I am not a mathematician, but I was wondering if the proposed proof of the abc conjecture (PDF) by Shinichi Mochizuki of Kyoto University would contain insights and mathematical tools that would lead to a weakening of elliptic curve cryptography.
If the abc conjecture has been proven what implication does that have for elliptic curve cryptography?
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number-theory
prime-numbers
cryptography
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1As far as I understand currently, Mochizuki's proof does not provide explicit/effective bounds, so no such implications are (immediately) expected. – 2012-09-12
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1Not exactly your specific question, but a similar question (RSA crypto) was recently asked on the Cryptography sister site. Maybe you'll have some luck there? http://crypto.stackexchange.com/questions/3780/abc-conjectures-impact-on-rsa-encryption – 2012-09-12
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0@jtolds thank you for the crypto site link - much appreciated. – 2012-09-13
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0@AndresCaicedo That's reassuring to know, I'll keep this question open for a while to let the implications of the papers be digested and perhaps elicit a full answer. – 2012-09-13
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1You may find this interesting: http://rjlipton.wordpress.com/2012/09/12/the-abc-conjecture-and-cryptography/ – 2012-09-14
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1A short update: I was actually wrong, and Mochizuki's approach can be made effective in fairly explicit ways. Whether it is correct is another issue, and I wouldn't be able to tell. Anyway, the following answer in MathOverflow discusses the effective bounds: http://mathoverflow.net/questions/106560/philosophy-behind-mochizukis-work-on-the-abc-conjecture/107279#107279 – 2012-09-27