[Cryptography] Trapdoor symmetric key

Phillip Hallam-Baker hallam at gmail.com
Sun Sep 8 13:18:53 EDT 2013

On Sun, Sep 8, 2013 at 12:19 PM, Faré <fahree at gmail.com> wrote:

> On Sun, Sep 8, 2013 at 9:42 AM, Phillip Hallam-Baker <hallam at gmail.com>
> wrote:
> > Two caveats on the commentary about a symmetric key algorithm with a
> > trapdoor being a public key algorithm.
> >
> > 1) The trapdoor need not be a good public key algorithm, it can be
> flawed in
> > ways that would make it unsuited for use as a public key algorithm. For
> > instance being able to compute the private key from the public or deduce
> the
> > private key from multiple messages.
> >
> Then it's not a symmetric key algorithm with a trapdoor, it's just a
> broken algorithm.

But the compromise may only be visible if you have access to some
cryptographic technique which we don't currently have.

The point I am making is that a backdoor in a symmetric function need not
be a secure public key system, it could be a breakable one. And that is a
much wider class of function than public key cryptosystems. There are many
approaches that were tried before RSA and ECC were settled on.

> > 2) The trapdoor need not be a perfect decrypt. A trapdoor that reduced
> the
> > search space for brute force search from 128 bits to 64 or only worked on
> > some messages would be enough leverage for intercept purposes but make it
> > useless as a public key system.
> >
> I suppose the idea is that by using the same trapdoor algorithm or
> algorithm family
> and doubling the key size (e.g. 3DES style), you get a 256-bit
> symmetric key system
> that can be broken in 2^128 attempts by someone with the system's private
> key
> but 2^256 by someone without. If in your message you then communicate 128
> bits
> of information about your symmetric key, the guy with the private key
> can easily crack your symmetric key, whereas others just can't.
> Therefore that's a great public key cryptography system.

2^128 is still beyond the reach of brute force.

2^64 and a 128 bit key which is the one we usually use on the other hand...

Perhaps we should do a test, move to 256 bits on a specific date across the
net and see if the power consumption rises near the NSA data centers.

Website: http://hallambaker.com/
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