WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

GenerateAsymmetricKeyPair
✖
GenerateAsymmetricKeyPair

✖

randomly generates a PrivateKey and corresponding PublicKey object for use with public-key cryptographic functions.

✖

randomly generates private and public keys of the specified type.

✖

randomly generates keys using the specified options.

Details and Options

  • GenerateAsymmetricKeyPair returns an association of the form <|"PrivateKey"…,"PublicKey" …|>.
  • GenerateAsymmetricKeyPair[] by default uses the "RSA" type, with a system-specific, high-entropy randomness source.
  • In GenerateAsymmetricKeyPair[type], the following types can be specified:
  • "RSA"RSA with default parameters
    "EllipticCurve"elliptic curve secp256k1
    "EdwardsCurve"twisted Edwards curve ed25519
    "Bitcoin","Ethereum"keys suitable for blockchains
    Method"curve" named elliptic curve
  • GenerateAsymmetricKeyPair has the following option:
  • MethodAutomaticdetails of key generation method
  • With the setting Method->assoc, the association assoc gives details of the key generation method to use.
  • The following element should be included in the association:
  • "Type""RSA"type of keys to produce
  • Possible settings for "Type" are "RSA" , "EllipticCurve" and "EdwardsCurve".
  • For "RSA", the following elements can be given in the association:
  • "KeySize"2048target size of key in bits
    "PublicExponent"65537public exponent
  • For "EllipticCurve", the following elements can be given in the association:
  • "CurveName""secp256k1"elliptic curve to use
    "Compressed"Falsewhether the public key is in compressed form
  • For "EdwardsCurve", the following elements can be given in the association:
  • "CurveName""ed25519"twisted Edwards curve to use
  • Possible settings for "CurveName" and Methodcurve are listed in $CryptographicEllipticCurveNames.
  • "Bitcoin" uses "CurveName""secp256k1" and "Compressed"True.
  • "Ethereum" uses "CurveName""secp256k1" and "Compressed"False.

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Generate corresponding public and private keys:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-1hx3su
Out[1]=1

Encrypt using the public key:

In[2]:=2
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-6z1w1u
Out[2]=2

Decrypt with the private key:

In[3]:=3
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-20xaef
Out[3]=3

Alternatively, encrypt with the private key:

In[4]:=4
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-id5ph0
Out[4]=4

Decrypt with the public key:

In[5]:=5
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-0wsah8
Out[5]=5

Generate an elliptic curve key pair using the default curve secp256k1:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-86tbxj
Out[1]=1

Generate a twisted Edwards elliptic curve key pair using the default curve ed25519:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-cqms5e
Out[1]=1

Scope  (6)Survey of the scope of standard use cases

Default Method  (1)

Generate a key pair without arguments, using RSA as the default method:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-jqwjaz
Out[1]=1

Named Methods  (4)

Generate an RSA key pair:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-mijyzi
Out[1]=1

Generate an elliptic curve key pair using the default curve secp256k1:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-wbkxee
Out[1]=1

Generate a twisted Edwards elliptic curve key pair using the default curve ed25519:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-3gvfs
Out[1]=1

Generate key pairs compatible with cryptocurrency networks:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-v5sn4t
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-il816
Out[2]=2

Particular Settings  (1)

Provide an association with particular settings in the Method option:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-k9vdc4
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-fh1vl0
Out[2]=2

Options  (6)Common values & functionality for each option

Method  (6)

Generate a key pair with a 4096-bit key:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-2dliy2
Out[1]=1

Generate a key pair with a public exponent of 17:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-cxmocd
Out[1]=1

Generate a Bitcoin key pair with a compressed public key:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-g3i65l
Out[1]=1

Generate an Ethereum key pair with an uncompressed public key:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-hucp38
Out[1]=1

Generate a twisted Edwards curve–based key specifying a particular curve name:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-6wu2a
Out[1]=1

Generate an elliptic curve–based key pair using a curve name as method:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-rhgrwp
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-incklb
Out[2]=2

Applications  (2)Sample problems that can be solved with this function

Generate a personal pair of elliptic curve–based keys to sign and verify a message using the Elliptic Curve Digital Signature Algorithm:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-d5sr1b
Out[1]=1

Generate a digital signature using your private key:

In[2]:=2
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-0xni17
In[3]:=3
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-h6f4d6
Out[3]=3

Verify a digital signature using your public key:

In[4]:=4
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-234bz
Out[4]=4

Write simple RSA-based signing and verification functions:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-isk1hv
In[2]:=2
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-65xzmd

Generate a pair of public and private RSA keys:

In[3]:=3
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-qbo127
Out[3]=3

Define an expression to sign:

In[4]:=4
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-7fxog
Out[4]=4

Generate a signature:

In[5]:=5
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-thz5mt
Out[5]=5

Verify that the signature is authentic:

In[6]:=6
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-d3elvz
Out[6]=6

Verifying with another expression will fail:

In[7]:=7
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-pk0bzd
Out[7]=7

Possible Issues  (2)Common pitfalls and unexpected behavior

Incompatible Private Keys  (1)

Encryption with elliptic curve–based keys is not currently supported:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-owi8hw
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-yojv82
Out[2]=2

Timing  (1)

Generating larger keys takes longer:

In[1]:=1
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-2o922l
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0e2y906xt0t1e4an2jtu-lm7y7w
Out[2]=2
Wolfram Research (2015), GenerateAsymmetricKeyPair, Wolfram Language function, https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html (updated 2020).
✖
Wolfram Research (2015), GenerateAsymmetricKeyPair, Wolfram Language function, https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html (updated 2020).

Text

Wolfram Research (2015), GenerateAsymmetricKeyPair, Wolfram Language function, https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html (updated 2020).

✖
Wolfram Research (2015), GenerateAsymmetricKeyPair, Wolfram Language function, https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html (updated 2020).

CMS

Wolfram Language. 2015. "GenerateAsymmetricKeyPair." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html.

✖
Wolfram Language. 2015. "GenerateAsymmetricKeyPair." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html.

APA

Wolfram Language. (2015). GenerateAsymmetricKeyPair. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html

✖
Wolfram Language. (2015). GenerateAsymmetricKeyPair. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html

BibTeX

@misc{reference.wolfram_2025_generateasymmetrickeypair, author="Wolfram Research", title="{GenerateAsymmetricKeyPair}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html}", note=[Accessed: 25-March-2025 ]}

✖
@misc{reference.wolfram_2025_generateasymmetrickeypair, author="Wolfram Research", title="{GenerateAsymmetricKeyPair}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html}", note=[Accessed: 25-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_generateasymmetrickeypair, organization={Wolfram Research}, title={GenerateAsymmetricKeyPair}, year={2020}, url={https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html}, note=[Accessed: 25-March-2025 ]}

✖
@online{reference.wolfram_2025_generateasymmetrickeypair, organization={Wolfram Research}, title={GenerateAsymmetricKeyPair}, year={2020}, url={https://reference.wolfram.com/language/ref/GenerateAsymmetricKeyPair.html}, note=[Accessed: 25-March-2025 ]}