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I came across various definitions of what authenticity means in cryptography. I would like to know which one is correct.

The first definition - the one I always used - is the following:

Data authenticity means that the initial message sender is who he/she claims to be.

According to this definition, we can have data authenticity without data integrity.

The second definition defines authenticity as authentication + integrity.

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  • $\begingroup$ We cannot have data authenticity without integrity. If I write a letter and the mailman changes a letter in the letter I wrote, then the letter I wrote is no longer authentic since it is not the same letter I sent; it is now, in a way, a new letter created by the mailman. · $\endgroup$ – Daniel Jun 23 '16 at 15:47
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It is hard to have message authenticity without integrity. To authenticate the message you need to know what message is being authenticated. If you could change the message the authentication tag should become invalid. Message authenticity means that you can establish that the message originated from a trusted entity. For this reason message authenticity often implies integrity.

This doesn't go the other way around because of checksums. Checksums can be used to protect integrity of a message. Checksums however do not protect against active attacks as anybody is able to calculate a checksum. If you need to protect against active attacks then the message is usually authenticated as well.

I'm not sure that "data authenticity means that the initial message sender is who he/she claims to be" is a correct definition. That seems the definition for entity authentication. The data may not be an identifying aspect for the entity. I would rather say that message authenticity proves that the message originated from a specific entity. In that case - as explained in the first section - integrity is probably implied.

As an example, say we find a bunch of paintings all bearing the same signature. We however do not know who created the paintings. All we know is that there is some unknown painter that painted the messages - the identity of the painter is not really established. What we do know however is that all the paintings belong to a single painter. That says quite a lot about the paintings themselves.

If you look at entity authentication then no explicit message needs to be involved, so data integrity may not be required. So there you are: authentication without integrity.

Authenticity and integrity are different concepts, even if used in the context of data/messages. It doesn't make sense to mix those concepts even if one implies the other. So I try to write "message authentication and integrity" instead of just "message authenticity" or "message integrity".

In text you have to distinguish between message and entity authentication. If you have message authentication you know that integrity is very likely implied. This is not the case for entity authentication. So you do need to look at context to see if integrity is implied.

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  • $\begingroup$ We can imagine a system where authenticity is provided without integrity, for instance let's take an example where a sender sends to a receiver over a trusted channel a random unique identifier embeded in the message, the message itself is going to be sent over an untrusted channel. We'll assume an identifier is never used twice. In this case the receiver knows that the message has been generated by the sender, however the receiver doesn't have the proof that the message hasn't been altered during transmission. $\endgroup$ – Othman Sep 10 '15 at 11:47
  • $\begingroup$ As for the paintings, if the painting is signed by a painter and this signature has been authenticated by an expert, we can reasonnably say that the painting is authentic however we can not say the painting hasn't been altered (time alone can alter a painting). $\endgroup$ – Othman Sep 10 '15 at 11:50
  • $\begingroup$ C1: In your first example: it seems to me that the only thing that the receiver knows is that a message has been generated. So the data itself is not authenticated. C2: The painting example was put in to show the difference between entity authentication and message authentication. Replace the signature with a digital signature generated by an otherwise unknown private key. The idea is to put the strain on the message itself, instead of on the entity that originated it. $\endgroup$ – Maarten - reinstate Monica♦ Sep 10 '15 at 12:02
  • $\begingroup$ Note that we are discussing human definitions here; I'm not sure if there are precise mathematical constructs to explain the difference between the concepts, but if there are, they are probably hotly debated :) $\endgroup$ – Maarten - reinstate Monica♦ Sep 10 '15 at 12:05
  • $\begingroup$ You're right, in the first case, the reveiver only knows that the sender wrote a message, it doesn't proof the data have been written by the sender. I wish there was some where a clear definition of what authenticity means. $\endgroup$ – Othman Sep 10 '15 at 12:12
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There is no single "correct" one. There are different notions of authenticity that make sense in different context and encode slightly different goals.

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  • $\begingroup$ In this case I think you need to show some different context and different goals. $\endgroup$ – Maarten - reinstate Monica♦ Sep 10 '15 at 11:11

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