It decodes ASN.1, and only requires OpenSSL if the key has a passphrase. Here’s a bash script that will decode a private key and output variable definitions and functions for bc, so that you can play around with it without having to do the copy-paste work yourself. This is an annotated hex dump of parts of a base64-decoded private key 30 82 01 ca - Sequence, 0x01CA bytesĠ0 d8 f7 ae 5d c5 87 39 8e 96. This gives you an ASN.1 encoded sequence of integers. If you want to decode the private key by hand, base64-decode the middle bit.
Finally, 00 00 00 61 followed by 0圆1 = 97 bytes of our modulus n. Then 00 00 00 01, followed by one byte of 0x23 (35, our e). Mine is 00 00 00 07, followed by 7 bytes “ssh-rsa”. You will then have key type, e and n, respectively. Simply base64-decode the middle string, and then read 4 bytes of length, followed by that many bytes of data. Ssh-rsa AAAAB3NzaC1yc2EAAAABIwAAAGEA2PeuXcWHOY6WhUJdd6xU+zVZr758gFfsEJnm3iWYyHfoobORCaeMMlyb472diGg/HoF/5r3LPQd/Nt8Dk6mpADIL+9FNUOAeEZdjocU/+XJZDwNHMKG2y4/p6r1FgefH is a very simple file format, but I don’t know of any tools that will decode it. Yay, we’ve successfully encrypted and decrypted a value using real life RSA parameters! #Define some variables (this time unabbreviated) # If you don't want to do this yourself, see end for a ~/.ssh $ If we have one of these hex strings on one line, without colons, and in uppercase, then bc can work on them and optionally convert to decimal. Otherwise, finding e given (d,n) is just as hard as finding d given (e,n), except e is conventionally chosen to be small and easy to guess for efficiency purposes. This is how it can generate public keys given the private ones. It’s interesting to note that even though the private key from RSA’s point of view is (d,n), the OpenSSH private key file includes e, p, q and the rest as well. The latter three are for optimization and the primes are for verification. Only the first three are strictly required to perform encryption and decryption. Here, modulus is n, publicExponent is e, privateExponent is d, prime1 is p, prime2 is q, exponent1 is d P from the Wikipedia article, exponent2 is d Q and coefficient is q Inv. How can we get our nice RSA parameters from this mess? TsuP6eq9RYHnxwIBIwJhAKdf+4oqqiUWOZn//vXrV3/19LrGJYeU JDJcm+O9nYhoP圆Bf+a9yz0HfzbfA5OpqQA圜/vRTVDgHhGXY6HFP/lyWQ8DRzCh MIIBygIBAAJhANj3rl3FhzmOloVCXXesVPs1Wa++fIBX7BCZ5t4lmMh36KGzkQmn
Here’s a bit from the private key id_rsa (no passphrase): This is very simple modular arithmetic, but when you generate a key pair with ssh-keygen, you instead get a set of opaque and scary looking files, id_rsa and id_rsa.pub.
#Openssh rsa mod#
To encrypt a number/message m, let the ciphertext c ≡ m^e mod n. The public key is then (e, n), while your private key is (d, n). Pick a number e coprime to φ, and let d ≡ e^-1 mod φ. I’ll use mostly the same symbols as Wikipedia: you generate two large primes, p and q. This post is not meant as an intro to RSA, but here’s a quick reminder. RSA is based on primes, and the difficulty of factoring large numbers. RSA is a very simple and quite brilliant algorithm, and this article will show what a SSH RSA key pair contains, and how you can use those values to play around with and encrypt values using nothing but a calculator. Chances are good that it’s based on RSA, the default choice in ssh-keygen. You probably have your own closely guarded ssh key pair.
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