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I checked RSA's patent application, which was registered in 1983. As patents don't last more than 20 years, it seems to me it should be free. But my friend said to use RSA I have to buy a license from MIT. Is it true ?

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You are correct, anyone can use it without asking for permission or paying anybody. The RSA patent US 4,405,829 expired in 2000, and the RSA algorithm was never patented anywhere else (because the rest of the world won't allow you to patent something that has already been published; the US gives you a year).

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However, that unconditional freedom does not extend to multiprime RSA, as supported by PKCS#1v2, which remains covered by non-expired patents US 5,848,159 and perhaps 7,231,040. I do not know that these patents have been enforced, and doubt they can be (I learnt of the technique from Pr. Jean-Jacques Quisquater before the patent was filed), but the FUD remains. –  fgrieu Jul 9 '12 at 14:34
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Also, "without asking for permission" does not apply in many countries, where sale (sometime use) of strong cryptography remains regulated. Just keeping up with what the law requires is a nightmare. See for example the European Council Regulation No 428/2009 of 5 May 2009, amended and search "Factorisation" (thats on page 184 out of 309). –  fgrieu Jul 9 '12 at 15:14
    
@fgrieu: good point; I was thinking about patents only; I forgot about local country regulations. On the other hand, if samir was worried about use in the US, and he won't export his effort outside of the US (and Canada), then there are no such regulations. On the third hand, if he has to ask, perhaps he shouldn't be reimplementing RSA; it has various nuances; perhaps he should reuse an existing implementation. –  poncho Jul 9 '12 at 15:20

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