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In normal asymmetric crpyto like RSA, if Alice encrypts something using her private key, Bob can decrypt it using Alice's public key. Is the same possible in Identity-Based Cryptography, where the public key is usually the user's email address?

So if Alice encrypts something using her private key, can Bob decrypt it using her email address?

I am asking this because in all the literature I have come across, it says that Encrypt operation encrypts messages using the public key ID, and Decrypt operation decrypts messages using the corresponding private key.

  • In normal Asymmetric crypto Alice encrypts something with Bob's public key. So that he can decrypt it with his private key. – RoraΖ Aug 20 '14 at 15:42
  • In your example if Alice did encrypt with her private key, then yes anyone could decrypt it with her public key. This is why private keys are used for digital signatures. Because anyone can verify the signature using the public key. – RoraΖ Aug 20 '14 at 15:48
  • Yes, but I am inquiring about IBE. I know that this works fine in normal asymmetric crypto like RSA and DSA etc., but why not in IBE? Can you show me some reference in case this works in IBE? – xkcd Aug 20 '14 at 16:11
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    IBE is just a type of public key cryptography. The concepts are the same, just how key pairs are generated is different. This diagram shows that the key management is different, but encryption, decryption and signing concepts remain the same. en.wikipedia.org/wiki/ID-based_encryption#Usage – RoraΖ Aug 20 '14 at 16:40
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    I think I see what you're trying to say. No you can't use the key ID (i.e. email) to directly decrypt it. The point of IDE is to authenticate to a server with an easy key ID to retrieve keys needed to for encryption and decryption. You can think of it like a hashmap, where you the encryption key pairs are uniquely identified by a Key ID. They Key ID itself is not what's used, but it is used to retrieve what's needed from the PKG (example from the diagram above). – RoraΖ Aug 20 '14 at 16:49
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So I think I have a complete grasp on the question, and IBE. I'm going to attempt an answer. There is an end to my madness.

IBE is based on bilinear pairings in cryptography. Page 23 of that paper is where they start talking about pairings, but I think the whole paper is relevant. A pairing scheme often used by IBE is Weil Pairing (also described in that document). These are based in elliptic curves math magic.

Elliptic curves are a lot like Diffie Hellman in that they're both based in the discrete log problem. Here's a question and answer as to why DH can not be used for digital signatures. There are some digital signature schemes that use Elliptic curves as a base, but additions are needed (such as hashing algorithms). ECC Based Digital Signature Schemes.

My line of thinking is that the statement "Alice encrypts with her private key." is not as simple as it seems. Like Elliptic curves and DH, a pairing can be generated for a given input. But you first need to have the input in order to get the generated private key. Which implies that encrypting with the private key would not result in a successful decrypt by the public key. In the same way that you have separate decrypt and encrypt functions in some modes of symmetric encryption.

I'm not saying that you can't provide a means for this. There are standards out there for ECC based IBE Signatures (RFC 6507), but they have to be built into IBE scheme for such verification to work.

I learned something in all this, my previous comment about public key cryptography concepts generally the same was completely wrong. I hope this answers your question. I tried to keep Wikipedia articles to a minimum :)

  • Thanks for the RFC, that was really helpful. It also led me to search google scholar for "IBE Signatures". Turns out there are tons of papers on this subject. TLDR: The short answer is 'yes' :) – xkcd Aug 22 '14 at 11:20
  • Yeah IBE is so dependent on the scheme chosen. There were so many different papers on the subject. In some cases no, in some cases it's possible. Interesting reads though. – RoraΖ Aug 22 '14 at 11:22
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You can only encrypt with the public key and only decrypt with the private key. So, no, you can't decrypt e-mails with an e-mail address or the senders public key. This would completely defeat the purpose of public key crypto.

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    No, I respectfully disagree, google "Digital Signatures". – xkcd Aug 22 '14 at 11:18

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