Cryptographic system and protocol for establishing secure authenticated remote access

Claim 2

In a cryptographic protocol for a first participant and one or more second participants, a method for said first participant to establish a shared secret with said second participants, said first participant and said second participants sharing a first authentication factor, said method comprising the steps of: receiving a private signal, generating a first public signal by obtaining an initial transformation of said private signal using shared parameters shared with said second participants, receiving a respective second public signal from each of said second participants, sending said first public signal to at least one of said second participants, and generating a shared-secret signal representing said shared secret by obtaining a combining transformation of said private signal with said second public signals and said first authentication factor using said shared parameters, said combining transformation having a property that distinct values of said shared-secret signal are generated by varying only said first authentication factor, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 3

A method according to claim 1 that further comprises decrypting said second public signal using a decryption key derived at least in part from said first authentication factor.

Claim 4

A method according to claim 1 wherein said shared parameters comprise a first number and a second number, said initial transformation includes a function equivalent to raising said first number to a first power represented by said private signal, modulo said second number, and said combining transformation includes a function equivalent to raising number represented by said second public signal to a second power representing said private signal, modulo said second number.

Claim 5

A method according to claim 3 wherein said second power also represents said first authentication factor.

Claim 6

A method according to claim 3 wherein said combining transformation includes a hashing function.

Claim 7

A method according to claim 3 wherein said combining transformation includes a hashing function.

Claim 8

A method according to claim 1 wherein said combining transformation is also of a second authentication factor shared by said first participant and said second participants, said combining transformation having a property that distinct values of said shared-secret signal are generated by varying only said second authentication factor.

Claim 9

A method according to claim 7 wherein said shared parameters comprise a first number and a second number, said initial transformation includes a function equivalent to raising said first number to a first power represented by said private signal, modulo said second number, and said combining transformation includes a function equivalent to raising a number represented by said second public signal to a second power representing said private signal, modulo said second number.

Claim 10

A method according to claim 8 wherein said second power also represents said first authentication factor and said second authentication factor.

Claim 11

A method according to claim 1 further comprising the steps of: said first participant receiving a second private signal, said first participant generating a first transformed signal by obtaining a first transformation of said second private signal, first participant generating a third public signal by encrypting said first transformed signal according to said shared secret, said first participant receiving a fourth public signal, said first participant obtaining a first decrypted signal by decrypting said fourth public signal according to said shared secret, said first participant generating a second transformed signal by obtaining a second transformation of said second private signal with said first decrypted signal, said first participant receiving a third private signal, said first participant generating one or more fifth public signals by encrypting said second transformed signal and said third private signal according to said shared secret, said first participant obtaining a third transformed signal by transforming said third private signal, said first participant receiving a sixth public signal, said first participant obtaining a second decrypted signal by decrypting said sixth public signal according to said shared secret, and said first participant comparing said third transformed signal with said second decrypted signal and generating an authentication signal in response thereto, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 12

A method according to claim 1 further comprising the steps of: said first participant receiving a second private signal, said first participant generating a first transformed signal by obtaining a first transformation of said second private signal, said first participant generating a third public signal by encrypting said first transformed signal according to said shared secret, said first participant receiving a fourth public signal, said first participant obtaining a first decrypted signal by decrypting said fourth public signal according to said shared secret, said first participant generating a second transformed signal by obtaining a second transformation of said second private signal with said first decrypted signal, said first participant receiving a fifth public signal, said first participant obtaining a second decrypted signal by decrypting said fifth public signal according to said shared secret, and said first participant comparing said second decrypted signal with said second transformed signal and generating an authentication signal in response thereto, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 13

A medium readable by a machine embodying a program of instructions executable by said machine to perform a method in a cryptographic protocol, said method comprising the steps of claim 1.

Claim 14

In a cryptographic protocol for a plurality of participants, a method for a first participant to establish a shared secret with a second participant, said first participant and said second participant sharing a first authentication factor, said method comprising the steps of: said first participant receiving a first private signal, said second participant receiving a second private signal, said first participant generating a first public signal by obtaining a first initial transformation of said first private signal using shared parameters shared with said second participants, said second participant generating a second public signal by obtaining a second initial transformation of said second private signal using said shared parameters, said first participant receiving said second public signal, said second participant receiving said first public signal, said first participant generating a first shared-secret signal representing said shared secret by obtaining a first combining transformation of said first private signal with said second public signal and said first authentication factor using said shared parameters, said first combining transformation having a property that distinct values of said first shared-secret signal are generated by varying only said first authentication factor, and said second participant generating a second shared-secret signal representing said shared secret by obtaining a second combining transformation of said second private signal with said first public signal and said first authentication factor using said shared parameters, said second combining transformation having a property that distinct values of said second shared-secret signal are generated by varying only said first authentication factor, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 15

In a cryptographic protocol for a plurality of participants, a method for a first participant to establish a shared secret with a second participant, said first participant and said second participant sharing a first authentication factor, said method comprising the steps of: said first participant receiving a first private signal, said second participant receiving a second private signal, said first participant generating a first public signal by obtaining a first initial transformation of said first private signal using shared parameters shared with said second participants, said second participant generating a second public signal by obtaining a second initial transformation of said second private signal using said shared parameters, said first participant receiving said second public signal, said second participant receiving said first public signal, said first participant generating a first shared-secret signal representing said shared secret by obtaining a first combining transformation of said first private signal with said second public signal and said first authentication factor using said shared parameters, said first combining transformation having a property that distinct values of said first shared-secret signal are generated by varying only said first authentication factor, and said second participant generating a second shared-secret signal representing said shared secret by obtaining a second combining transformation of said second private signal with said first public signal and said first authentication factor using said shared parameters, said second combining transformation having a property that distinct values of said second shared-secret signal are generated by varying only said first authentication factor, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 16

A method according to claim 13 that further comprises decrypting said second public signal using a decryption key derived at least in part from said first authentication factor.

Claim 17

A method according to claim 13 wherein said shared parameters comprise a first number and a second number, said first initial transformation includes a function equivalent to raising said first number to a first power represented by said first private signal, modulo said second number, said second initial transformation includes a function equivalent to raising said first number to a second power represented by said second private signal, modulo said second number, said first combining transformation includes a function equivalent to raising a number represented by said second public signal to a third power representing said first private signal, modulo said second number, and said second combining transformation includes a function equivalent to raising a number represented by said first public signal to a fourth power representing said second private signal, modulo said second number.

Claim 18

A method according to claim 15 wherein said third power also represents said first authentication factor and said fourth power also represents said first authentication factor.

Claim 19

A method according to claim 15 wherein said first combining transformation includes a hashing function and said second combining transformation includes a hashing function.

Claim 20

A method according to claim 13 wherein said first combining transformation is also of a second authentication factor shared by said first participant and said second participant, said second combining transformation is also of said second authentication factor, and said first and second combining transformations each have a property that distinct values of said shared-secret signal are generated by varying only said second authentication factor.

Claim 21

A method according to claim 18, wherein said shared parameters comprise a first number and a second number, said first initial transformation includes a function equivalent to raising said first number to a first power represented by said first private signal, modulo said second number, said second initial transformation includes a function equivalent to raising said first number to a second power represented by said second private signal, modulo said second number, said first combining transformation includes a function equivalent to raising a number represented by said second public signal to a third power representing said first private signal, modulo said second number, and said second combining transformation includes a function equivalent to raising a number represented by said first public signal to a fourth power representing said second private signal, modulo said second number.

Claim 22

A method according to claim 19 wherein said third power also represents said first authentication factor and said second authentication factor, and said fourth power also represents said first authentication factor and said second authentication factor.

Claim 23

A method according to claim 1, 7, 13, or 18 further comprising said first participant obtaining an established cryptographic key associated with said first participant by receiving and decrypting a message from another of said participants, said decrypting proceeding according to said shared secret.

Claim 24

A method according to claim 13 further comprising the steps of: said first participant receiving a third private signal, said second participant receiving a fourth private signal, said first participant generating a first transformed signal by obtaining a first transformation of said third private signal, said second participant generating a second transformed signal by obtaining a second transformation of said fourth private signal, first participant generating a third public signal by encrypting said first transformed signal according to said first shared-secret signal, said second participant generating a fourth public signal by encrypting said second transformed signal according to said second shared-secret signal, said first participant receiving said fourth public signal, said second participant receiving said third public signal, said first participant obtaining a first decrypted signal by decrypting said fourth public signal according to said first shared-secret signal, said second participant obtaining a second decrypted signal by decrypting said third public signal according to said second shared-secret signal, said first participant generating a third transformed signal by obtaining a third transformation of said third private signal with said first decrypted signal, said second participant generating a fourth transformed signal by obtaining a fourth transformation of said fourth private signal with said second decrypted signal, said first participant receiving a fifth private signal, said first participant generating one or more fifth public signals comprising a first encrypted element and a second encrypted element by encrypting said third transformed signal and said fifth private signal, respectively, according to said first shared-secret signal, said second participant receiving said one or more fifth public signals and obtaining one or more third decrypted signals comprising a first decrypted element and a second decrypted element, said first decrypted element and said second decrypted element obtained by decrypting said first encrypted element and said second encrypted element, respectively, according to said second shared-secret signal, said second participant comparing said first decrypted element with said fourth transformed signal and, if equal, generating a sixth public signal by encrypting a fifth transformed signal according to said second shared-secret signal, said fifth transformed signal obtained by transforming said second decrypted element, said first participant receiving said sixth public signal, said first participant obtaining a fourth decrypted signal by decrypting said sixth public signal according to said first shared-secret signal, said first participant obtaining a sixth transformed signal by transforming said fifth private signal, and said first participant comparing said fourth decrypted signal with said sixth transformed signal, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 25

A method according to claim 13 that further comprises decrypting said first public signal using a decryption key derived at least in part from said first authentication factor.

Claim 26

In a cryptographic protocol for a first participant and a second participant, a method for detecting a prior occurrence of an unauthorized party masquerading as said first participant, said method comprising the steps of: said first participant generating one or more signals in response to a first retained token in possession of said first participant; said second participant receiving said signals and authenticating said first participant by verifying said signals with a second retained token in possession of said second participant; said second participant generating a first notification signal and updating said second retained token in response to a successful verification of said signals, and restricting future communications with said first participant in response to an unsuccessful verification of said signals; and said first participant receiving said first notification signal and, in response thereto, updating said first retained token to permit successful verification in future communications with said second retained token as updated by said second participant.

Claim 27

In a cryptographic protocol for a first participant and a second participant, a method for detecting a prior occurrence of an unauthorized party masquerading as said first participant, said method comprising the steps of: said first participant generating one or more signals in response to a first retained token in possession of said first participant; said second participant receiving said signals and authenticating said first participant by verifying said signals with a second retained token in possession of said second participant; said second participant generating a first notification signal and updating said second retained token in response to a successful verification of said signals, and restricting future communications with said first participant in response to an unsuccessful verification of said signals; and said first participant receiving said first notification signal and, in response thereto, updating said first retained token to permit successful verification in future communications with said second retained token as updated by said second participant.

Claim 28

In a cryptographic protocol for a first participant and a second participant, a method for said first participant to obtain a key, said first participant and said second participant sharing an authentication factor, said method comprising the steps of: said first participant generating one or more signals in response to said authentication factor; said second participant receiving said signals and, in response thereto, authenticating said first participant using said authentication factor; said second participant generating a message in response to a value associated with said first participant; said first participant receiving said message and deriving said key in response thereto; and said first participant using said key to encrypt or decrypt information stored on a computer for use on said computer.

Claim 29

In a cryptographic protocol for a first participant and a second participant, a method for said first participant to obtain a key, said first participant and said second participant sharing an authentication factor, said method comprising the steps of: said first participant generating one or more signals in response to said authentication factor; said second participant receiving said signals and, in response thereto, authenticating said first participant using said authentication factor; said second participant generating a message in response to a value associated with said first participant; said first participant receiving said message and deriving said key in response thereto; and said first participant using said key to encrypt or decrypt information stored on a computer for use on said computer.

Claim 30

In a cryptographic protocol, an authentication method comprising the steps of: receiving a first private signal, generating a first transformed signal by obtaining a first transformation of said first private signal, generating a first public signal by encrypting said first transformed signal according to a key, receiving a second public signal, obtaining a first decrypted signal by decrypting said second public signal according to said key, generating a second transformed signal by obtaining a second transformation of said first private signal with said first decrypted signal, receiving a second private signal, generating one or more third public signals by encrypting said second transformed signal and said second private signal according to said key, obtaining a third transformed signal by transforming said second private signal according to said key, receiving a fourth public signal, obtaining a second decrypted signal by decrypting said fourth public signal according to said key, and comparing said third transformed signal with said second decrypted signal and generating an authentication signal in response thereto, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 31

In a cryptographic protocol, an authentication method comprising the steps of: receiving a first private signal, generating a first transformed signal by obtaining a first transformation of said first private signal, generating a first public signal by encrypting said first transformed signal according to a key, receiving a second public signal, obtaining a first decrypted signal by decrypting said second public signal according to said key, generating a second transformed signal by obtaining a second transformation of said first private signal with said first decrypted signal, receiving a second private signal, generating one or more third public signals by encrypting said second transformed signal and said second private signal according to said key, obtaining a third transformed signal by transforming said second private signal according to said key, receiving a fourth public signal, obtaining a second decrypted signal by decrypting said fourth public signal according to said key, and comparing said third transformed signal with said second decrypted signal and generating an authentication signal in response thereto, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 32

In a cryptographic protocol, an authentication method comprising the steps of: receiving a first private signal, generating a first transformed signal by obtaining a first transformation of said first private signal, generating a first public signal by encrypting said first transformed signal according to a key, receiving a second public signal, obtaining a first decrypted signal by decrypting said second public signal according to said key, generating a second transformed signal by obtaining a second transformation of said first private signal with said first decrypted signal, receiving a third public signal, obtaining a second decrypted signal by decrypting said third public signal according to said key, comparing said second decrypted signal with said second transformed signal and generating an authentication signal in response thereto, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 33

In a cryptographic protocol, an authentication method comprising the steps of: receiving a first private signal, generating a first transformed signal by obtaining a first transformation of said first private signal, generating a first public signal by encrypting said first transformed signal according to a key, receiving a second public signal, obtaining a first decrypted signal by decrypting said second public signal according to said key, generating a second transformed signal by obtaining a second transformation of said first private signal with said first decrypted signal, receiving a third public signal, obtaining a second decrypted signal by decrypting said third public signal according to said key, comparing said second decrypted signal with said second transformed signal and generating an authentication signal in response thereto, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 34

In a cryptographic protocol, a method for a first participant and a second participant to authenticate one another, said method comprising the steps of: said first participant receiving a first private signal, said second participant receiving a second private signal, said first participant generating a first transformed signal by obtaining a first initial transformation of said first private signal, said second participant generating a second transformed signal by obtaining a second initial transformation of said second private signal, said first participant generating a first public signal by encrypting said first transformed signal according to a first key, said second participant generating a second public signal by encrypting said second transformed signal according to a second key, said first participant receiving said second public signal, said second participant receiving said first public signal, said first participant obtaining a first decrypted signal by decrypting said second public signal according to said first key, said second participant obtaining a second decrypted signal by decrypting said first public signal according to said second key, said first participant generating a third transformed signal by obtaining a first combining transformation of said first private signal with said first decrypted signal, said second participant generating a fourth transformed signal by obtaining a second combining transformation of said second private signal with said second decrypted signal, said first participant receiving a third private signal, said first participant generating one or more third public signals comprising a first encrypted element and a second encrypted element by encrypting said third transformed signal and said third private signal, respectively, according to said first key, said second participant receiving said one or more third public signals and obtaining one or more third decrypted signals comprising a first decrypted element and a second decrypted element, said first decrypted element and said second decrypted element obtained by decrypting said first encrypted element and said second encrypted element, respectively, according to said second key, said second participant comparing said first decrypted element with said fourth transformed signal and, if equal, generating a fourth public signal by encrypting a fifth transformed signal according to said second key, said fifth transformed signal obtained by transforming said second decrypted element, said first participant receiving said fourth public signal, said first participant obtaining a fourth decrypted signal by decrypting said fourth public signal according to said first key, said first participant obtaining a sixth transformed signal by transforming said third private signal, and said first participant comparing said fourth decrypted signal with said sixth transformed signal, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.

Claim 35

In a cryptographic protocol, a method for a first participant and a second participant to authenticate one another, said method comprising the steps of: said first participant receiving a first private signal, said second participant receiving a second private signal, said first participant generating a first transformed signal by obtaining a first initial transformation of said first private signal, said second participant generating a second transformed signal by obtaining a second initial transformation of said second private signal, said first participant generating a first public signal by encrypting said first transformed signal according to a first key, said second participant generating a second public signal by encrypting said second transformed signal according to a second key, said first participant receiving said second public signal, said second participant receiving said first public signal, said first participant obtaining a first decrypted signal by decrypting said second public signal according to said first key, said second participant obtaining a second decrypted signal by decrypting said first public signal according to said second key, said first participant generating a third transformed signal by obtaining a first combining transformation of said first private signal with said first decrypted signal, said second participant generating a fourth transformed signal by obtaining a second combining transformation of said second private signal with said second decrypted signal, said first participant receiving a third private signal, said first participant generating one or more third public signals comprising a first encrypted element and a second encrypted element by encrypting said third transformed signal and said third private signal, respectively, according to said first key, said second participant receiving said one or more third public signals and obtaining one or more third decrypted signals comprising a first decrypted element and a second decrypted element, said first decrypted element and said second decrypted element obtained by decrypting said first encrypted element and said second encrypted element, respectively, according to said second key, said second participant comparing said first decrypted element with said fourth transformed signal and, if equal, generating a fourth public signal by encrypting a fifth transformed signal according to said second key, said fifth transformed signal obtained by transforming said second decrypted element, said first participant receiving said fourth public signal, said first participant obtaining a fourth decrypted signal by decrypting said fourth public signal according to said first key, said first participant obtaining a sixth transformed signal by transforming said third private signal, and said first participant comparing said fourth decrypted signal with said sixth transformed signal, wherein the steps of said method are performed in any order such that all signals required by a respective step are available when said respective step is performed.