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    @Ashwin - As D.W. said, asymmetric cryptography is roughly 10000 times slower/more CPU intensive than using a block cipher. So it makes sense to only transfer enough info to then use the much faster key. Commented Apr 11, 2012 at 14:30
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    RC4, not AES in this particular case, but past the particular symmetric algorithm used.. Commented Apr 12, 2012 at 12:54
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    @drjimbob not to mention key generation, we only use likely primes not guaranteed primes cause of that one :/ Commented Apr 12, 2012 at 12:55
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    @ewanm89 - Yes, we only use likely primes -- but with astronomical odds they actually are prime. With random entropy input the chance of getting a false positive prime in openssl with default settings is 1 in ~2^80 ~ 10^24 So until you check about ~10^23 numbers for primality with overwhelming odds you can assume your numbers are truly prime. E.g., if you check a billion potential primes a second, it will take ~10 million years before you are likely to have a false positive prime in your keypair. Edited for RC4/AES mixup. Commented Apr 12, 2012 at 15:23
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    factoring is not NP hard. It's just there is no known algorithm that can factor in polynomial time but AFAIK no one has proven it can't be done. en.wikipedia.org/wiki/Integer_factorization Commented Apr 13, 2012 at 2:02