US3657476A
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Cryptography
Assignee: Individual
•
Filing: 1970-01-23
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Granted: 1972-04-18
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Expires: 1990-01-23
Abstract
Abstract The cryptographic system to be described is based on a unique number theoretical approach to the generation of pseudo-random digits derived from the N (m-1)mn 1 DISTINCT POWERS OF R MODULO M where M mn, M IS A PRIME, AND R IS A PROPERLY CHOSEN PRIMITIVE ROOT OF M. The digits of the powers of r are transformed into Boolean vectors, and these in turn are used as arguments of a Boolean function employed to generate pseudo-random digits. Subsequently, the pseudo-random digits are combined with digits representing the data to be encoded in a manner facilitating the decoding. Security is provided by the very great periodicy that the invention provides. Known electrical components are arranged in a manner to provide solid state circuitry for the implementation of the cryptographic method.
Inventors
- 👤 Howard H Aiken
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-28 05:18
CPC Classifications
H; H04; H04L; H04L9/00; H04L9/06; H04L9/065; H04L9/0656; H04L9/0662
Claims Analysis
Total Claims: 32
Claim 1
Independent Claim
84 words
A cryptographic method of the type using pseUdo-random digits to encode and decode data, comprising: a. means for generating a sequence of powers rp M where M mn, m is a prime and r is a primitive root of m, so chosen that the number of distinct powers is N (m-1)m(n 1), b. transforming the digits of the powers rp M obtained in step (a) into Boolean vectors, c. entering the Boolean vectors as arguments of Boolean functions to generate pseudo-random digits of radix-r.
Claim 2
Dependent Claim
84 words
A cryptographic method of the type using pseUdo-random digits to encode and decode data, comprising: a. means for generating a sequence of powers rp M where M mn, m is a prime and r is a primitive root of m, so chosen that the number of distinct powers is N (m-1)m(n 1), b. transforming the digits of the powers rp M obtained in step (a) into Boolean vectors, c. entering the Boolean vectors as arguments of Boolean functions to generate pseudo-random digits of radix-r.
Claim 3
Dependent Claim
65 words
A method as in claim 1 wherein r 2 and the Boolean vectors are partitioned into two subsets each having 2n 1 vectors and each having an equal number of vector occurrences en toto as the powers rp M are generated in the interval 0 < or = p < N thus providing binary pseudo-random digits having substantially an equal number of 0''s and 1''s.
Claim 4
Dependent Claim
47 words
A method as in claim 2 wherein the Boolean vectors are partitioned in accordance with the following, 0..0000 0..0001 0..0011 0..0010 0..0101 0..0100 0..0110 0..0111 0..1001 0.1000 0..1010 0..1011 .... .... so that the Boolean function defining the pseudo-random digits may be implemented by a mod-2 adder.
Claim 5
Dependent Claim
11 words
A method as in claim 1 wherein r 3, m 7.
Claim 6
Dependent Claim
109 words
A cryptographic method using pseudo-random digits derived from N (m-1)mn 1 distinct powers of rp M where M mn, m is a prime, and r is a primitive root of m, the pseudo-random digits being obtained by a. generating the powers of r modulo M by the recurrence relationship rp 1 M r . rp M, b. transforming the digits of rp M into Boolean vectors by means of the transformation T(d) 0, 671, . . . delta m 1 where the delta ''s are all 0''s or 1''s so that 2m such transformations exist, c. entering the Boolean vectors into Boolean functions to generate pseudo-random digits of radix-r.
Claim 7
Dependent Claim
109 words
A cryptographic method using pseudo-random digits derived from N (m-1)mn 1 distinct powers of rp M where M mn, m is a prime, and r is a primitive root of m, the pseudo-random digits being obtained by a. generating the powers of r modulo M by the recurrence relationship rp 1 M r . rp M, b. transforming the digits of rp M into Boolean vectors by means of the transformation T(d) 0, 671, . . . delta m 1 where the delta ''s are all 0''s or 1''s so that 2m such transformations exist, c. entering the Boolean vectors into Boolean functions to generate pseudo-random digits of radix-r.
Claim 8
Dependent Claim
17 words
A cryptographic method as in claim 5 wherein r 2, for the generation of radix-2 pseudo-random digits.
Claim 9
Dependent Claim
20 words
A cryptographic method as in claim 5 where r 3 and m 7 for the generation of radix-3 pseudo-random digits.
Claim 10
Dependent Claim
21 words
A cryptographic method as defined in claim 5 further comprising additional encrypting means to modify the order of the pseudo-random digits.
Claim 11
Dependent Claim
91 words
A cryptographic system including a method of generating pseudo-random digits of extremely great periodicy comprising; a. generating the powers of rp M where M mn, m prime number, r primitive root of m, and r is chosen such that the number of distinct powers of r modulo M is N (m-1)m(n 1) b. applying the transformation T(dpq) to the digits of rp M to form Boolean vectors having all digits 0 and 1, c. using the results of (b) as arguments of a Boolean function f(p) to produce pseudo-random binary digits.
Claim 12
Dependent Claim
91 words
A cryptographic system including a method of generating pseudo-random digits of extremely great periodicy comprising; a. generating the powers of rp M where M mn, m prime number, r primitive root of m, and r is chosen such that the number of distinct powers of r modulo M is N (m-1)m(n 1) b. applying the transformation T(dpq) to the digits of rp M to form Boolean vectors having all digits 0 and 1, c. using the results of (b) as arguments of a Boolean function f(p) to produce pseudo-random binary digits.
Claim 13
Dependent Claim
124 words
Apparatus for generating pseudo-random digits used in a cryptographic system, the apparatus comprising a serial delay line with means for entering a cryptographic key number rp0 M where m is a prime, and r is a primitive root of m so chosen that the number of distinct powers of r modulo-M is N (m-1)mn 1, a multiply by r means in a recirculation circuit of the delay line to produce the powers rp M successively beginning with rp0 M the key, means for transforming the output of the delay line into Boolean vectors, means for entering the Boolean vectors as arguments of Boolean functions to generate pseudo-random digits, and means for combining the pseudo-random digits with a message for encrypting or decrypting the same.
Claim 14
Dependent Claim
124 words
Apparatus for generating pseudo-random digits used in a cryptographic system, the apparatus comprising a serial delay line with means for entering a cryptographic key number rp0 M where m is a prime, and r is a primitive root of m so chosen that the number of distinct powers of r modulo-M is N (m-1)mn 1, a multiply by r means in a recirculation circuit of the delay line to produce the powers rp M successively beginning with rp0 M the key, means for transforming the output of the delay line into Boolean vectors, means for entering the Boolean vectors as arguments of Boolean functions to generate pseudo-random digits, and means for combining the pseudo-random digits with a message for encrypting or decrypting the same.
Claim 15
Dependent Claim
19 words
Apparatus as in claim 10 further comprising additional encrypting means in combination to modify the order of pseudo-random digits.
Claim 16
Dependent Claim
22 words
Apparatus as in claim 11 wherein the additional encrypting means includes trigger pairs controlled by puller functions, interruption means, and delay line.
Claim 17
Dependent Claim
75 words
Apparatus as in claim 12 wherein the two states of the trigger pairs are used to complement or not complement the digits of f(p) according to trigger state; delete or not delete the digits of f(p) according to the trigger state; open or close the gates at the input and output of a delay line so that blocks of digits can be deleted from or inserted into the digit stream according to the trigger state.
Claim 18
Dependent Claim
117 words
A cryptographic apparatus comprising; a serial delay line, means for manually entering a crytographic key in the serial delay line representing rp0 M where M mn, m 5 r 2, a multiply by 2 circuit connected to the output of the delay line, and having one output connected to the input of the delay line, an output of the multiply by 2 circuit to provide carry digits, a mode 2 adder connected to the times 2 circuit to receive the carry digits and produce binary pseudo-random digits f(p), the output of the mod 2 adder connected to another mod 2 adder for combining with a clear or encrypted message to provide an encrypted or clear message respectively.
Claim 19
Dependent Claim
117 words
A cryptographic apparatus comprising; a serial delay line, means for manually entering a crytographic key in the serial delay line representing rp0 M where M mn, m 5 r 2, a multiply by 2 circuit connected to the output of the delay line, and having one output connected to the input of the delay line, an output of the multiply by 2 circuit to provide carry digits, a mode 2 adder connected to the times 2 circuit to receive the carry digits and produce binary pseudo-random digits f(p), the output of the mod 2 adder connected to another mod 2 adder for combining with a clear or encrypted message to provide an encrypted or clear message respectively.
Claim 20
Dependent Claim
42 words
A cryptographic method for encrypting the letters of the alphabet comprising; regarding the alphabet letters as integers of a radix 27 number system represented by three ternary digits, and operating upon the ternary digits in accordance with the rules of ternary arithmetic.
Claim 21
Dependent Claim
42 words
A cryptographic method for encrypting the letters of the alphabet comprising; regarding the alphabet letters as integers of a radix 27 number system represented by three ternary digits, and operating upon the ternary digits in accordance with the rules of ternary arithmetic.
Claim 22
Dependent Claim
77 words
A method as in claim 15 wherein the alphabet letters are regarded as the following triples of ternary digits in the radix 27 number system: * 000I 100 R 200 A 001J 101 S 201 B 002 K 102 T 202 C 010 L 110 U 210 D 011 M 111 V 211 E 012 N 112 W 212 F 020 O 120 X 220 G 021 P 121 Y 221 H 022 Q 122 Z 222
Claim 23
Independent Claim
56 words
A method of generating a sequence of pseudo-random digits by utilizing the carry digits arising in the formation of rp 1 M by multiplication of rp M by r modulo M where m is a prime M mn, r is a primitive root of m so chosen that N (m-1)mn 1 and that (m-1)/r an integer.
Claim 24
Independent Claim
56 words
A method of generating a sequence of pseudo-random digits by utilizing the carry digits arising in the formation of rp 1 M by multiplication of rp M by r modulo M where m is a prime M mn, r is a primitive root of m so chosen that N (m-1)mn 1 and that (m-1)/r an integer.
Claim 25
Independent Claim
80 words
A method of generating a sequence of binary digits based upon Boolean vectors obtained from transforms of the digits in the powers 2p M where m is a prime, M mn, r 2 is a primitive root of m and m is so chosen that the number of distinct power is N (m-1)mn 1 and the transform is defined by and thus made identical with the carry digits generated by multiplying 2p M by 2 modulo M to form .
Claim 26
Independent Claim
80 words
A method of generating a sequence of binary digits based upon Boolean vectors obtained from transforms of the digits in the powers 2p M where m is a prime, M mn, r 2 is a primitive root of m and m is so chosen that the number of distinct power is N (m-1)mn 1 and the transform is defined by and thus made identical with the carry digits generated by multiplying 2p M by 2 modulo M to form .
Claim 27
Independent Claim
51 words
A method of generating a sequence of pseudo-random binary digits by utilizing thE carry digits arising in the formation of 2p 1 M by multiplication of 2p M by r 2 modulo M when m is a prime being 2 as a primitive root and so chosen that N (m-1)mn 1.
Claim 28
Independent Claim
51 words
A method of generating a sequence of pseudo-random binary digits by utilizing thE carry digits arising in the formation of 2p 1 M by multiplication of 2p M by r 2 modulo M when m is a prime being 2 as a primitive root and so chosen that N (m-1)mn 1.
Claim 29
Dependent Claim
148 words
A cryptographic system for encrypting the programs, input, and output of computers and data processing machines comprising: a. generating the powers 2p M where M mn, m is a prime having r 2 as a primitive root, and m is so chosen that the number of distinct powers of 2 modulo M is N (m-1)mn 1 b. applying the transformation T(dpq) to digits of 2p M to form Boolean vectors having all digits 0 or 1, c. partitioning the Boolean vectors into two subsets such that each subset has an equal number of vectors and an equal number of vector occurrences in the range 0 < or = p < N, d. using one of the subsets to define a Boolean function to produce pseudo-random binary digits, e. combining the pseudo-random digits with the digits representing program input data, and output data for purposes of encoding and decoding.
Claim 30
Dependent Claim
148 words
A cryptographic system for encrypting the programs, input, and output of computers and data processing machines comprising: a. generating the powers 2p M where M mn, m is a prime having r 2 as a primitive root, and m is so chosen that the number of distinct powers of 2 modulo M is N (m-1)mn 1 b. applying the transformation T(dpq) to digits of 2p M to form Boolean vectors having all digits 0 or 1, c. partitioning the Boolean vectors into two subsets such that each subset has an equal number of vectors and an equal number of vector occurrences in the range 0 < or = p < N, d. using one of the subsets to define a Boolean function to produce pseudo-random binary digits, e. combining the pseudo-random digits with the digits representing program input data, and output data for purposes of encoding and decoding.
Claim 31
Dependent Claim
48 words
A cryptographic system for encrypting the programs, input, and output of computers and data processing machines comprising: a. generating a sequence of pseudo-random digits of great period, and b. combining the pseudo-random digits with digits representing program input data, and output data for purposes of encoding and decoding.
Claim 32
Dependent Claim
48 words
A cryptographic system for encrypting the programs, input, and output of computers and data processing machines comprising: a. generating a sequence of pseudo-random digits of great period, and b. combining the pseudo-random digits with digits representing program input data, and output data for purposes of encoding and decoding.
References Cited (Backward Citations)
No citation records indexed.
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1975-04-18 | 1975-10-18 | 1976-04-18 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1979-04-18 | 1979-10-18 | 1980-04-18 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1983-04-18 | 1983-10-18 | 1984-04-18 | $7700.00 | Window Closed / Lapsed |