How can cryptographic signatures be somehow linked to a physical signature? A few days ago, I was asked to sign an online document over DocuSign as well as on SignEasy, any the signature were accepted just by a physical signature sent over email or on the app. They did not even ask me to generate a private key whose public key I should upload to their website. So, I felt that the process quite fake and superficial; it just satisfies the naive users. But these apps are quite famous all around. 

So, I feel that I think that I am missing out something somewhere. Can you please explain how the physical signatures in these apps are linked to the cryptographic digital signatures?
The short answer is that there's no link between your physical signature and any cryptographic signature. Indeed, from the high-level description of how DocuSign works and their security manifesto there's no reason to believe that any cryptography goes into the signature process itself.

Note that “signature” is an overloaded word. In this post, I will refer to three different concepts that can be called “signature”:


Your physical signature — a scrawling on paper.
A cryptographic signature which mathematically authenticates a message as having been validated by the owner of a key. (There are actually two meanings here: the process of generating a signed message from a key and a bare message, and the bytes that encode the authenticity information in the signed message. But this distinction won't matter in important ways here.)
A validation assertion: a statement that a message has been approved by a certain party.


Physical signatures play a dual role.


They're often used as an authentication factor, because they're supposedly hard to reproduce. But as an authentication factor, they're very broken: not only they're not that hard to reproduce in a way that will fool most people, but mostly because in most cases they can easily be copied and grafted onto a different document. With a scanned signature, grafting it onto any document is trivial.
Physical signatures are also used as a validation assertion. Signing a legal document indicates that you agree to abide by it. Historically, this is the reason they've been used on contracts — even people who couldn't read had the contract read to them and then made a cross at the bottom to signify that they accepted it.


Uploading your physical signature to DocuSign's servers doesn't provide any security. Anybody could find some document that you signed and upload your signature. What it does is partly to provide an illusion of security (we need to demonstrate visible security measures, so let's do something visible and say it's for security), and partly to add a bit of friction and ceremony so that you can't later claim “oh, I must have clicked by mistake, I know nothing about this”. Because your signature is personal to you, you can't claim that it was uploaded by mistake — it had to be you or someone with the intent to commit fraud.

With or without your signature, what DocuSign can attest is:


There is someone with access to an account which has your name and other personal information attached to it. Hopefully they verify that this person has (or at least has had) access to the email account attached to the DocuSign account.
That person made a conscious decision to validate a certain document at a certain time.


Still no crypto so far, except for the trivial (in engineering terms) aspect of using TLS to communicate with their servers.

What can cryptography bring to the table? At this point, nothing, really. DocuSign may well generate a cryptographic key that's specific to your account, and produce a version of the document that's cryptographically signed with your key. That would be a validation assertion for the document on your behalf. They don't need cryptography for that, though: they could put up a web page on their server that states “Rahul approved this document”, and it would serve just as well.

Where cryptography adds something is that a cryptographic signature remains valid in any context. A web page that states “Rahul approved this document” is only useful if you access it on DocuSign's website, because anybody could write that on their own website and it wouldn't have any importance. On the other hand, nobody but the holder of the private key can produce a cryptographically signed document, so the authenticity of that document can be verified offline.

It would be sufficient for that purpose for DocuSign to have a single key and use it to sign all documents. The downside of this approach is that if the key was ever leaked or used in an unauthorized way, it would throw suspicion on all of DocuSign's validation assertion. Using separate keys per user allows the keys to be repudiated separately. For example, if your account is breached because someone hijacked your browser, you could arrange to repudiate signatures made with your key after the breach, which would be a lot less disruptive than repudiating signatures made by all DocuSign customers.

If DocuSign does use a cryptographic signature, it isn't part of the security of the validation assertion, and nothing ties it to your physical signature other than the integrity of your account information on DocuSign's servers. This is the same thing that guarantees the relation between you (via your account, and in particular via your account's credentials) and the validation assertions on your behalf.

You'll note that DocuSign's security page includes a lot of hype, assertions about encryption (which does make sense to improve data confidentiality in case backups are stolen), and assertions about physical security (which makes sense as well, since a breach of their servers would compromise the system) and availability, as well as assertions about following religious regulatory processes. Nothing firm about signing.

As long as the signing key is on DocuSign's servers, the advantage of cryptography is to make the validation assertions easier to use, not to make them harder to forge (i.e. no added security). What if the signing key was only held only on your client? That would reduce the trust that you need to put in DocuSign, since they would not be able to generate arbitrary signatures as you. You would still have to worry about the security of your client environment(s). That would also have practical disadvantages because people use multiple client machines, don't back them up, etc. DocuSign's approach requires no technical competence from the user and no setup on the client side. People who are technical enough to manage signing keys are probably using PGP already anyway.