An Elementary Transition to Abstract Mathematics by Effinger Gove; Mullen Gary L.;

Author:Effinger, Gove; Mullen, Gary L.;
Language: eng
Format: epub
Publisher: Taylor & Francis Group
Published: 2019-09-26T00:00:00+00:00

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which she can easily translate to “MATH IS FUN!” (At which point she rolls her eyes, wondering why he bothered to encrypt such a message.)

We finish this chapter by discussing the need for authenticity as well as security in modern digital communication. In Example 20.1 Alice decrypts Bob’s message to meet him at 8, but how can she be sure that Bob sent the message? Perhaps it was the evil Eve who actually sent it and plans to trick her into giving up her decrypting exponent d when they meet. Alice would like to know that the message from Bob is authentic. Well, it turns out that RSA can also be used to establish authenticity as well as guarantee security, via what’s called a digital signature. This can be done by having as the last packet in a message a “signature” which, unlike the main part of the message, is encoded using the sender’s public modulus and private decoding exponent.

Here’s how it works. Let us now denote Alice’s public keys by nA and eA and her private decrypting key by dA. Of course Bob can also have public and private keys which we shall denote by nB, eB and dB. Now Bob wants to send the message m and his signature s to Alice. As before he uses her public modulus and encrypting exponent on the m, but for the signature part he uses his own public modulus and his private decrypting exponent. Hence Alice receives two numbers c and t, say, which are

c = meA (mod nA); t = sdB (mod nB).

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