The problem with a simple cipher code is that both the sending and the receiving party have to know the key. For millitary or intelligence applications, it may be possible to distribute a key through a secure network to all parties that need the key on a monthly/weekly/daily basis. So encryptions using something like AES may be used for those types of applications.
For e-commerce, there's no easy 'secure network' for distributing unique keys to the all the parties who want to trade information or do business with each other. If the key is transmitted in the first message, then anyone who intercepts the first message can also intercept all the subsequent message. So most e-commerce (including when you type information into a secure web-browser page) makes use of so-called 'public key' encryption techniques.
Public Key encryption schemes are based on finding big prime numbers. An explanation of how public key encryption works, with only one very simple equation, goes like this. Let: C = A x B, where A and B are very big prime numbers. By very big, we might mean 40, 50, or 60 digits long. The public key is C, which you can give out to the whole world, so that they can send you encrypted messages. However, the public key C only lets you encypt the message; it doesn't let you decrypt. In order to decrypt the message, you have to know A or B. Thus your computer can tell anyone in the world how to send it an encrypted message, but only your own computer knows the private keys A & B needed to decrypt the message.
For somebody to intercept the message, they need to know not only know the public key C, but also the two prime factors A & B. If C is 100 digits long, finding those factors is VERY difficult. A computer using a brute force technique (trying every number to see if it divides into C) would take many years to find A & B.
This is where the Reimann Hypothesis comes in, because it says certain things about how prime numbers are distibuted. If the Reimann Hypothesis is proved true for very large numbers, then perhaps there are smarter ways to go about searching for A & B. If instead of checking every number, a bad guy has to check only certain ranges of numbers where A & B are likely to be, it might perhaps be possible to finish the search process in a much shorter period of time, and the public key encryption systems in use today may not be nearly as secure as people believe.
That said, the world banking system isn't going to crumble overnight because of those darn mathematicians. The Reimann Hypothesis does not provide a listing of all the prime numbers, just merely a description of their distribution. It is not clear that knowing the distribution will drastically reduce the time to break specific encryption keys, or that just doubling the number of digits in the keys wouldn't be an effective countermeasure to more efficient searching. The Reimann Hypothesis has already been known for about 100 years, and most mathematicians already believe it to be true. All the mathematicians are debating is whether someone has rigorously proved it.
Hah, I knew this was alarmist eurotrash nonsense. Thanks for explaining this Captain. Besides, there are so many ways to confuse and deceive your adversaries with computer software. I'm not too concerned about the future of e-commerce.
Using your example, wouldn't it be a simple experiment to attempt to find A, B, and C in parallel using a brute-force technique and a Riemannesque search? Then with enough repetitions using different values of A, B, and C, we'd find out?
Granted, I'm an experimentalist at heart...