Digital Signatures

We have to make sure that the message digest itself has not been modified in transit. This can be done by signing it using the private key from our public/private key set. We’ve seen how the following relationship holds:

Plaintext ® Encryption Algorithm(Plaintext, Public Key) ® Ciphertext ® Decryption(Ciphertext, Private Key) ® Plaintext

However for public key algorithms such as RSA the following also holds:

Plaintext ® Decryption Algorithm(Plaintext, Private Key) ® Ciphertext ® Encryption(Ciphertext, Public Key) ® Plaintext

That is to say if we run the algorithms in reverse swapping the private and public keys we can carry out the same encryption/decryption process.

The recipient of a message decrypts the message digest using the sender’s public key. They then recompute the message digest of the attached message. If the two do not match, then either the message has been modified in transit or it is not from who it claims to be from. This means that we can now both sign and authenticate a message simply by signing its message digest.

This solution is called a Digital Signature, these are a clever addition to the functionality we already have provided by public key cryptography. This means that if we know for sure that a particular public key belongs to a particular party and we receive a message that can be decrypted using that public key to provide a sensible message then we know that the message came from them - since only their private key could have generated ciphertext that would work with the public key we have. This does of course assume that they managed to keep their private key secret!

We could just sign the whole message but using public key encryption would be slow. Instead we only sign the message digest. This process is shown on the previous slide.

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