Cryptosystems with elliptic curves chosen by users
AssigneeCitibank, N.A.
InventorArjen K. Lenstra
Life of this patent
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Abstract
Participants in a cryptosystem select their own elliptic curve and finite field, rather than using a centrally chosen elliptic curve. The curve is chosen from a predetermined set of elliptic curves expressed as Weierstraβ model equations. The public key is based on a participant's unique ID, which must be exchanged during communication setup for non-cryptographic reasons, and a randomly chosen bitstring having a length based on security considerations. The public key can be readily constructed from parameters and mapping functions which are known system-wide and from a small amount of participant dependent data.
Claims17
A method for establishing a cryptographic system among participants, comprising:
- selecting a curve E from a predetermined set of elliptic curves;
- selecting a finite field;
- selecting a secret key;
- and
- obtaining a public key,
- wherein the selecting of the curve E, the selecting of the finite field, the selecting of the secret key, and the obtaining of the public key are performed locally by each of the participants, and
- wherein the predetermined set of elliptic curves are expressed as Weierstraβ model equations.
A method of reconstructing a public key for a participant in a cryptographic system, comprising:
- forming intermediate integers a and b based on a unique ID for the participant;
- obtaining a prime number p as a function of the intermediate integers a and b;
- selecting a curve E from a predetermined set of elliptic curves;
- picking a point Q on the curve E based on the unique ID for the participant;
- and
- constructing the public key from the prime number p, the curve E, and the point Q.
Dependencies are inferred from the claim text.