represents the public part of a key pair for a public-key cryptographic system.


creates a matching public key for the given private key.


  • PublicKey objects can be used with functions such as Encrypt, Decrypt and VerifyDigitalSignature.
  • Data encrypted with a particular PublicKey object must be decrypted with a corresponding PrivateKey object.
  • Corresponding pairs of PrivateKey and PublicKey objects can be generated with GenerateAsymmetricKeyPair.
  • PublicKey[]["prop"] can be used to extract properties of the public key.
  • Basic properties for PublicKey include:
  • "Type"type of cryptography
    "PublicByteArray"public key as a byte array
    "PublicHexString"public key as a hex string
    "PublicKeySize"size of public key in bits
  • Possible types of cryptography include "RSA" and "EllipticCurve".
  • Additional properties for "RSA" include:
  • "PublicExponent"public exponent
    "PublicModulus"public modulus
    "Padding"padding mode
  • Additional properties for "EllipticCurve" include:
  • "CurveName"name of elliptic curve (e.g. "sec256k1")
    "PublicCurvePoint"public curve point
    "Compressed"whether the public key is in compressed form
  • Possible settings for "CurveName" are listed in $CryptographicEllipticCurveNames.
  • PublicKey[]["Parameters"] gives all the information contained in the object, as an association.
  • PublicKey[]["Properties"] gives a list of available properties.


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Basic Examples  (2)

Generate public and private keys:

Encrypt using the public key:

Decrypt using the private key:

Generate an elliptic curvebased public key:

Check the elliptic curve used to create the key pair:

Check if the public key was compressed:

Discover all available properties of the public key:

Scope  (2)

You can use PublicKey as a constructor for a valid public key object.

Generate public and private keys:

Obtain the public key:

Construct a valid public key object from the pre-generated values:

Test whether it matches the original key:

You can construct a public key from a private key.

Generate a private key:

Use PublicKey to construct a corresponding public key object:

Properties & Relations  (2)

PublicKey objects created by GenerateAsymmetricKeyPair contain a complete set of properties for the key:

It is not necessary to provide all properties to reconstruct a valid public key object. For an elliptic curve, it is sufficient to specify only the public curve point:

Verify that the keys are identical:

Alternatively, use a hex string representation of the public curve point:

Verify that all keys are identical:

Use a ByteArray representation:

Verify that all keys are identical:

To reconstruct a PublicKey object for RSA, provide the public modulus in integer, hex or ByteArray representations:

Recreate the same object as initially obtained from GenerateAsymmetricKeyPair:

Verify that both keys are identical:

Wolfram Research (2015), PublicKey, Wolfram Language function, (updated 2020).


Wolfram Research (2015), PublicKey, Wolfram Language function, (updated 2020).


Wolfram Language. 2015. "PublicKey." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020.


Wolfram Language. (2015). PublicKey. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2023_publickey, author="Wolfram Research", title="{PublicKey}", year="2020", howpublished="\url{}", note=[Accessed: 08-December-2023 ]}


@online{reference.wolfram_2023_publickey, organization={Wolfram Research}, title={PublicKey}, year={2020}, url={}, note=[Accessed: 08-December-2023 ]}