[Cryptography] Simple non-invertible function?

[Jerry Leichter]

On Sep 18, 2014, at 12:13 PM, Sandy Harris <sandyinchina at gmail.com> wrote:
>> The world's simplest block cipher is just IDEA multiplication of
>> plaintext and key, and that could be made non-invertible with an XOR.
>> The small block size (16 bits) does not appear to matter in my
>> application and a transform that mixes those blocks could easily be
>> added just in case it does matter.
> 
> My current code uses idea_multiply(x, key) xor x which I think
> is non-invertible. Then there's a GCM hash mixing step so I do
> not think the 16-bit blocks are a problem.
> 
> Comment?
Please define "non-invertible".  F(x) = 0 is non-invertible - but likely not what you had in mind.  Presumably you mean something like a 1-1 function such that computing F(x) is easy but computing its inverse is hard - for some appropriate definition of "easy" and "hard".  The example you give is 1-1 and easy to compute, but the inverse isn't likely to be that hard, or we'd be using it in place of much more complex functions like the SHA's.
                                                        -- Jerry


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