Generate Public Key From Ecdsa Private Key
- Generate Public Key From Ecdsa Private Key West
- Generate Rsa Public Private Key
- Generate Public Key From Ecdsa Private Key Software
- Create Public Key From Private
- Ssh Keygen Generate Public Key From Private
In the previous article, we looked at different methods to generate a private key. Whatever method you choose, you’ll end up with 32 bytes of data. Here’s the one that we got at the end of that article:
Creating a new key pair for authentication. To create a new key pair, select the type of key to generate from the bottom of the screen (using SSH-2 RSA with 2048 bit key size is good for most people; another good well-known alternative is ECDSA). Then click Generate, and start moving the mouse within the Window. Putty uses mouse movements to collect randomness. Generate an ECDSA SSH keypair with a 521 bit private key. Ssh-keygen -t ecdsa -b 521 -C 'ECDSA 521 bit Keys' Generate an ed25519 SSH keypair- this is a new algorithm added in OpenSSH. Ssh-keygen -t ed25519 Extracting the public key from an RSA keypair. Openssl rsa -pubout -in privatekey.pem.
If this is the case, then what is the purpose of ever generating an ECC public key? For a project I am working on, it is necessary to generate a public key to be placed in a certificate signing request to connect with AWS. Also, there is openssl functionality for creating ECC public keys: openssl ec -in eccprivate.pem -pubout -out eccpublic.pem. To install the public key, Log into the server, edit the authorizedkeys file with your favorite editor, and cut-and-paste the public key output by the above command to the authorizedkeys file. Save the file. Configure PuTTY to use your private key file (here keyfile.ppk). Then test if login works. See configuring public key authentication for.
ECDSA with secp256k1 in C# - Generate Keys, Sign, Verify - ECDSA-secp256k1-example.cs. Keys can be generated from the ecparam command, either through a pre-existing parameters file or directly by selecting the name of the curve. To generate a private/public key pair from a pre-eixsting parameters file use the following: openssl ecparam -in secp256k1.pem -genkey -noout -out secp256k1-key.pem.
60cf347dbc59d31c1358c8e5cf5e45b822ab85b79cb32a9f3d98184779a9efc2
Mar 03, 2020 The service uses the device public key (uploaded before the JWT is sent) to verify the device's identity. Cloud IoT Core supports the RSA and Elliptic Curve algorithms. For details on key formats, see Public key format. Generating an RSA key. You can generate a 2048-bit RSA key pair with the following commands.
We’ll use this private key throughout the article to derive both a public key and the address for the Bitcoin wallet.
What we want to do is to apply a series of conversions to the private key to get a public key and then a wallet address. Most of these conversions are called hash functions. These hash functions are one-way conversions that can’t be reversed. We won’t go to the mechanics of the functions themselves — there are plenty of great articles that cover that. Instead, we will look at how using these functions in the correct order can lead you to the Bitcoin wallet address that you can use.
Elliptic Curve Cryptography
The first thing we need to do is to apply the ECDSA or Elliptic Curve Digital Signature Algorithm to our private key. An elliptic curve is a curve defined by the equation y² = x³ + ax + b with a chosen a and b. There is a whole family of such curves that are widely known and used. Bitcoin uses the secp256k1 curve. If you want to learn more about Elliptic Curve Cryptography, I’ll refer you to this article.
By applying the ECDSA to the private key, we get a 64-byte integer. This consists of two 32-byte integers that represent the X and Y of the point on the elliptic curve, concatenated together.
For our example, we got: 1e7bcc70c72770dbb72fea022e8a6d07f814d2ebe4de9ae3f7af75bf706902a7b73ff919898c836396a6b0c96812c3213b99372050853bd1678da0ead14487d7.
In Python, it would look like this:
Note: as you can see from the code, before I used a method from the ecdsa module, I decoded the private key using codecs. This is relevant more to the Python and less to the algorithm itself, but I will explain what are we doing here to remove possible confusion.
In Python, there are at least two classes that can keep the private and public keys: “str” and “bytes”. The first is a string and the second is a byte array. Cryptographic methods in Python work with a “bytes” class, taking it as input and returning it as the result.
Now, there’s a little catch: a string, say, 4f3c does not equal the byte array 4f3c, it equals the byte array with two elements, O<. And that’s what codecs.decode method does: it converts a string into a byte array. That will be the same for all cryptographic manipulations that we’ll do in this article.
Public key
Once we’re done with the ECDSA, all we need to do is to add the bytes 0x04 at the start of our public key. The result is a Bitcoin full public key, which is equal to: 041e7bcc70c72770dbb72fea022e8a6d07f814d2ebe4de9ae3f7af75bf706902a7b73ff919898c836396a6b0c96812c3213b99372050853bd1678da0ead14487d7 for us.
Compressed public key
Generate Public Key From Ecdsa Private Key West
But we can do better. As you might remember, the public key is some point (X, Y) on the curve. We know the curve, and for each X there are only two Ys that define the point which lies on that curve. So why keep Y? Instead, let’s keep X and the sign of Y. Later, we can derive Y from that if needed.
The specifics are as follows: we take X from the ECDSA public key. Now, we add the 0x02 if the last byte of Y is even, and the byte 0x03 if the last byte is odd.
In our case, the last byte is odd, so we add 0x03 to get the compressed public key: 031e7bcc70c72770dbb72fea022e8a6d07f814d2ebe4de9ae3f7af75bf706902a7. This key contains the same information, but it’s almost twice as short as the uncompressed key. Cool!
Previously, wallet software used long, full versions of public keys, but now most of it has switched to compressed keys.
Encrypting the public key
From now on, we need to make a wallet address. Whatever method of getting the public key you choose, it goes through the same procedure. Obviously, the addresses will differ. In this article, we will go with the compressed version.
What we need to do here is to apply SHA-256 to the public key, and then apply RIPEMD-160 to the result. The order is important.
SHA-256 and RIPEMD-160 are two hash functions, and again, we won’t go into the details of how they work. What matters is that now we have 160-bit integer, which will be used for further modifications. Let’s call that an encrypted public key. For our example, the encrypted public key is 453233600a96384bb8d73d400984117ac84d7e8b.
Here’s how we encrypt the public key in Python:
Adding the network byte
Generate Rsa Public Private Key
The Bitcoin has two networks, main and test. The main network is the network that all people use to transfer the coins. The test network was created — you guessed it — to test new features and software.
We want to generate an address to use it on the mainnet, so we need to add 0x00 bytes to the encrypted public key. The result is 00453233600a96384bb8d73d400984117ac84d7e8b. For the testnet, that would be 0x6f bytes.
Checksum
Now we need to calculate the checksum of our mainnet key. The idea of checksum is to make sure that the data (in our case, the key) wasn’t corrupted during transmission. The wallet software should look at the checksum and mark the address as invalid if the checksum mismatches.
To calculate the checksum of the key, we need to apply SHA-256 twice and then take first 4 bytes of the result. For our example, the double SHA-256 is 512f43c48517a75e58a7ec4c554ecd1a8f9603c891b46325006abf39c5c6b995 and therefore the checksum is 512f43c4 (note that 4 bytes is 8 hex digits).
The code to calculate an address checksum is the following:
Getting the address
Finally, to make an address, we just concatenate the mainnet key and the checksum. That makes it 00453233600a96384bb8d73d400984117ac84d7e8b512f43c4 for our example.
That’s it! That’s the wallet address for the private key at the start of the article.
But you may notice that something is off. You’ve probably seen a handful of Bitcoin addresses and they didn’t look like that. Well, the reason is that they are encoded with Base58. It’s a little bit odd.
Here’s the algorithm to convert a hex address to the Base58 address:
What we get is 17JsmEygbbEUEpvt4PFtYaTeSqfb9ki1F1, a compressed Bitcoin wallet address.
Conclusion
The wallet key generation process can be split into four steps:
Generate Public Key From Ecdsa Private Key Software
- creating a public key with ECDSA
- encrypting the key with SHA-256 and RIPEMD-160
- calculating the checksum with double SHA-256
- encoding the key with Base58.
Depending on the form of public key (full or compressed), we get different addresses, but both are perfectly valid.
Here’s the full algorithm for the uncompressed public key:
If you want to play with the code, I published it to the Github repository.
I am making a course on cryptocurrencies here on freeCodeCamp News. The first part is a detailed description of the blockchain.
I also post random thoughts about crypto on Twitter, so you might want to check it out.
OpenSSL provides two command line tools for working with keys suitable for Elliptic Curve (EC) algorithms:
The only Elliptic Curve algorithms that OpenSSL currently supports are Elliptic Curve Diffie Hellman (ECDH) for key agreement and Elliptic Curve Digital Signature Algorithm (ECDSA) for signing/verifying.
x25519, ed25519 and ed448 aren't standard EC curves so you can't use ecparams or ec subcommands to work with them. If you need to generate x25519 or ed25519 keys then see the genpkey subcommand.
EC Private Key File Formats[edit]
By default OpenSSL will work with PEM files for storing EC private keys. These are text files containing base-64 encoded data. A typical traditional format private key file in PEM format will look something like the following, in a file with a '.pem' extension:
Or, in an encrypted form like this:
You may also encounter PKCS8 format private keys in PEM files. These look like this:
Or, in an encrypted form like this:
PKCS8 private key files, like the above, are capable of holding many different types of private key - not just EC keys.
You can convert between these formats if you like. All of the conversion commands can read either the encrypted or unencrypted forms of the files however you must specify whether you want the output to be encrypted or not. To convert a PKCS8 file to a traditional encrypted EC format use:
You can replace the first argument 'aes-128-cbc' with any other valid openssl cipher name (see Manual:enc(1) for a list of valid cipher names). To convert a PKCS8 file to a traditional unencrypted EC format, just drop the first argument:
Or to convert from a traditional EC format to an encrypted PKCS8 format use:
Or to a non-encrypted PKCS8 format use:
Note that by default in the above traditional format EC Private Key files are not encrypted (you have to explicitly state that the file should be encrypted, and what cipher to use), whilst for PKCS8 files the opposite is true. The default is to encrypt - you have to explicitly state that you do not want encryption applied if appropriate using the '-nocrypt' option. Office professional plus 2016 full verison free product key generator.
As well as PEM format all of the above types of key file can also be stored in DER format. This is a binary format and so is not directly human readable - unlike a PEM file. A PEM file is essentially just DER data encoded using base 64 encoding rules with a header and footer added. Often it is more convenient to work with PEM files for this reason.
The openssl commands typically have options '-inform DER' or '-outform DER' to specify that the input or output file is DER respectively. So for example the command to convert a PKCS8 file to a traditional encrypted EC format in DER is the same as above, but with the addition of '-outform DER':
Note that you cannot encrypt a traditional format EC Private Key in DER format (and in fact if you attempt to do so the argument is silently ignored!). The same is not true for PKCS8 files - these can still be encrypted even in DER format. So for example the following will convert a traditional format key file to an ecrypted PKCS8 format DER encoded key:
EC Public Key File Formats[edit]
EC Public Keys are also stored in PEM files. A typical EC public key looks as follows:
This format is used to store all types of public keys in OpenSSL not just EC keys.
It is possible to create a public key file from a private key file (although obviously not the other way around!):
As above a DER encoded version can be created using '-outform DER':
Generating EC Keys and Parameters[edit]
An EC Parameters file contains all of the information necessary to define an Elliptic Curve that can then be used for cryptographic operations (for OpenSSL this means ECDH and ECDSA). OpenSSL contains a large set of pre-defined curves that can be used. The full list of built-in curves can be obtained through the following command:
An EC parameters file can then be generated for any of the built-in named curves as follows:
Replace secp256k1 in the above with whichever curve you are interested in.
Keys can be generated from the ecparam command, either through a pre-existing parameters file or directly by selecting the name of the curve. To generate a private/public key pair from a pre-eixsting parameters file use the following:
Or to do the equivalent operation without a parameters file use the following:
Information on the parameters that have been used to generate the key are embedded in the key file itself.
By default, when creating a parameters file, or generating a key, openssl will only store the name of the curve in the generated parameters or key file, not the full set of explicit parameters associated with that name. For example:
This will simply confirm the name of the curve in the parameters file by printing out the following:
If you wish to examine the specific details of the parameters associated with a particular named curve then this can be achieved as follows:
The above command shows the details for a built-in named curve from a file, but this can also be done directly using the '-name' argument instead of '-in'. The output will look similar to the following:
The meaning of each of these parameters is discussed further on this page.
Parameters and key files can be generated to include the full explicit parameters instead of just the name of the curve if desired. This might be important if, for example, not all the target systems know the details of the named curve. In OpenSSL version 1.0.2 new named curves have been added such as brainpool512t1. Attempting to use a parameters file or key file in versions of OpenSSL less than 1.0.2 with this curve will result in an error:
This problem can be avoided if explicit parameters are used instead. So under OpenSSL 1.0.2 you could create a parameters file like this:
Looking at the parameters file you will notice that it is now much longer:
The full parameters are included rather than just the name. This can now be processed by versions of OpenSSL less than 1.0.2. So under 1.0.1:
This will correctly display the parameters, even though this version of OpenSSL does not know about this curve.
Create Public Key From Private
The same is true of key files. So to generate a key with explicit parameters:
This key file can now be processed by versions of openssl that do not know about the brainpool curve.
It should be noted however that once the parameters have been converted from the curve name format into explicit parameters it is not possible to change them back again, i.e. there is no utility to take a set of explicit parameters and work out which named curve they are associated with.