In 1978 three mathematicians from MIT in Cambridge, Massachusetts, published a paper which introduced the world to the concept of public key encryption. To anyone with an interest in cryptology this was a fascinating and previously unthought-of technique. Its major advantage over other methods was the way it solved the problem of key management. The significance of this was instantly realised, and the three inventors Rivest, Shamir and Adleman, soon patented their algorithms and set up a company, RSA Security, to exploit the financial implications of their discovery.
Today, the RSA algorithms underpin the majority of internet security, allowing correspondents who have never met to establish identity and secure communications without the expensive and time-consuming business of exchanging secret keys. Without this innovation, e-commerce almost certainly would not have become the phenomenon it is, and since commercial interests have largely pushed the development of the world wide web, the internet may have remained largely a technical oddity.
Back in 1978, there were three other men who were probably not so astonished at the announcements of RSA. These three were James Ellis, Clifford Cocks and Malcolm Williamson, who at that time were working for the British Government at GCHQ, in Cheltenham. These three were the true inventors of public key cryptography, and had defined a working system, which they called non-secret encryption, some four years before RSA was published.
Ellis was working at Cheltenham in the 1960's, within the Communications-Electronics Security Group (CESG), a subdivision of GCHQ, at a time when the armed forces were becoming increasingly concerned about the future of secure telecommunications. With the growth in electronic communications traffic it was becoming clear that key distribution may well be the limiting factor preventing future expansion.
Ellis was realised to be a brilliant, if eccentric, character, and he was charged with finding a solution to this dilemma. He got to work, reading a wide range of scientific reports in search of possible solutions, and in 1970, after apparently being inspired by a thirty year old report from Bell Telephone labs, he devised the proof of concept that would found the later development of public key encryption.
Unfortunately, although he knew that public key encryption was possible, he lacked the mathematical knowledge to make it work. It would appear that no-one else at GCHQ could find a solution either, and the problem was shelved for the next three years.
In 1973, Clifford Cocks started work at GCHQ, as a maths graduate fresh out of Cambridge University. Within a few weeks of him starting, he was introduced to Ellis' problem, which he grasped immediately. It only took him a half hour over lunch to work out the maths necessary to make Ellis' system a reality, and public key encryption was born.
The final pieces of the puzzle fell into place the next year when Malcolm Williamson joined GCHQ and became acquainted with Cocks' work. It was he who was responsible for developing the principles of key exchange, as was later discovered and published separately by Diffie and Hellman. By 1974, after Williamson's refinements, the system of public key encryption and digital signatures was complete, and this was four years before the announcements of Rivest, Shamir and Adleman.
GCHQ, and more specifically CESG, are government agencies involved in national security and cryptography, so it is not surprising that they kept their discovery to themselves. It is not even clear whether the system was ever even used. It is likely that these ideas were a few short years ahead of their time, however, because although the algorithms of public key encryption are highly useful, they do require substantial computer power to be practical, and this was not widely available at the time.
To claim this cache you will have to dip your toes into the murky waters of modular arithmetic, and crack the public key encryption system!
At the above co-ordinates is a box containing the log book. To claim this cache you must sign the log book as usual. Although the box is in a public place, it needs a secret number to get inside it, and there are 10,000 possibilities to choose from.
The combination to unlock the cache has been encrypted using the public key (13, 21305411) (the larger number is the modulus), and the encrypted combination is 11819932.
All you have to do is work out what private key matches this public key, and then decrypt the secret combination.
Please make sure that the cache is replaced securely once opened, and that you re-lock it, set the combination to 0-0-0-0 and replace the lock cover to keep the water out.
There is an SD card inside with a professional public key encryption program on it for the FTF