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I've read a lot about non-abelian group based cryptography recently and I am wondering why they only use infinite groups as platform. Is there a special reason or is this an area open for research?

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Can you please give a reference? –  gmoktop Feb 1 at 18:07
    
Well in all articles about nonabelian cryptography they only use infinite groups as platforms. For example in the AAG scheme first proposed by Anshel-Anshel-Goldfeld they suggest the braid groups as platform groups see (citeseerx.ist.psu.edu/viewdoc/…). I'm quite aware of the advantages the braid groups brings to cryptography but would it be possible to use finite groups as well? If they are big enough so that a brute-force-attack is not possible. –  RSA5000 Feb 20 at 17:11
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