(Source: RFC 2828)

2. That key of an entity's asymmetric key pair which should only be used by that entity.

(Source: ISO/IEC 11770-1:1996)

3. The secret part of an asymmetric key pair that is typically used to digitally sign or decrypt data.

(Source: NIST SP 800-63)

4. A cryptographic key, used with a public key cryptographic algorithm, that is uniquely associated with an entity and is not made public. In an asymmetric (public) cryptosystem, the private key is associated with a public key. Depending on the algorithm, the private key may be used to:

1) compute the corresponding public key,

2) compute a digital signature that may be verified by the corresponding public key,

3) decrypt data that was encrypted by the corresponding public key, or

4) compute a piece of common shared data, together with other information.

(Source: NIST SP 800-57)