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 2020-11-10, 13:20 #1 mattmill30   Aug 2015 2·23 Posts Compounding prime-numbers to create a unique identity of personas I realise this is computer science related, and may be more appropriate in a cryptographic forum, but I'm hoping to establish a mathematical foundational knowledge of the subject before I then consider it's application. I imagine the application would relate to something similar to: https://superuser.com/questions/8022...eople-into-one My basic understanding of private/public key encryption is that two prime numbers are generated, one which enables encoding of data which the other can decode. I'm wondering whether it is mathematically possible to create a keyring of multiple public/private keys, which can be derived from a single master key. The rationale is that the different public/private key-pairs could then be associated to different personas for peer-to-peer social media or other uses. e.g. pre-teen me, teenage me, young-adult me, parent me, grandparent me, professional me, dating me, legal me. These persona keys would be created from a master me key-pair, which is turn could be recoverable using something similar to a 24-word cryptographic recovery phrase. The 24 words could then, for example, be held in a Will, or individually entrused to others. It would be even better if the derived keys each in turn had their own 6 or 12 word recovery phrases, derived from the 24 words.
2020-11-10, 13:27   #2
xilman
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Quote:
 Originally Posted by mattmill30 I realise this is computer science related, and may be more appropriate in a cryptographic forum, but I'm hoping to establish a mathematical foundational knowledge of the subject before I then consider it's application. I imagine the application would relate to something similar to: https://superuser.com/questions/8022...eople-into-one My basic understanding of private/public key encryption is that two prime numbers are generated, one which enables encoding of data which the other can decode. I'm wondering whether it is mathematically possible to create a keyring of multiple public/private keys, which can be derived from a single master key. The rationale is that the different public/private key-pairs could then be associated to different personas for peer-to-peer social media or other uses. e.g. pre-teen me, teenage me, young-adult me, parent me, grandparent me, professional me, dating me, legal me. These persona keys would be created from a master me key-pair, which is turn could be recoverable using something similar to a 24-word cryptographic recovery phrase. The 24 words could then, for example, be held in a Will, or individually entrused to others. It would be even better if the derived keys each in turn had their own 6 or 12 word recovery phrases, derived from the 24 words.
Your basic understanding is profoundly wrong.

Hint: PK crypto need not use primes at all. Any group in which the discrete logarithm problem is hard will serve. I strongly recommend that you read and understand https://arxiv.org/pdf/0711.3941.pdf

Last fiddled with by xilman on 2020-11-10 at 13:28 Reason: Minor tweaks.

2020-11-10, 13:37   #3
mattmill30

Aug 2015

2·23 Posts

Quote:
 Originally Posted by xilman Your basic understanding is profoundly wrong. Hint: PK crypto need not use primes at all. Any group in which the discrete logarithm problem is hard will serve. I strongly recommend that you read and understand https://arxiv.org/pdf/0711.3941.pdf Go away, learn more about PK crypto, and then rephrase your questions if you still have them.
I will read the document you've attached.

Though could you confirm whether this document answers my question? And if so, which section addresses automatic generation/recovery of keyrings?

Quote:
 Originally Posted by mattmill30 I'm wondering whether it is mathematically possible to create a keyring of multiple public/private keys, which can be derived from a single master key.
Thanks

2020-11-10, 13:58   #4
retina
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Quote:
 Originally Posted by mattmill30 I'm wondering whether it is mathematically possible to create a keyring of multiple public/private keys, which can be derived from a single master key.
Mathematically, yes, of course, you can do whatever you want. But it would be weak and silly.

Practically, no. Keys should not be derived from some sort of master code, better that they are each generated randomly. There should be no master key, that would make them insecure.

2020-11-10, 14:28   #5
mattmill30

Aug 2015

2·23 Posts

Quote:
 Originally Posted by retina Mathematically, yes, of course, you can do whatever you want. But it would be weak and silly. Practically, no. Keys should not be derived from some sort of master code, better that they are each generated randomly. There should be no master key, that would make them insecure.
Since keys are generated by an algorithm, which can be brute forced with enough calculations, why would a master key be insecure?

The master key is what I'm describing as a compound key, so if there's 10 persona key pairs, the master key could be massive, and the recovery phrase could be hundreds of words.

Could you elaborate on your response?

2020-11-10, 16:33   #6
xilman
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Quote:
 Originally Posted by retina Mathematically, yes, of course, you can do whatever you want. But it would be weak and silly. Practically, no. Keys should not be derived from some sort of master code, better that they are each generated randomly. There should be no master key, that would make them insecure.
To be perhaps a little bit more precise: it would make them at most as secure as the master key.

Security is not a binary quality and it encompasses many more aspects than computational effort.

Last fiddled with by xilman on 2020-11-10 at 16:34

 2020-11-10, 16:46 #7 chris2be8     Sep 2009 37038 Posts A better way to do it is to generate several public/private key pairs, each independently generated from random noise. Then encrypt the private keys with a symmetric key generated from a secure passphrase. That way the private keys all have the same (maximum) strength. And stealing one of them gives no help cracking the rest. As long as the master keyphrase is securely locked away and unguessable you are as secure as possible. In practice you would need to keep a copy of the pair you are using now unencrypted (or encrypted with a different passphrase). That would be more vulnerable but there is no way round that. Your first step should be to look for existing key management products that will do what you want. It's not easy to build a DIY system without making any mistakes. And read up on cryptography so you know what you are doing. Chris

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