![]() ![]() The Diffie-Hellman method illustrates the concept of'public-key cryptography', where people can give out publicinformation that enables other people to send them encryptedinformation.When we use machines to communicate over the internet, we often want those exchanges to be secure: protected against modification in transit, scrambled in a way that only we and the intended recipient can read it, and linked with a specific identity (a specific server or person) so that we know who we are communicating with.Diffie-Hellman does have a weakness: If an intruderCharlie can intercept and resend email between Alice and Bob,then the intruder can pretend to be Bob for Alice and pretend tobe Alice for Bob, substituting his own y C and tricking eachof Alice and Bob into having a shared secret key with him.There are ways to fix this problem.(For example, 5 and 11 are prime and11 = 2 x 5 + 1.) Then half the integers 1,2.,p-1 aregenerators, and it is possible to check whether g is agenerator just by seeing whether g q -1 (mod p). The Diffie-Hellman method works best ifp = 2q+1 where q is also a prime. ![]() More generally, there is a theorem saying that for anyprime p and for any a from 1 to p-1 we get a p-1 1(mod p).
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