Abstract: An implicit certificate is based on a ring learning with errors (“RLWE”) public keys that are, in some examples, resistant to quantum-based computing attacks. Various methods are described that request, generate, verify, and use the implicit certificates. In some examples, the system provides an implicit certificate that enables communication between two parties that are identified at the time of certificate generation. In another example, the system provides a certificate that may be used to communicate with a variety of different parties. The implicit certificate generation algorithm yields a public key purportedly bound to U. Confirmation that the public key is bound to U is obtained after use of the corresponding private key. Binding of an entity to its associated public key and accessibility to the private key, are verified as a result of successful key use.

Abstract: A first entity and a second entity establish a protected authenticated communication channel using an implicit certificate issued by a certificate authority. In some examples, the implicit certificate is generated based at least in part on the ring learning with errors (“RLWE”) problem. Using the implicit certificate, the first entity and the second entity exchange information that enables the entities to negotiate a shared secret. The shared secret may be used to establish a cryptographically protected communication channel. Successful use of the shared secret authenticates the identity of the first entity and the second entity.

Abstract: Two parties to a communication establish public and private keys through the use of implicit certificates. Each party establishes a new static key pair, and determines a difference between the new static key pair and the previously established keys. The differences are exchanged and used to determine new public static keys. Each party generates an ephemeral key pair from the static key pair, and a shared secret is derived from a combination of the ephemeral keys and the new static keys.

Abstract: A first entity and a second entity establish a protected authenticated communication channel using an implicit certificate issued by a certificate authority. In some examples, the implicit certificate is generated based at least in part on the ring learning with errors (“RLWE”) problem. Using the implicit certificate, the first entity and the second entity exchange information that enables the entities to negotiate a shared secret. The shared secret may be used to establish a cryptographically protected communication channel. Successful use of the shared secret authenticates the identity of the first entity and the second entity.

Abstract: An implicit certificate is based on a ring learning with errors (“RLWE”) public keys that are, in some examples, resistant to quantum-based computing attacks. Various methods are described that request, generate, verify, and use the implicit certificates. In some examples, the system provides an implicit certificate that enables communication between two parties that are identified at the time of certificate generation. In another example, the system provides a certificate that may be used to communicate with a variety of different parties. The implicit certificate generation algorithm yields a public key purportedly bound to U. Confirmation that the public key is bound to U is obtained after use of the corresponding private key. Binding of an entity to its associated public key and accessibility to the private key, are verified as a result of successful key use.

Abstract: Two parties to a communication establish public and private keys through the use of implicit certificates. Each party establishes a new static key pair, and determines a difference between the new static key pair and the previously established keys. The differences are exchanged and used to determine new public static keys. Each party generates an ephemeral key pair from the static key pair, and a shared secret is derived from a combination of the ephemeral keys and the new static keys.