5.1. Code-Based Digital Signatures
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Descriptif
Welcome to the lastweek of this MOOC on code-based cryptography. This week, we will bediscussing other cryptographic constructionsrelying on coding theory. We have seen how to dopublic key encryption and now we will see other kind of constructions. This first sequence we'llbe having a look at digital signatures and how to designcode-based digital signatures. So, what is digital signature? A digital signature is meantto replace a paper signature on a digital document.Exactly like a paper signature, only one person should beable to create a digital signature which ties theidentity of the signer to the document. And like a normalsignature, everyone should be able to verify that the signature iscorrect and so repudiation is impossible. This is kind of theopposite of what we do with an encryption operation ina public key cryptosystem where everyone can encryptand only one person can decrypt. That is why most digitalsignatures use a decryption operation in the process. So, how do weimplement a digital signature? The first operation isusually to hash the document into something of fixed sizewhich is a ciphertext. Why do we do this? For tworeasons: one is that we want to be able to signdocuments of arbitrary length, which means that we need, atsome point, to go from a large document to a small ciphertext. And then, we want to tie thehash ciphertext to the document. So, we need something whichis a one way, for which it is difficult to buildcollisions and everything which is exactly theproperties of hash function. Once we have this hash in theciphertext space, we simply decrypt it. This operation requires theknowledge of the secret key as you have seen inthe previous sessions. And that is why only thelegitimate signer can perform this operation and cancompute the signature. Once you have this signaturein the plaintext space, you simply append it to thedocument and that is it. For the verification, theverifier just does the opposite operation: first, takesthe signature outside of the document, encrypts itusing the public key which is something that everyone can do.
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