The Elliptic-Curve Diffie–Hellman (ECDH) is an anonymous key agreement protocol that allows two parties, each having an elliptic-curve public–private key pair, to establish a shared secret over an insecure channel. String Hash Calculator String HMAC Calculator One-Time Password Calculator. Base64 Converter Bitcoin Address Generator. Diffie-Hellman Key Exchange. Diffie-Hellman key exchange allows two parties to generate a shared secret over an insecure channel. Diffie-Hellman Calculator A small Javascript tool to play with the Diffie-Hellman algorithm and help with decoding it Kathy specifies B1 on Calculate Diffie-Hellman Secret Key to create another public value K2, which she sends to Terry.
- Diffie Hellman Merkle Key Exchange Calculator
- Diffie-hellman Key Exchange Calculator
- Diffie-hellman Calculator
- Diffie-hellman Calculator
You already use modulo computation when you look at the clock and e.g. needs to figure out what time it's 3 hours after 11 o'clock, which is 2 o'clock. In math we write that as:
( (11 + 3) : mod : 12 = 2 )
where 12 is the modulus because we want the time as an integer between 0 and 11 (12 o'clock is in this case denoted by 0). In words we say 11 plus 3 modulo 12 is equal 2. The result of a modulo computation is an integer between 0 and the modulus minus 1. E.g. with the modulus 3 we have that:
- ( 1 : mod : 3 = 1 )
- ( 2 : mod : 3 = 2 )
- ( 3 : mod : 3 = 0 )
- ( 4 : mod : 3 = 1 )
- ( 5 : mod : 3 = 2 )
- ( 6 : mod : 3 = 0 )
- etc.
If we e.g. look at ( 27 : mod : 5 ) then modulo computes the number of times 5 divides 27 and then returns the remainder of the result which is 2 in this case, i.e. ( 27 : mod : 5 = 2 ). But how did we get this result?
First we compute the number of times it's possible to multiply 5 with the number ( x ) such that we get an integer as close as possible to 27 without exceeding it, i.e. we have to find the maximun value of ( x ) such that ( 5 cdot x leq 27 ). In this case we have that ( x = 5 ) because ( 5 cdot 5 = 25 leq 27 ). Then by subtracting 27 with 25 we get the answer ( 27 - 25 = 2).
If the integer is negative e.g. ( -27 : mod : 5 ) we have to do it slightly different and the answer is ( -27 : mod : 5 = 3 ). In this case the integer ( x ) is negative and should be the closest integer that exceed -27, i.e. we have to find the minimum value of ( -x ) such that ( 5 cdot -x geq -27 ). Now we have that ( -x = -6 ) because ( 5 cdot -6 = -30 geq -27 ). Then by subtracting -27 with -30 we get the answer ( -27 - (-30) = -27 + 30 = 3).
It's important that ( x ) or ( -x ) is an integer such as ( -14, 3, 17 ) etc. and NOT a fraction or float such as ( frac{1}{4}, frac{-3}{7}, 2.5, 5.1 ) etc.
If two integers ( a ) and ( b ) modulo the same modulus ( c ) returns the same remainder ( r ), then we say that ( a ) and ( b ) are congruent modulo ( c ). I.e. if ( a : mod : c = r ) and ( b : mod : c = r ) then ( a equiv b : (mod : c) ). Also, notice that if the modulus ( c ) is greater than the integer ( a ), i.e. ( c > a ), the result will always be equal ( a : mod : c = a ).
Diffie-Hellman key exchange allows two parties to generate a shared secret over an insecure channel.
You
Partner
Shared secret
Description
This tool will generate a key pair for you, of which you can send the public key to a partner. Once your partner sends you their public key, paste it into their public key box. If done successfully, you two should have an identical shared secret. You may use the shared secret to encrypt messages to each other, possibly by using the AES String Encryption and Decryption tool.
Do It Yourself
OpenSSL can help you perform a Diffie-Hellman key exchange, but it is not directly compatible with this tool. The principle, however, is the same.
Diffie Hellman Merkle Key Exchange Calculator
During this process, we will need to generate 5 elements before deriving a shared secret:
Diffie-hellman Key Exchange Calculator
- A common base
- Partner 1's private key
- Partner 1's public key
- Partner 2's private key
- Partner 2's public key
Generate a Common Base
Use this command to generate a common base, dhp.pem. This DH Parameters key can be shared in a public manner between the two parties. It is not a secret. The library used by CryptoTools.net uses a constant value for its base.
Partner 1's Key Pair
Partner 1 should be in possession of the dhp.pem file, then they can generate their private and public keys, dhpriv1.pem and dhpub1.pem, respectively.
Partner 2's Key Pair
Diffie-hellman Calculator
Likewise, Partner 2 should be in posession of the same dhp.pem file and generate their own private and public keys.
Derive Shared Secret
Partner 1 should share dhpub1.pem with Partner 2, and Partner 2 should share dhpub2.pem with Partner 1. Once they have exchanged public keys, they may derive the shared secret. Partner 1's copy of the shared secret will be named shared1.bin, and Partner 2's will be named shared2.bin.
Diffie-hellman Calculator
The content of files shared1.bin and shared2.bin should be exactly the same. Since they are binary files and not easily readable by humans, you may verify that they are the same like so: