Hello, On Mon, 16 Nov 2009, Mano wrote: > On matters mathematics I would trust Dr. Kapil more than anyone else > on this list!
Never (at least almost never) _trust_ someone else's mathematics. The whole point of mathematics is that if it is correct you should be able to verify things for yourself. A bit like open source --- if the program has a flaw you can check it! In this case, perhaps I interpreted incorrectly what Girish had to say. My only justification is his obtuse style of writing! :-) Though this is a little OT now, I am explaining this since Girish has no time! Here is a brief description of RSA which ignores some technical points: Take a number N which is a product of two (large primes) p and q. Take a smallish prime r like 23 or 31 which does not divide (p-1) or (q-1). Using p, q, r you can calculate s so that (p-1)(q-1) divides (rs-1). Your public key is (N,r). Your private key is (N,s). It is assumed that the p and q are not known to anyone except the person who holds the private key. Encryption takes m | 0 < m < N and takes it to (m^r modulo N). Decryption takes n | 0 < n < N and takes it to (n^s modulo N). One can show that (m^(rs)-m) is divisible by N providing that m is different from p and q. I hope this explains my remark that encryption and decryption are inverses of each other. Here is a brief description of Diffie-Hellman key exchange which also ignores some technical points: Let P be a large prime and g | 1<g<P be a "suitable" number. I choose a number a | 1 < a < (P-1) and broadcast k=(g^a modulo P). You choose a number b | 1 < b < (P-1) and broadcast l=(g^b modulo P). Now, we use the "shared" key m=g^(ab) modulo P which: - I can get by taking m=(l^a modulo P) - You can get by taking m=(k^b modulo P) It is generally believed that someone who does not know a or b cannot calculate m. I hope this clarifies why I thought that Girish was talking about the Diffie-Hellman key exchange. Regards, Kapil. -- _______________________________________________ To unsubscribe, email ilugc-requ...@ae.iitm.ac.in with "unsubscribe <password> <address>" in the subject or body of the message. http://www.ae.iitm.ac.in/mailman/listinfo/ilugc