US5751808A
Expired / Lapsed
US
⏱️ 0.0 years remaining
Multi-purpose high speed cryptographically secure sequence generator based on zeta-one-way functions
Assignee: Individual
•
Filing: 1996-11-19
•
Granted: 1998-05-12
•
Expires: 2016-11-19
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 lax 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
2026-11-09 10:40
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: 16
Claim 1
Independent Claim
69 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 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 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
69 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 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 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
93 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 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 variety; means for incrementing said input parameter.
Claim 4
Dependent Claim
93 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 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 variety; means for incrementing said input parameter.
Claim 5
Dependent Claim
32 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 variety.
Claim 6
Dependent Claim
76 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 a 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 7
Dependent Claim
76 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 a 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 8
Dependent Claim
31 words
A distributed public key transfer method according to claim 4, wherein the step of combining said first subset of primes is accomplished by multiplying members of said first subset of primes.
Claim 9
Dependent Claim
42 words
A distributed public key transfer method according to claim 5, 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 10
Dependent Claim
36 words
A distributed public key transfer method according to claim 6, 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 11
Dependent Claim
46 words
A distributed public key transfer method 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 primes are at least partially defined by congruence to 1(mod 4).
Claim 12
Dependent Claim
44 words
A distributed public key transfer method 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
45 words
A distributed public key transfer method according to claim 9, 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 14
Dependent Claim
19 words
A distributed public key transfer method according to claim 10, wherein the step of selecting is a pseudorandom selection.
Claim 15
Dependent Claim
21 words
A distributed public key transfer method according to claim 11, wherein the step of combining chosen codes multiplies the chosen codes.
Claim 16
Dependent Claim
42 words
A distributed public key transfer method according to claim 11, 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.
References Cited (Backward Citations)
US5577124A
Cited
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 2001-05-11 | 2001-11-10 | 2002-05-12 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2005-05-11 | 2005-11-10 | 2006-05-12 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2009-05-11 | 2009-11-10 | 2010-05-12 | $7700.00 | Window Closed / Lapsed |