Exercise 1.5 Primes, Powers And Square Roots Worksheet - Heinemann Maths Zone Page 6
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11Prime numbers versus terrorism
Terrorism has cost many innocent lives so far this century, and mathematics has a role to
play in stopping terrorist acts before they happen. Terrorists are able to commit these acts
because they can plan and communicate in secret. Government intelligence agencies all
over the world try to intercept terrorist computer e-mails and decode them.
At the time of the terrorist attacks in 2001, encryption or coding techniques existed that
couldn’t be cracked. These encryption techniques are based on prime numbers.
All encryption is based on a key, which is a word or a number. These keys give the
information needed to decode or decrypt the message. The keys currently most
commonly used to encrypt e-mails are numbers that are the products of two prime
numbers. To crack the code, you have to work out the original two prime numbers. When
the numbers involved are very large, this is almost impossible to do because there are so
many possibilities. The largest prime ever found has over 2 million digits in it, and there are
always new primes being found. Even the most powerful computers in the world would
take centuries to find the two primes involved in encryption. Multiplying two primes is an
effective key for encryption because it is easy to do in one direction (multiplication), but
extremely difficult to do in the other direction (finding factors).
Governments are hoping that in the future quantum computers that can process
calculations simultaneously will be able to find the two prime numbers quickly and enable
them to crack the terrorists’ codes. Breaking an encryption code is called decryption.
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