This is a fancy way of saying that we can use math to prove who sent us some data, without actually having to physically send anything over. It’s like signing your name on an email or text message, but with numbers instead of letters.
So how does it work? Well, let me break it down for you in simpler terms:
1. First, we need a secret key and a public key. The secret key is something that only the sender knows (like their password), while the public key can be shared with anyone who needs to verify the signature.
2. When someone wants to send us some data, they use our public key to encrypt it. This creates what’s called a “hash” of the original message, which is basically just a shorter version that still contains all the important information.
3. Next, we take our secret key and multiply it by another number (called the base point) on an elliptic curve. This gives us a new point on the curve, which represents our signature for that particular message.
4. Finally, we send both the original hash and our signature to the recipient. They can then use our public key to verify that the signature matches the hash of the original message. If it does, they know that the sender really did send that data (and not someone else pretending to be them).
Here’s an example in Ruby:
require 'digest/sha256' # Import the SHA256 module from the Digest library
require 'openssl' # Import the OpenSSL library for generating key pairs and signing/verifying messages
# Generate a new key pair using OpenSSL
key_pair = OpenSSL::PKey::RSA.new(1024) # Generate a new RSA key pair with a key length of 1024 bits
private_key = key_pair.to_pem # Convert the private key to PEM format for easier storage and transmission
public_key = key_pair.public_key.to_der # Convert the public key to DER format for easier storage and transmission
# Define the message we want to sign (in this case, "Hello, world!")
message = "Hello, world!" # Define the message we want to sign
hash = Digest::SHA256.hexdigest(message) # Generate a hash of the message using SHA-256
# Sign the hash with our private key and get the signature in DER format (which is what we'll send to the recipient)
signature_der, _ = OpenSSL::PKey::RSA.private_encrypt(hash.hex.unpack("C*").map(&:to_i), private_key) # Sign the hash using our private key and get the signature in DER format (which is what we'll send to the recipient)
signature = Base64.strict_encode64(signature_der).gsub("\n", "") # Convert the signature from DER format to base64 format for easier transmission over email or text message
# Verify that the signature matches the hash of the original message using our public key (which is what the recipient will do)
OpenSSL::PKey::RSA.new(public_key).verify(hash, Base64.strict_decode64(signature)) # Verify the signature using our public key and make sure it matches the hash of the original message
And that’s pretty much all there is to it! Digital signatures are a powerful tool for ensuring data integrity and authenticity in a variety of applications, from email encryption to online banking.