a predetermined language by using a floating-point computing device to generate a sequence of values of said nonlinear map.

65. An enciphering method comprising the steps of:

generating a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map having an equidistributivity of the invariant measure, symmetric property of the invariant measure and symmetric property of the map, using a real value, indicated by a first common key, as an initial seed;

performing binarization on each real value in said generated real-valued sequence with 2M+1 (M being an integer equal to or greater than

     1) values indicated by a second common key as thresholds to generate 2M+1 binary sequences;

performing an exclusive OR of said generated 2M+1 binary sequences to generate a keystream sequence; and

performing an exclusive OR of a binary sequence of a plaintext and said keystream sequence to generate a binary sequence of a ciphertext,

whereby a binary sequence of ideal random variables is generated by using, as said nonlinear map, one having an equidistributivity of the invariant measure, symmetric property of the invariant measure and symmetric property of the map, and permitting said 2M+1 thresholds t_r (r=0 to 2M) to satisfy relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take.

66. A deciphering apparatus, comprising:

chaos generation means for generating a real-valued sequence along a chaotic orbit in accordance with a predetermined number of first common keys and a predetermined nonlinear map;

bit generation means for normalizing individual real values in said real-valued sequence over a predetermined interval and for binarizing said normalized real values using values indicated by a predetermined number of second common keys as thresholds to generate a binary sequence; and

means for executing a predetermined logic operation on a binary sequence of an input ciphertext and said generated keystream sequence bit by bit to generate a binary sequence of an original ciphertext.

67. A keystream generating apparatus for use in a stream enciphering apparatus or a stream deciphering apparatus for performing a logic operation on a binary sequence of a plaintext or a ciphertext and a keystream sequence generated based on a predetermined common key to generate a ciphertext or an original plaintext, said keystream generating apparatus comprising:

chaos generation means for generating a real-valued sequence along a chaotic orbit in accordance with a predetermined number of first common keys and a predetermined nonlinear map; and

bit generation means for normalizing individual real values in said real-valued sequence over a predetermined interval and for binarizing said normalized real values using values indicated by a predetermined number of second common keys as thresholds to generate to binary sequence.

68. An enciphering method comprising the steps of:

generating a real-valued sequence along a chaotic orbit in accordance with a predetermined number of first common keys and a predetermined nonlinear map;

normalizing individual real values in said real-valued sequence over a predetermined interval and binarizing said normalized real values using values indicated by a predetermined number of second common keys as thresholds to generate to binary sequence; and

executing a predetermined logic operation on a binary sequence of an input plaintext and said generated keystream sequence bit by bit to generate a binary sequence of a ciphertext.

69. A deciphering method comprising the steps of:

generating a real-valued sequence along a chaotic orbit in accordance with a predetermined number of first common keys and a predetermined nonlinear map;

normalizing individual real values in said real valued sequence over a predetermined interval and binarizing said normalized real values using values indicated by a predetermined number of second common keys as thresholds to generate a binary sequence; and

executing a predetermined logic operation on a binary sequence of an input ciphertext and said generated keystream sequence bit by bit to generate a binary sequence of an original plain text.

70. A keystream generating method for a keystream generating apparatus for use in a stream for use in a stream enciphering apparatus or a stream deciphering apparatus for performing a logic operation on a binary sequence of a plaintext or a ciphertext and a keystream sequence generated based on a predetermined common key to generate a ciphertext or an original plaintext, said keystream generating method comprising the steps of:

generating a real-valued sequence along a chaotic orbit in accordance with a predetermined number of first common keys and a predetermined nonlinear map and

normalizing individual real values in said real-valued sequence over a predetermined interval and binarizing said normalized real values using values indicated by a predetermined number of second common keys as thresholds to generate a binary sequence.

71. A computer readable storage medium storing a program for generating a random variable and for controlling a computer, said program comprising:

a computer readable program code means for generating a real-valued sequence along a chaotic orbit in accordance with a predetermined number of first common keys and a predetermined nonlinear map;

a computer readable program code means for normalizing individual real values in said real-valued sequence over a predetermined interval and binarizing said normalized real values using values indicated by a predetermined number of second common keys to generate to binary sequence; and

a computer readable program code means for executing a predetermined logic operation on a binary sequence of an input plaintext and the generated keystream sequence bit by bit to generate a binary sequence of a ciphertext.

72. A random variable generating apparatus comprising:

real-valued sequence generation means for generating a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map with a given real value as an initial seed;

binarization means for performing binarization on each real value in said generated real-valued sequence with given 2M+1 (M being an integer equal to or greater than

     1) values as thresholds to generate 2M+1 binary sequence, said 2M+1 thresholds t_r (r=0 to 2M) satisfying relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take; and

logic operation means for executing a predetermined logic operation based on said generated 2M+1 binary sequence to generate random variables.

73. A storage medium readable by a computer and having stored a program for generating random variables and controlling said computer in such a manner as to generate a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map with a given real value as an initial seed;

perform binarization on each real value in said generated real-valued sequence with given 2M+1 (M being an integer equal to or greater than

     1) values as thresholds to generate 2M+1 binary sequences, said 2M+1 thresholds t_r (r=0 to 2M) satisfying relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take; and

execute a predetermined logic operation based on said generated 2M+1 binary sequence to generate random variables.

74. A deciphering apparatus comprising:

real-valued sequence generation means for generating a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map using a real value, indicated by a first common key, as an initial seed;

binary sequence generation means for performing binarization on each real value in said generated real-valued sequence with 2M+1 ( M being an integer equal to or greater than

     1) values indicated by a second common key as thresholds to generate 2M+1 binary sequences, said 2M+1 thresholds t_r (r=0 to 2M) satisfying relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take;

first logic operation means for executing a predetermined first logic operation based on said generated 2M+1 binary sequences to generate a keystream sequence; and

second logic operation means for executing a predetermined second logic operation based on a binary sequence of a ciphertext and said keystream sequence to generate a binary sequence of a plaintext.

75. A keystream generating apparatus for use in a stream enciphering apparatus or a stream deciphering apparatus for performing a logic operation on a binary sequence of a plaintext or a ciphertext and a keystream sequence generated based on a predetermined common key to generate a ciphertext or an original plaintext, said keystream generating apparatus comprising:

real-valued sequence generation means for generating a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map using a real value, indicated by a first common key, as an initial seed;

binary sequence generation means for performing binarization on each real value in said generated real-valued sequence with 2M+1 (M being an integer equal to or greater than

     1) values indicated by a second common key as thresholds to generate 2M+1 binary sequences, said 2M+1 thresholds t_r (r=0 to 2M) satisfying relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take; and

logic operation means for executing a predetermined logic operation based on said generated 2M+1 binary sequences to generate a keystream sequence.

76. An enciphering method comprising the steps of:

generating a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map using a real value, indicated by a first common key, as an initial seed;

performing binarization on each real value in said generated real-valued sequence with 2M+1 (M being an integer equal to or greater than

     1) values indicated by a second common key as thresholds to generate 2M+1 binary sequence, said 2M=+1 thresholds t_r (r=0 to 2M) satisfying relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take;

executing a predetermined first logic operation based on said generated 2M+1 binary sequences to generate a keystream sequence; and

executing a predetermined second logic operation based on a binary sequence of a plaintext and said keystream sequence to generate a binary sequence of a ciphertext.

77. A deciphering method comprising the steps of:

generating a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map using a real value, indicated by first common key, as an initial seed;

performing binarization on each real value in said generated real-valued sequence with 2M +1 (M being an integer equal to or greater than

     1) values indicated by a second common key as thresholds to generate 2M+1 binary sequences, said 2M+1 thresholds t_r (r=0 to 2M) satisfying relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take;

executing a predetermined first logic operation based on said generated 2M+1 binary sequences to generate a keystream sequence; and

executing a predetermined second logic operation based on a binary sequence of a ciphertext and said keystream sequence to generate a binary sequence of a plaintext.

78. A keystream generating method in a keystream generating apparatus for use in a stream enciphering apparatus or a stream deciphering apparatus for performing a logic operation on a binary sequence of a plaintext or a ciphertext and a keystream sequence generated based on a predetermined common key to generate a ciphertext or an original plaintext, said keystream generating method comprising the steps of:

generating a real-valued sequence along a chaotic orbit in accordance with a predetermined nonlinear map using a real value, indicated by a first common key, as an initial seed;

performing binarization on each real value in said generated real-valued sequence with 2M+1 (M being an integer equal to or greater than

     1) values indicated by a second common key as thresholds to generate 2M+1 binary sequences, said 2M+1 thresholds t_r (r=0 to 2M) satisfying relationships t_r +t_2M-r =d+e and t_i ≠

t_j (when i≠

j) where d and e are respectively a minimum value and a maximum value said nonlinear map can take; and

executing a predetermined logic operation based on said generated 2M+1 binary sequences to generate a keystream sequence.