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As I know, signing is used to ensure integrity and authenticity of sender. What is the advantage of group digital signing over individual signing? Can anyone explain this using a scenario?

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    What do you mean by group signing? – cpast Mar 7 '15 at 22:43
  • group of people have same private key..........group signature – Exbury Mar 8 '15 at 5:37
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A digital signature binds a message to a private key in a way that ensures that no one without the private key can create a signature for any message that they didn't just get a signature for from the real signer, even if they have the public key needed to verify it. The key is that it binds things to keys, not individuals.

When should you use a group signature? When the signature should associate it with the group, and don't care about linking a message to a person in the group. Why do this? That's not actually a question information security can answer; the discipline is about helping you better express your security goals and finding a way to achieve them, but infosec isn't about "what are your security goals in the first place?"

Companies have a security goal -- only authorized company personnel should be able to get something signed. So they establish a corporate key and give access to only people who should be able to do it. Or a group of friends (say, Alexander, John, and James) without some formal association want to write a series of things in the same persona. They want things to be associated with the group of them, and are not interested in showing who wrote an individual message, so they create a key and share it to sign things for the persona.

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What is the advantage of group digital signing over individual signing?

There are a couple different ways about implementing this. The two in the front of my mind are Shamir's Secret Sharing and some form of access-gated control of a single key. Here are the upsides:

Imagine group signing as a group Twitter account. Typically a company account has an internal interface that authenticates company users who are allowed to post. This interfaces with the API to Twitter using a single credential that's protected by very limited access. When a user leaves the company, their access is cut. It's easy to tell what's going on with the account because all access is occurring through a single system. The person posting probably never has direct access to the account credentials.

With individual accounts, things would be much more confusing in regards of tracking activity, controlling access, and preventing spoof accounts or fraud since it's not clear to users that JeffAtAirline might not really be representative of AirlineCo.

Sharmir's Secret Sharing allows splitting a key in a way that requires a defined quorum of users perform an action. Finally one might be lazy and just give everybody a key, but that's a terrible idea.

In both cases of sharing systems, auditing or external attestation is desirable. In both cases, it's also clearer that the entity making the signature is meant to represent the organization and internal control of key access provides clearer demonstration of who is authorized to represent an organization's signature. Further internal control might be available, such as a software package signing system for a Linux distribution only allowing a package maintainer to sign their own package with the distribution key. It's much easier to trust that as a person than to try and keep track of all the personal keys that might be used by packagers that have come and gone over time.

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