Granted Patent B2

US 11,616,994 · App. 17/317,598 · Granted Mar 28, 2023

Inventors: Tat Keung Chan (San Diego, CA); Alexander Medvinsky (San Diego, CA); Eric J. Sprunk (Carlsbad, CA)

Assignee: ARRIS Enterprises LLC

H04N21/2347H04L9/088H04L9/3066H04L9/3242

Abstract

Claims (40)

1. A method of selecting a base point domain parameter G=(G x , G y ) of an elliptic curve (EC) for use in elliptic curve cryptography for encoding data, the method comprising:

(a) generating a candidate base point domain parameter G of an elliptic curve (EC), comprising:

generating a candidate base point domain parameter x coordinate(G x ) of an elliptic curve (EC), the base point domain parameter x coordinate (G x ) comprising:

a candidate base point domain parameter x coordinate (G x ) first portion; and

a candidate base point domain parameter x coordinate (G x ) second portion;

wherein at least a portion of the candidate base point domain parameter x-coordinate (G x ) first portion is random and the candidate base point domain parameter x-coordinate (G x ) second portion comprises information for authenticating the generated candidate base point domain parameter G;

generating at least one of two possible base point domain parameter y-coordinates (G y ) based on the candidate base point domain parameter x-coordinate(G x ) and an equation of the elliptic curve;

(b) determining if the generated candidate base point domain parameter G=(G x , G y ) is a valid domain parameter of the elliptic curve (EC);

(c) if the generated candidate base point domain parameter G is a not a valid base point domain parameter G;

selecting another base point domain parameter G first portion; and

repeating steps (a)-(c); and

(d) if the generated base point domain parameter G is a valid base point domain parameter G, selecting the generated candidate base point domain parameter G and communicating the generated base point domain parameter G to another entity for use as the generated base point domain parameter G in at least one EC based cryptographic operation

(e) using the base point domain parameter G of the EC to encrypt and digitally sign the data; where

(f) steps (a)-(d) are performed to select an updated base point domain parameter G according to an update condition comprising an expiration of time and a command from a third entity.

2. The method of claim 1 , wherein determining if the generated candidate base point domain parameter G is a valid domain parameter of the elliptic curve (EC) comprises:

computing a product of a cofactor (h) of the elliptic curve (EC) and the generated candidate base point domain parameter G;

computing a product of an order (n) of the generated candidate base point domain parameter G, the cofactor (h) of the elliptic curve (EC) and the generated candidate base point domain parameter G; and

determining that the generated candidate base point domain parameter G is a valid base point domain parameter G only if the product of a cofactor (h) of the elliptic curve (EC) and the generated base point domain parameter G is not an additive identity of the elliptic curve (EC) and if the product of the order (n) of the generated base point domain parameter G, the cofactor (h) of the elliptic curve and the generated base point domain parameter G is the additive identity of the elliptic curve (EC), otherwise determine that the generated candidate base point parameter G is not a valid domain parameter.

3. The method of claim 2 , wherein:

steps (a)-(d) are performed by first entity and the another entity is a second entity, and the method further comprises:

communicating the generated base point domain parameter G to another entity for use as the generated base point domain parameter G in at least one EC based cryptographic operation comprises:

transmitting the generated base point domain parameter G from the first entity to the second entity; and

validating, in the second entity, the generated base point domain parameter G using the base point domain parameter G second portion.

4. The method of claim 3 , wherein:

the candidate base point domain parameter x coordinate (G x ) first portion comprises at least one of an identifier of domain parameters of the elliptic curve and session parameters; and

the second portion comprises a message authentication code (MAC).

5. The method of claim 4 , wherein the domain parameters identifier is a group identifier for a communication group sharing the domain parameters.

6. The method of claim 4 , wherein the session parameters include a validity period of the base point domain parameter G.

7. The method of claim 4 , wherein the candidate base point domain parameter x-coordinate (G x ) second portion comprises the message authentication code (MAC) and wherein:

generating the base point domain parameter G of an elliptic curve (EC) comprises:

generating, in the first entity, a first entity version of a message authentication code (MAC) key at least in part from a secret (S) shared between the first entity and the second entity;

generating, in the first entity, the candidate base point domain parameter x-coordinate (G x ) first portion; and

generating, in the first entity, a first entity version of a message authentication code (MAC) at least in part from the first entity version of message authentication code (MAC) key and the candidate base point domain parameter x-coordinate (G x ) first portion.

8. The method of claim 7 , wherein, validating, in the second entity, the generated base point domain parameter (G) using the base point domain parameter (G) second portion comprises:

generating, in the second entity, a second entity version of the message authentication code (MAC) key from the secret (S);

generating, in the second entity, a second entity version of the message authentication code (MAC) from the second entity version of the message authentication code (MAC) key and the candidate base point domain parameter x-coordinate (G x ) first portion;

validating, in the second entity, the generated base point domain parameter x-coordinate (G x ) using the second entity version of the message authentication code (MAC) and the first entity version of the message authentication code (MAC);

generating a second entity version of the base point domain parameter y-coordinate (G y ) based on the generated base point domain parameter x-coordinate (G x ) and the equation of the elliptic curve; and

validating, in the second entity, the generated second entity version of the base point domain parameter y-coordinate (G y ) based on the received first entity version of the generated base point domain parameter y-coordinate;

wherein the generated basepoint domain parameter G is used in the at least one EC based cryptographic operation only if the generated base point domain parameter x-coordinate (G x ) and the generated base point domain parameter y-coordinate (G y ) is valid.

Assignments (8)

Continuity (2)