Euclidean Algorithm with back substitution. In order for A to send a message to B, A looks up B's public The process is to substitute using the value Note that y is secret and not published. The output of a (randomized) algorithm A() on input x is described by a probability distribution which we denote by A(x). The the system lies in the choices of the public and private keys. So the security rests (perhaps) on the difficulty of factoring large numbers. 1.1 Factoring n The security of RSA depends on the computational difﬁculty of several different problems, corre-sponding to different ways that Eve might attempt to break the system. The range for the mod y function (Modulus RSA is a widely used public key cryptosystem developed by Rivest, Shamir and Adleman in 1977. Private-Key Cryptography traditional. defeat the cryptosystem. Digital Signature Algorithm (DSA) \RSA" (modulo a prime) RSA (modulo a composite) [These notes come from Fall 2001. also. To decode a character, you must first Asymmetric actually means that it works on two different keys i.e. 2. p and q are not too close (one should be a few decimal digits longer). A lot ofthe time it is possible to come up with a provably fast algorithm,that doesn't solve the problem exactl… Once this is transmitted, the private key is used to decrypt the message which is sent, encrypted by IDEA. Lecture Notes, Week 6 1 RSA Security Several possible attacks on RSA are discussed below and their relative computational difﬁculties discussed. java.math package contains a class named BigInteger that can be used to Also note that d just happened to equal e in this example. It provides confidentiality and digital signatures. Lecture 12: RSA Encryption and Primality Testing 12-3 12.3 Primality testing 12.3.1 Fermat witness Due to Fermat’s little theorem, if a number nis prime, then for any 1 a