Code and ciphers: Julius Caesar, the Enigma and the internet

(1) X precedes M with information which includes the date and time as
well as his identity, thus M is extended to a longer message M1, say,
which is something like
M1: ‘I am X, the date is 13-06-2001 and the time is 1827. M’
where M is the original message.
(2) X decrypts M1 using his private key, D X , producing a cipher message
D X (M1) which he sends to Y.
(3) Y applies X’s public encipherment key, E X, to this cipher message and so
recovers the extended message, M1, since
Now:
E X (D X (M1))�M1.
(1) Y can be sure that X sent M1 since only X can produce D X (M1).
(2) If Y claims that he received a different message, M�, X challenges Y to
produce the cipher text D X (M�). Y will be unable to do this since he
doesn’t know X’s secret key, D X .
(3) If X claims that he sent a different message, M�, to Y the latter can show
the cipher message, D X (M1), to a judge who will ask X for his secret key
so that he can check whether the message M1 was sent. Since Y doesn’t
know X’s secret key he couldn’t have constructed D X (M1). If X refuses
to give his secret key to the judge he will lose his case.
It is important that the extended message M1 includes the date and
time otherwise an old message could be substituted for M1 which would
invalidate the point made in (2) above.
Elliptic curve cryptography
Encipherment and the internet 189
In recent years an interesting method for signature verification has
received a lot of attention both in the Universities and in industry. The
method, known as Elliptic Curve Cryptography (ECC for short), is based
upon deeper mathematical ideas than the RSA algorithm and is claimed
to be more secure. The mathematics behind the method is too advanced
to be described here but interested readers are invited to turn to M28.