Cryptographic system using chaotic dynamics
AssigneeApple Inc.
InventorRichard E. Crandall
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Abstract
The invention is a cryptographic system using chaotic dynamics. A chaotic system is used to generate a public key and an adjustable back door from a private key. The public key is distributed and can be used in a public key encryption system. The invention can also be used for authentication purposes. The adjustable back door of the invention can be used in conjunction with the public key to derive the private key. The degree of difficulty involved in deriving the private key is dependent on the adjustable back door. That is the value of the back door can be adjusted to vary the difficulty involved in deriving the private key.
Claims21
A method comprising:
- generating a private key;
- deriving a set of initial conditions using the private key;
- applying the set of initial conditions as input to a chaotic system,
- the chaotic system generating a set of final conditions from the set of initial conditions, wherein the chaotic system includes an N-body system;
- and
- generating on one or more computers a public key from the set of final conditions.
A computer-implemented method, comprising:
- receiving a public key and a back door, the back door including interim conditions in an N-body chaotic system which has initial conditions, the public key being generated from the N-body chaotic system based on the initial conditions and the interim conditions;
- performing backward iterations on the public key, the backward iteration including applying one or more equations in a motion model to bodies in the N-body chaotic system;
- and
- generating a private key based on the public key and the backward iterations.
A computer program stored on a storage device, operable to cause one or more computers to perform operations comprising:
- generating a private key;
- deriving a set of initial conditions using the private key;
- applying the set of initial conditions as input to a chaotic system, the chaotic system generating a set of final conditions from the set of initial conditions, wherein the chaotic system includes an N-body system;
- and
- generating a public key from the set of final conditions.
A computer program stored on a storage device, operable to cause one or more computers to perform operations comprising:
- receiving a public key and a back door, the back door including interim conditions in an N-body chaotic system which has initial conditions, the public key being generated from the N-body chaotic system based on the initial conditions and the interim conditions;
- performing backward iterations on the public key, the backward iteration including applying one or more equations in a motion model to bodies in the N-body chaotic system;
- and
- generating a private key based on the public key and the backward iterations.
A system comprising:
- one or more computers configured to perform operations comprising:
- generating a private key;
- deriving a set of initial conditions using the private key;
- applying the set of initial conditions as input to a chaotic system, the chaotic system generating a set of final conditions from the set of initial conditions, wherein the chaotic system includes an N-body system;
- and
- generating a public key from the set of final conditions.
A system comprising:
- one or more computers configured to perform operations comprising:
- receiving a public key and a back door, the back door including interim conditions in an N-body chaotic system which has initial conditions, the public key being generated from the N-body chaotic system based on the initial conditions and the interim conditions;
- performing backward iterations on the public key, the backward iteration including applying one or more equations in a motion model to bodies in the N-body chaotic system;
- and
- generating a private key based on the public key and the backward iterations.
Dependencies are inferred from the claim text.