Bottomley: Using Elliptic Curve Cryptography with TPM2 [LWN.net]

Bottomley: Using Elliptic Curve Cryptography with TPM2

Posted Oct 16, 2017 12:40 UTC (Mon) by Wol (subscriber, #4433)
In reply to: Bottomley: Using Elliptic Curve Cryptography with TPM2 by luto
Parent article: Bottomley: Using Elliptic Curve Cryptography with TPM2

> Please clarify. There are certainly insecure curves, but I've never heard that you can take an otherwise-okay curve, compute something, and thus "solve" the curve.

Bear in mind I'm not a cryptography expert but ...

I believe that with RSA you publish PQ (the product of your two big primes) as part of your public key. Crack that PQ, and EVERYBODY who is using that PQ has had their key broken. Which is why most people calculate their own PQ.

On the other hand, while there are very many elliptic curves (an infinite number?) for the most part we only use a few of them, so very many people share the same elliptic curve. Crack one person using a curve, and again everyone else using the same curve has been cracked.

That's really my point - cracking an individual PQ doesn't get you very far as the chances of many people using it is slim, cracking an elliptic curve will probably get you major crack as each curve is widely used.

Cheers,
Wol

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Bottomley: Using Elliptic Curve Cryptography with TPM2

Posted Oct 16, 2017 15:17 UTC (Mon) by MattJD (subscriber, #91390) [Link] (1 responses)

> I believe that with RSA you publish PQ (the product of your two big primes) as part of your public key. Crack that PQ, and EVERYBODY who is using that PQ has had their key broken. Which is why most people calculate their own PQ.

To be clear, P and Q are basically the secret of an RSA key (technically there is a third value, d, but that can be easily computed from the P, Q, and the e value in the public certificate). People use a different P and Q (and thus PQ value) as otherwise they would be basically sharing keys.

Note that actual RSA keys are described slightly differently, but doesn't change the fact people can't share a P and Q.

Bottomley: Using Elliptic Curve Cryptography with TPM2

Posted Oct 20, 2017 0:31 UTC (Fri) by Wol (subscriber, #4433) [Link]

Or if, as is theoretically possible, two people come up with the same PQ by chance, they can solve the other person's encrypted communications ...

Cheers,
Wol