I have the binary blobs for the components of a private key including modulus, publicExponent, privateExponent, prime1, prime2, exponent1, exponent2 and coefficient, what is the easiest way to generate a PEM/DER file from them? Is there a easy to use Python API that can be used or do I have to use C? Likewise if I have the components of a public key as binary blobs, including modulus and exponent, what's the easiest method there? Another question in this process: are the python APIs to test the property of the components, like weather the prime is a prime or weather the public and private components match?
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2 Answers
This can be achieved pretty easily with pycryptodome
Here are some sample values that were generated as a test
In [1]: from Crypto.PublicKey import RSA
In [2]: k = RSA.generate(1024)
In [3]: k
Out[3]: RsaKey(n=143130316039186356537289646457342957029055874083006179752018267628632429252822850383503747585724799519287456198657693682737294996945803556004091588888862734842876499600553435771912216934557891984348187747076769031035627391163918136413321448399135545921574551907381303095829931709226724033859864712257647103161, e=65537, d=17576525985067546537255398853909945804199790570517932383908982984806045296957723116505762555043916971042700268349132837308234281938749515826493875328098129245342983246848248582675980856522190387684789361785762364603511517782326537037037597067485821717857467592522600776711703683226858254562757226108937574081, p=10753783485237760558106558145489319968952855295476064861811826896190777901077938075707538967825984471343848916518461647244807051451613883176849073895898863, q=13309763604192726567108341676142815607992017489636400387824449743334965995406164568181340806599419803897222088829477205186369416995900434016351317269868247, u=11832702411409256011378550201142107940763428930323983942371881106145078470279115081362293142803804740351361635022958520667847860090448209808590495750654916)
In [4]: n = k.n
In [5]: e = k.e
In [6]: d = k.d
In [7]: p = k.p
In [8]: q = k.q
Once you have a (n,e) tuple you can export a public key. Once you have a (n,e,d) tuple you can generate a private key too (p,q are optional).
In [9]: print(RSA.construct((n,e)).public_key().export_key())
b'-----BEGIN PUBLIC KEY-----\nMIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQDL0weqmsQCfkL6OLdalWlVFGgN\nw2FLrXujCsTo9SwEkSyab5UsUvX0fTnl/uH9d18g9136zsQPpsv1Ylh4ElW7/BCX\n8TBa4exSdKUTS7ishHYfNJ2kXKZMlws9aLCkS4weagvF83c9fMjoQ74E69BkqQDE\ndDlIBdcLA3fNSSdMuQIDAQAB\n-----END PUBLIC KEY-----'
In [10]: print(RSA.construct((n,e,d,p,q)).public_key().export_key())
b'-----BEGIN PUBLIC KEY-----\nMIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQDL0weqmsQCfkL6OLdalWlVFGgN\nw2FLrXujCsTo9SwEkSyab5UsUvX0fTnl/uH9d18g9136zsQPpsv1Ylh4ElW7/BCX\n8TBa4exSdKUTS7ishHYfNJ2kXKZMlws9aLCkS4weagvF83c9fMjoQ74E69BkqQDE\ndDlIBdcLA3fNSSdMuQIDAQAB\n-----END PUBLIC KEY-----'
In [12]: print(RSA.construct((n,e,d,p,q)).export_key())
b'-----BEGIN RSA PRIVATE KEY-----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\noH4Hp2POjAqF29CXlZpjCyhWOmPn7LMZgrTDSnDOS3I=\n-----END RSA PRIVATE KEY-----'
pycryptodome
You could give pycryptodome a try. Beware, it is meant as a replacement of pycrypto. If you have the need to run pycrypto in parallel, you can use the separate, stand-alone package pycryptodomex.
It implements all crypto primitives from scratch (instead of relying on external libraries) and it offers a Key Construct Method that allows to construct a key from the components. If switched on, it can also perform a consistency check on the entered key components.
