[cryptography] cryptanalysis of 923-bit ECC?

Matthew Green matthewdgreen at gmail.com
Wed Jun 20 18:32:23 EDT 2012


For a proper answer, You should follow pbarreto on Twitter and ask him. He's a nice guy and *very* willing to talk about this. Mostly because he found the press release so misleading. 

But in any case, the answer to your question is: this is not a standard choice for a pairing friendly curve. It's a field of small characteristic, which makes it unusually vulnerable to these attacks. They could not use this attack against a similar MNT or BN curve.

My understanding is that a 256-bit BN curve gives 128-bit security.

Matt 

On Jun 20, 2012, at 5:12 PM, Jon Callas <jon at callas.org> wrote:

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> On Jun 20, 2012, at 8:35 AM, Matthew Green wrote:
> 
>> I'm definitely /not/ an ECC expert, but this is a pairing-friendly curve, which means it's vulnerable to a type of attack where EC group elements can be mapped into a field (using a bilinear map), then attacked using an efficient field-based solver. (Coppersmith's).
>> 
>> NIST curves don't have this property. In fact, they're specifically chosen so that there's no efficiently-computable pairing.
>> 
>> Moreover, it seems that this particular pairing-friendly curve is particularly tractable. The attack they used has an estimated running time of 2^53 steps. While the 'steps' here aren't directly analogous to the operations you'd use to brute-force a symmetric cryptosystem, it gives a rough estimate of the symmetric-equivalent key size.
>> 
>> (Apologies to any real ECC experts whose work I've mangled here… :)
> 
> Thanks, anyway, as things seem to be detail-lite where I'm getting them.
> 
> Do we have anyone who can speak authoritatively on this? I am also not at all an expert on pairing-friendly curves.
> 
> Is this merely a case where 973 bits is equivalent to ~60 bits symmetric? If so, what's equivalent to AES-128 and 256? Is there something inherently weak in pairing-friendly curves, like there are in p^n curves?
> 
> I have no idea what this result *means* and would love to know. 
> 
>    Jon
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