We are now in possession of the information required to encrypt a message, and also the information required to decrypt it. Now comes a tricky bit: the decryption index must be the multiplicative inverse of modulo :Ī small amount of experimentation shows that so is the decryption index. The encryption index must be coprime with, so we choose a small prime value. The quantity is Euler’s totient function, given by. However, for illustration, we choose two small primes, and so that. Normally, the factors are huge, making the task of splitting practically impossible. The number is chosen to be a product of two primes.
Notation for RSA system, and sample values. The notation is summarised in the Table below. The number is the private key, known only to the recipient of the message.īefore continuing, let us review the short list of important numbers required to implement the RSA system. The pair of numbers comprise the public key. The effect of the two operations is to reproduce the original number: The indices and are chosen in such a way that corresponds to the plaintext of the original message. The inverse process of decryption is achieved by raising the number to another number and again taking the remainder modulo : The resulting number,, is the ciphertext. The essential idea is simple: a message, represented by a number (for plaintext), is encrypted by raising to a high power ( for encryption) and taking the remainder modulo a large number : It has played a crucial role in computer security since its publication in 1978. The RSA encryption system is the earliest implementation of public key cryptography. The purpose of this note is to give an example of the method using numbers so small that the computations can easily be carried through by mental arithmetic or with a simple calculator. L2R: Ron Rivest, Adi Shamir, Len Adleman (2003).
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