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Monday, November 16, 1998

Mathematics offers new
ways of making a mark

Security: John B. Cosgrove introduces the idea of digital signatures

"Digital history made in Dublin" was the headline (Irish Times, September 5th) after President Clinton and the Taoiseach digitally signed a US-Irish communiqué on ecommerce using cryptographic software by Baltimore Technologies (

Just what is a digital signature? It is a mathematically driven electronic form of a normal signature, a revolutionary development made possible through "publickey" cryptography.

How does it work? The following is a highly idealised comparison that captures the essential idea. Imagine that I have two paints, P (for public, and available to anyone) and S (for secret, available only to me), with these properties:

1. A surface painted with P is disguised. Subsequently painting it with S restores the original surface,

2. Conversely, a surface painted with S is disguised, but it can later be restored by painting it with P.

3. No one else can manufacture S from P.

Someone can then communicate with me by writing a message on a surface, painting over with P, and sending the painted surface to me. On receipt, by painting over with S, I recover the message.

Can the recipient have confidence the message came from the purported sender? No, not with this simple encryption.

There is, however, a solution. Suppose the sender has paints P1 and S1, with similar properties to P and S. She writes her message on a surface, and applies two disguising coats of paints: first her secret S1, then my public P.

On receipt of the doubly-disguised surface I apply two revealing coats of paint: first my secret S (stripping the top layer), then her public P1, revealing the original message. In this case the sender's identity is assured by the fact that her secret paint S1 has been used to prepare the message.

For paints in the above example, substitute mathematical concepts based on large prime numbers. The precise and beautiful mathematical ideas involved - toned (but not dumbed) down - will be covered in a public lecture next week.

"Bill Clinton, Bertie Ahern, and digital signatures" will take place in Room E201, St Patrick's College, Drumcondra, Dublin, at 8 p.m. on Wednesday, November 25th. The lecture will be given by John Cosgrave of St Patrick's College, using a computer and Maple software.

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