US5577124A
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Multi-purpose high speed cryptographically secure sequence generator based on zeta-one-way functions
Assignee: Arithmetica Inc
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Filing: 1995-03-09
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Granted: 1996-11-19
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Expires: 2015-03-09
Abstract
Abstract A method is disclosed whereby a high performance, high integrity, cryptographically secure sequence generator based on zeta one-way functions is specified for pseudorandom sequence generation, authentication, key transfer by public discussion, and message transmission by public-key encryption. The method encompasses a new one-way function with trapdoor based on Artin reciprocity in an algebraic number field. Public keys are pseudorandom sequences based on zeta one-way functions. In the simplest instance of this method, public keys are quadratic signatures, i.e. special sequences of Jacobi symbols. The generation, transfer, and sharing of private keys is a process based on the law of quadratic reciprocity. The computational complexity of the quadratic signature problem provides the foundation for the cryptographic security of this method. This new trapdoor one-way function is distinct from constructions in the prior art.
Inventors
- 👤 Michael M. Anshel
- 👤 Dorian Goldfeld
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-29 12:07
CPC Classifications
G; G06; G06F; G06F7/00; G06F7/58; G06F7/582; H; H04; H04L; H04L9/00; H04L9/06; H04L9/065; H04L9/0656; H04L9/0662; H04L9/30; H04L9/3093; G06F7/60; G06F7/72; G06F7/724; G06F7/725
Claims Analysis
Total Claims: 63
Claim 1
Independent Claim
73 words
A zeta one-way pseudorandom number generator comprising: an abelian variety classifier responsive to a modular encoder indicator and a probability distribution factor; a fast abelian variety generator responsive to an input key and said abelian variety classifier; a zeta function coefficient generator responsive to a prime sequence input and said fast abelian variety generator; a modular encoder acting under the influence of said modular encoder indicator responsive to said zeta function coefficient generator.
Claim 2
Dependent Claim
73 words
A zeta one-way pseudorandom number generator comprising: an abelian variety classifier responsive to a modular encoder indicator and a probability distribution factor; a fast abelian variety generator responsive to an input key and said abelian variety classifier; a zeta function coefficient generator responsive to a prime sequence input and said fast abelian variety generator; a modular encoder acting under the influence of said modular encoder indicator responsive to said zeta function coefficient generator.
Claim 3
Dependent Claim
96 words
A real time authentication system comprising: a zeta one-way pseudorandom number generator responsive to an input key and an input parameter to generate a primary zeta code; a zeta code transformer responsive to said zeta one-way pseudorandom number generator to generate variety generation parameters; a fast abelian variety generator responsive to said zeta code transformer variety generation parameters and connected to a zeta function coefficient generator; an announcer responsive to an output of said zeta function coefficient generator generating secondary zeta code; means for transmitting parameters specifying said abelian variety; means for incrementing said input parameter.
Claim 4
Dependent Claim
96 words
A real time authentication system comprising: a zeta one-way pseudorandom number generator responsive to an input key and an input parameter to generate a primary zeta code; a zeta code transformer responsive to said zeta one-way pseudorandom number generator to generate variety generation parameters; a fast abelian variety generator responsive to said zeta code transformer variety generation parameters and connected to a zeta function coefficient generator; an announcer responsive to an output of said zeta function coefficient generator generating secondary zeta code; means for transmitting parameters specifying said abelian variety; means for incrementing said input parameter.
Claim 5
Dependent Claim
33 words
A real time authentication system according to claim 2, further comprising means for regenerating secondary zeta code and for comparing to an announced zeta code based on said parameter specifying said abelian variety.
Claim 6
Dependent Claim
121 words
A distributed public key transfer system comprising: two subsystems operating symmetrically, each subsystem is responsive to an input key; means for selecting in each subsystem a first subset of primes from a predetermined second set of primes; means for combining said first subset of primes responsive to said means for selecting; means for generating an Artin L-function code table based on a second set of primes associated to the symmetric subsystem and responsive to said means for combining; in each subsystem a code table annunciator responsive to said means for generating; a code table receiver; a code chooser responsive to said means for selecting and connected to said code table receiver; means for combining chosen codes responsive to said code chooser.
Claim 7
Dependent Claim
121 words
A distributed public key transfer system comprising: two subsystems operating symmetrically, each subsystem is responsive to an input key; means for selecting in each subsystem a first subset of primes from a predetermined second set of primes; means for combining said first subset of primes responsive to said means for selecting; means for generating an Artin L-function code table based on a second set of primes associated to the symmetric subsystem and responsive to said means for combining; in each subsystem a code table annunciator responsive to said means for generating; a code table receiver; a code chooser responsive to said means for selecting and connected to said code table receiver; means for combining chosen codes responsive to said code chooser.
Claim 8
Dependent Claim
25 words
A distributed public key transfer system according to claim 4, wherein in each subsystem means for combining said first subset of primes is a multiplier.
Claim 9
Dependent Claim
44 words
A distributed public key transfer system according to claim 5, wherein in each subsystem means for selecting a first subset of primes selects from a first set of primes exhibiting evaluated Artin symbols with a second set of primes associates with the symmetric subsystem.
Claim 10
Dependent Claim
39 words
A distributed public key transfer system according to claim 6, wherein for each subsystem the second set of primes is chosen from an algebraic number field and specified by congruence conditions determined by Artin reciprocity in said number field.
Claim 11
Dependent Claim
47 words
A distributed public key transfer system according to claim 7, wherein said algebraic number field is an ordinary rational number field and said evaluated Artin symbols are Jacobi symbols and members of said first set of primes are at least partially defined by congruence to 1(mod 4).
Claim 12
Dependent Claim
44 words
A distributed public key transfer system according to claim 8, wherein one of said sets of primes is at least partially defined by congruence to 1(mod 8) and another of said sets of primes is at least partially defined by congruence to 5(mod 8).
Claim 13
Dependent Claim
50 words
A distributed public key transfer system according to claim 9, wherein in each subsystem means for generating further comprises a Jacobi symbol generator with a conductor input connected to an output of said multiplier and a prime input responsive to said second set of primes associated to the symmetric subsystem.
Claim 14
Dependent Claim
19 words
A distributed public key transfer system according to claim 10, wherein said means for selecting is a pseudorandom selector.
Claim 15
Dependent Claim
20 words
A distributed public key transfer system according to claim 11, wherein said means for combining chosen codes is a multiplier.
Claim 16
Dependent Claim
18 words
A distributed public key transfer system according to claim 11, wherein said code table annunciator is a transmitter.
Claim 17
Dependent Claim
20 words
A distributed public key transfer system according to claim 13, wherein said transmitter is a point to point communication interface.
Claim 18
Dependent Claim
20 words
A distributed public key transfer system according to claim 13, wherein said code table annunciator is an electronic bulletin board.
Claim 19
Dependent Claim
23 words
A distributed public key transfer system according to claim 11, wherein said code table receiver further comprises a point to point communication interface.
Claim 20
Dependent Claim
52 words
A distributed public key transfer system according to claim 11, further comprising; a pseudorandom number generator having a key input responsive to said means for combining chosen codes; and an encryption system having a plain text input, an encryption code input connected to said pseudorandom number generator, and a cipher text output.
Claim 21
Dependent Claim
38 words
A distributed public key transfer system according to claim 11, further comprising in each subsystem a selection variable designator connected to said means for selecting a predetermined number of a first set of primes, defining said predetermined number.
Claim 22
Dependent Claim
139 words
A distributed public key encryption system sending station comprising: means for selecting a first subset of primes from a predetermined second set of primes; means for combining said first subset of primes; means for generating an Artin L-function code table based on a second set of primes associated with a receiving station and responsive to said means for combining; a key receiver; a code chooser responsive to said means for selecting and connected to said key receiver; means for combining chosen codes responsive to said key receiver; means for comparing a text state to a state of the output of said means for combining chosen codes and correcting an output of said means for generating when said text state differs from said output of said means for combining chosen codes; a code transmitter responsive to said means for comparing.
Claim 23
Dependent Claim
139 words
A distributed public key encryption system sending station comprising: means for selecting a first subset of primes from a predetermined second set of primes; means for combining said first subset of primes; means for generating an Artin L-function code table based on a second set of primes associated with a receiving station and responsive to said means for combining; a key receiver; a code chooser responsive to said means for selecting and connected to said key receiver; means for combining chosen codes responsive to said key receiver; means for comparing a text state to a state of the output of said means for combining chosen codes and correcting an output of said means for generating when said text state differs from said output of said means for combining chosen codes; a code transmitter responsive to said means for comparing.
Claim 24
Dependent Claim
37 words
A distributed public key encryption system according to claim 19, wherein said means for selecting, selects an odd number of primes and said means for comparing and correcting an output inverts the output when the states differ.
Claim 25
Dependent Claim
23 words
A distributed public key encryption system according to claim 19, wherein said means for combining said first subset of primes is a multiplier.
Claim 26
Dependent Claim
42 words
A distributed public key encryption system according to claim 21, wherein said means for selecting a first subset of primes selects from a first set of primes exhibiting evaluated Artin symbols with a second set of primes associated with a receiving station.
Claim 27
Dependent Claim
39 words
A distributed public key encryption system according to claim 22, wherein for each subsystem the second set of primes is chosen from an algebraic number field and specified by congruence conditions determined by Artin reciprocity in said number field.
Claim 28
Dependent Claim
53 words
A distributed public key encryption system according to claim 23, wherein said algebraic number field is an ordinary rational number field and said evaluated Artin symbols are Jacobi symbols and members of said first set of primes and said second set of primes are at least partially defined by congruence to 1(mod 4).
Claim 29
Dependent Claim
45 words
A distributed public key encryption system according to claim 24, wherein one of said sets of primes is at least partially defined by congruence to 1(mod 8) and another of said sets of primes is at least partially defined by congruence to 5 (mod 8).
Claim 30
Dependent Claim
43 words
A distributed public key encryption system according to claim 22, wherein said means for generating further comprises a Jacobi symbol generator with a conductor input connected to an output of said multiplier and a prime input responsive to said second set of primes.
Claim 31
Dependent Claim
19 words
A distributed public key encryption system according to claim 26, wherein said means for selecting is a pseudorandom selector.
Claim 32
Dependent Claim
20 words
A distributed public key encryption system according to claim 27, wherein said means for combining chosen codes is a multiplier.
Claim 33
Dependent Claim
18 words
A distributed public key encryption system according to claim 27, wherein said code table annunciator is a transmitter.
Claim 34
Dependent Claim
20 words
A distributed public key encryption system according to claim 29, wherein said transmitter is a point to point communication interface.
Claim 35
Dependent Claim
20 words
A distributed public key encryption system according to claim 29, wherein said code table annunciator is an electronic bulletin board.
Claim 36
Dependent Claim
23 words
A distributed public key encryption system according to claim 27, wherein said code table receiver further comprises a point to point communication interface.
Claim 37
Dependent Claim
75 words
A zeta one-way pseudorandom number generator method comprising the steps of classifying an abelian variety in response to a modular encoder indicator and a probability distribution factor; generating a fast abelian variety from an input key and an abelian variety class; generating a zeta function coefficient from a prime sequence and the abelian variety; reducing the zeta function coefficients by a modular function; and encoding information with pseudorandom numbers created by said step of reducing.
Claim 38
Dependent Claim
75 words
A zeta one-way pseudorandom number generator method comprising the steps of classifying an abelian variety in response to a modular encoder indicator and a probability distribution factor; generating a fast abelian variety from an input key and an abelian variety class; generating a zeta function coefficient from a prime sequence and the abelian variety; reducing the zeta function coefficients by a modular function; and encoding information with pseudorandom numbers created by said step of reducing.
Claim 39
Dependent Claim
80 words
A real time authentication method comprising the steps of: utilize a zeta one-way function to generate a pseudorandom number sequence in response to an input key and an input parameter to yield a primary zeta code; transform the primary zeta code to generate variety generation parameters; generate an abelian variety from said variety generation parameters; generate a secondary zeta code from the variety parameters; announce the secondary zeta code; transmit the parameters specifying said abelian variety; increment the input key.
Claim 40
Dependent Claim
80 words
A real time authentication method comprising the steps of: utilize a zeta one-way function to generate a pseudorandom number sequence in response to an input key and an input parameter to yield a primary zeta code; transform the primary zeta code to generate variety generation parameters; generate an abelian variety from said variety generation parameters; generate a secondary zeta code from the variety parameters; announce the secondary zeta code; transmit the parameters specifying said abelian variety; increment the input key.
Claim 41
Dependent Claim
36 words
A method according to claim 34, further comprising the step of regenerating the secondary zeta code from the parameter specifying said abelian variety and comparing the announced secondary zeta code to the regenerated secondary zeta code.
Claim 42
Dependent Claim
78 words
A distributed public key transfer method comprising the steps of: selecting a first subset of primes from a predetermined second set of primes; combining said first subset of primes; generating an Artin L-function code table based on a second set of primes associated to a second subsystem; announcing the code table; receiving a second code table generated by an associated system; choosing codes from the second code table corresponding to the first subset of primes; combining chosen codes.
Claim 43
Dependent Claim
78 words
A distributed public key transfer method comprising the steps of: selecting a first subset of primes from a predetermined second set of primes; combining said first subset of primes; generating an Artin L-function code table based on a second set of primes associated to a second subsystem; announcing the code table; receiving a second code table generated by an associated system; choosing codes from the second code table corresponding to the first subset of primes; combining chosen codes.
Claim 44
Dependent Claim
30 words
A distributed public key transfer method according to claim wherein the step of combining said first subset of primes is accomplished by multiplying members of said first subset of primes.
Claim 45
Dependent Claim
42 words
A distributed public key transfer method according to claim 37, wherein the step of selecting a first subset of primes selects from a first set of primes exhibiting evaluated Artin symbols with a second set of primes associated with the second subsystem.
Claim 46
Dependent Claim
36 words
A distributed public key transfer method according to claim 38, wherein the second set of primes is chosen from an algebraic number field and specified by congruence conditions determined by Artin reciprocity in said number field.
Claim 47
Dependent Claim
46 words
A distributed public key transfer method according to claim 39, wherein said algebraic number field is an ordinary rational number field and said evaluated Artin symbols are Jacobi symbols and members of said first set primes are at least partially defined by congruence to 1(mod 4).
Claim 48
Dependent Claim
44 words
A distributed public key transfer method according to claim 40, wherein one of said sets of primes is at least partially defined by congruence to 1(mod 8) and another of said sets of primes is at least partially defined by congruence to 5(mod 8).
Claim 49
Dependent Claim
45 words
A distributed public key transfer method according to claim 41, wherein said step of generating further comprises generating a series of Jacobi symbols from said second set of primes associated to the second subsystem with a conductor specified by the multiplied first subset of primes.
Claim 50
Dependent Claim
19 words
A distributed public key transfer method according to claim 42, wherein the step of selecting is a pseudorandom selection.
Claim 51
Dependent Claim
21 words
A distributed public key transfer method according to claim 43, wherein the step of combining chosen codes multiplies the chosen codes.
Claim 52
Dependent Claim
42 words
A distributed public key transfer method according to claim 43, further comprising; generating a pseudorandom number sequence from a key input created by the step of combining chosen codes; and encrypting a plain text with the pseudorandom, an encryption code number sequence.
Claim 53
Dependent Claim
110 words
A distributed public key encryption sending method comprising the steps of: selecting a first subset of primes from a predetermined second set of primes; combining said first subset of primes; generating an Artin L-function code table based on a second set of primes associated with a receiving station from the combined first subset of primes; acquiring an encryption key; choosing codes from said encryption key corresponding to said first subset of codes; combining chosen codes; comparing a text state to a state of the combined chosen codes and correcting the Artin L-function code table when said text differs from said state of the combined codes; transmitting the corrected code table.
Claim 54
Dependent Claim
110 words
A distributed public key encryption sending method comprising the steps of: selecting a first subset of primes from a predetermined second set of primes; combining said first subset of primes; generating an Artin L-function code table based on a second set of primes associated with a receiving station from the combined first subset of primes; acquiring an encryption key; choosing codes from said encryption key corresponding to said first subset of codes; combining chosen codes; comparing a text state to a state of the combined chosen codes and correcting the Artin L-function code table when said text differs from said state of the combined codes; transmitting the corrected code table.
Claim 55
Dependent Claim
39 words
A distributed public key encryption method according to claim 46, wherein said step of selecting selects an odd number of primes and said steps of comparing and correcting inverts the output of the code table when the states differ.
Claim 56
Dependent Claim
20 words
A distributed public key encryption method according to claim 46, wherein said step of combining first subset of primes multiplies.
Claim 57
Dependent Claim
42 words
A distributed public key encryption method according to claim 48, wherein said step of selecting a first subset of primes selects from a first set of primes exhibiting evaluated Artin symbols with a second set of primes associated with a receiving station.
Claim 58
Dependent Claim
36 words
A distributed public key encryption method according to claim 49, wherein the second set of primes is chosen from an algebraic number field and specified by congruence conditions determined by Artin reciprocity in said number field.
Claim 59
Dependent Claim
53 words
A distributed public key encryption method according to claim 50, wherein said algebraic number field is an ordinary rational number field and said evaluated Artin symbols are Jacobi symbols and members of said first set of primes and said second set of primes are at least partially defined by congruence to 1(mod 4).
Claim 60
Dependent Claim
44 words
A distributed public key encryption method according to claim 51, wherein one of said sets of primes is at least partially defined by congruence to 1(mod 8) and another of said sets of primes is at least partially defined by congruence of 5(mod 8).
Claim 61
Dependent Claim
31 words
A distributed public key encryption method according to claim 49, wherein said step of generating generates Jacobi symbols from the second set of primes and the multiplied primes as a conductor.
Claim 62
Dependent Claim
18 words
A distributed public key encryption method according to claim 53, wherein said step selecting is a pseudorandom selection.
Claim 63
Dependent Claim
18 words
A distributed public key encryption method according to claim 54, wherein said step of combining chosen codes multiplies.
References Cited (Backward Citations)
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