The official management decision given by a senior agency official to authorize operation of an information system and to explicitly accept the risk to agency operations (including mission, functions, image, or reputation), agency assets, or individuals, based on the implementation of an agreed-upon set of security controls.
Sources:
NIST SP 800-18 Rev. 1 under Accreditation
NIST SP 800-60 Vol. 1 Rev. 1 under Accreditation from FIPS 200

  The right or a permission that is granted to a system entity to access a system resource.
Sources:
NIST SP 1800-10B under Authorization from NIST SP 800-82r3
NIST SP 1800-27C under Authorization from NIST SP 800-82r3

  Access privileges granted to a user, program, or process or the act of granting those privileges.
Sources:
CNSSI 4009-2015 under authorization
NIST SP 800-160 Vol. 2 Rev. 1 under authorization from CNSSI 4009-2015
NIST SP 800-53 Rev. 5 under authorization from CNSSI 4009-2015
NIST SP 800-53A Rev. 5 under authorization from CNSSI 4009-2015

  The official management decision given by a senior official to authorize operation of a system or the common controls inherited by designated organizations systems and to explicitly accept the risk to organizational operations (including mission, functions, image, and reputation), organizational assets, individuals, other organizations, and the Nation based on the implementation of an agreed-upon set of security and privacy controls. Also known as authorization to operate.
Sources:
NIST SP 800-12 Rev. 1 under Authorization

  The process of verifying that a requested action or service is approved for a specific entity.
Sources:
NIST SP 800-152 under Authorization
NIST SP 800-57 Part 2 Rev.1 under Authorization

  also known as authorize processing (OMB Circular A-130, Appendix III),and approval to operate. Accreditation (or authorization to process information) is granted by a management official and provides an important quality control. By accrediting a system or application, a manager accepts the associated risk. Accreditation (authorization) must be based on a review of controls. (See Certification.)
Sources:
NIST SP 800-16 under Accreditation

  See Accreditation.
Sources:
NIST SP 800-18 Rev. 1 under Authorize Processing

  Access privileges granted to an entity; conveys an “official” sanction to perform a cryptographic function or other sensitive activity.
Sources:
NIST SP 800-57 Part 2 Rev.1 under Authorization

  See authorization.
Sources:
CNSSI 4009-2015

  Access privileges that are granted to an entity that convey an “official” sanction to perform a security function or activity.
Sources:
NIST SP 800-57 Part 1 Rev. 5 under Authorization

  The official management decision of the Designated Authorizing Official to permit operation of an issuer after determining that the issuer’s reliability has satisfactorily been established through appropriate assessment processes.
Sources:
NIST SP 800-79-2 under Authorization

  The right or a permission that is granted to a system entity to access a system resource.
Sources:
NIST SP 800-82r3 under authorization from RFC 4949 - adapted

  The granting or denying of access rights to a user, program, or process.
Sources:
NISTIR 7316 under Authorization

  The process of initially establishing access privileges of an individual and subse­quently verifying the acceptability of a request for access.
Sources:
NISTIR 4734 under Authorization