Obtain Exponent and Modulus from RSA key in PEM Format

August 09, 2020

If you understand the math behind RSA algorithm, you should know that RSA consists of several components: $e$ , $d$ , and $n$ such that

m^{ed} \equiv m\, (mod\, n)

Here’s how you can obtain those values from RSA private and public key in PEM format with python.

from Crypto.PublicKey import RSA
private_key_pem='''-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
'''

public_key_pem='''-----BEGIN PUBLIC KEY-----
MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEA3fJtY+4/TSuZ07iVqGq6
Xa9QMFeor5JZwy7IfyyNOHeVFRSSdYBo8WDTHTe4flJsRspHa1pI72v1yoJQJ3M7
DFAtAxiHzqhAyYZ4wjdxTN8YBVl5qqbRr7OKTvM8s3Z+2O7aG+ayIyeFKf0DX2aj
FkOD3/ql6ne1pQUPCSjLNRSRYdCee03eKVw6ORSBUe262gEDf/UWHisg3o2JaVLc
mR3ps4ESRcdx0AZ9hYWONGmHn7FsNiSp1ry8SVTOnfdcuvjVVfKLVaOui7nntU5O
xQijz+/kk4vy58qDedyHxB24wMt6S+7a5P++ZO20K4/mBIFmdyGIuvOYJY0Gs7X/
EQIDAQAB
-----END PUBLIC KEY-----
'''


private_key = RSA.importKey(private_key_pem)
print("private key components:")
print("modulus:", private_key.n)
print("decryption key:", private_key.d, "\n")

public_key = RSA.importKey(public_key_pem)
print("public key components:")
print("modulus:", public_key.n)
print("encryption key:", public_key.e)

The code produces the following output.

private key components:
modulus: 28018210757639036701806576653473108663108237654992710644382580670706356521104503590269747243444881816860960886628707561729506054845669087158286487779668877579111045682687132130967542003640620395709760439291791359332971311569833464916696923708100648936544179482515518284015359758063690936170429993787988992366530178656661760648006433502964162950734482834691341055821131012179885041912952708019133191444259147492689058801662179466923034701521378053315755439283332003332125730956606219922314282161592457216832544141605338942735432555226858379903566758713188147527196578404934586961422561713661928243117076396507324088081
decryption key: 26593295115250601019258987963328215378793426844243199611260418512300199902937036198317581786338181920686317820343502527882298467058608112937639084575835373314784373493536023423023711533858143508166836113427630036711295107571141810758475600688751281969708624754419569088284349884654375863917259370028961766347968136242492409216019897338881947171652949409664617568373420518516510028969311296632860124215508429507388883135792513113188476224349460853934378076812541476273510991540179616816870490909273466785702119283308474487346009112179993007498269623263500977729040200031842282261746661152366200714995020265888356975473

public key components:
modulus: 28018210757639036701806576653473108663108237654992710644382580670706356521104503590269747243444881816860960886628707561729506054845669087158286487779668877579111045682687132130967542003640620395709760439291791359332971311569833464916696923708100648936544179482515518284015359758063690936170429993787988992366530178656661760648006433502964162950734482834691341055821131012179885041912952708019133191444259147492689058801662179466923034701521378053315755439283332003332125730956606219922314282161592457216832544141605338942735432555226858379903566758713188147527196578404934586961422561713661928243117076396507324088081
encryption key: 65537

Source