# MOAR codey stuff

I turned my last post on cryptography into a two-parter because there was a fair ton of stuff that I wasn’t able to cover in that particular 1200 words that I consider to be interesting/relevant, so here the rest of it comes.  I’m not going to bother for an intro this time though, so go and read my last post (if you haven’t already’ before this one to make sure we’re all on the same level here.

We all good? OK, let’s talk about public keys.

When one encodes or decodes a cipher, you perform a slightly different process when performing each process, but each process is mathematically related to the other. For example, when encrypting a Caesar cipher you ‘add three’ to the ‘value’ of each letter, and when decrypting you subtract three; the one process is the inverse of the other. These different types of key, or parts of the overall key, are known as the encryption and decryption keys. Since the two are mathematically related, knowledge of the one allows an enemy cryptanalyst to discover the other with relative ease in most cases; thus, both keys have to be kept very secret to avoid exposure, and making the distribution of keys a dangerous business.

However, in the RSA algorithms talked about at the end of the last post the tool for its encryption (the massive number M and the power P it is raised to) are no use to a foe if he does not have the two prime factors of M needed to decrypt it (I still don’t get how that works mathematically) with any degree of ease. Thus the encryption key needed to send messages to a person secretly can be distributed freely and be known to anyone who wants to, without fear of these secret messages being decoded; incredibly useful for spy networks, since it allows multiple operatives to use the same key to send messages to someone without fear that the capture of one agent could compromise everyone else’s security. In this kind of cryptography, the key distributed publically and which anyone can access is known as the ‘public key’, whilst the secret key used to decrypt it is called the ‘private key’.

RSA algorithms are not the only methods employed in public key cryptography, but any cryptographical methods it does employ are inherently secure ones. Public and private keys have other uses too beyond secure encryption; when encrypting a message using somebody else’s public key, it is possible to add a digital ‘signature’ using your private key. The recipient of your message, upon decrypting it with their private key, can then use your public key and a special algorithm to verify your signature, confirming that the message came from you (or at least someone in possession of your private key- I still don’t know how the maths works here). You can also ‘share’ private and public keys with another person to produce a ‘shared secret’, but here my concept of what the hell is going on takes another large step back so I think I’ll leave this subject there.

Despite all its inherent security, there is one risk still associated with public-key cryptography and techniques similar to the RSA algorithm. The weak link lies in the key itself; the transferring of a private key is (mostly) only ever necessary when old lines of communication are insecure, meaning that a key can often be intercepted by a sharp enemy cryptanalyst. If he is smart, he’ll then send the key straight on to its intended recipient, meaning they are likely to carry on using it oblivious of the fact that the other side can intercept and translate every message sent to him. Therefore, it is advantageous to remove this weak link by ensuring the recipient can tell if the message has been intercepted; and here we enter the weird and wonderful world of quantum cryptography.

The name is actually a misnomer; quantum theory and effects cannot be used to encrypt secure messages, and the term refers to two ideas that are only related to cryptography. One is the theoretical possibility that future quantum computers may be able to crack the RSA problem and throw the world of cryptanalysis wide open again, whilst the other, far more practical, side of things refers to this method of confirming that a message has not bee intercepted (known as quantum key distribution, or QKD). The theory behind it is almost as hard to get your head around as the maths of the RSA algorithm, but I’ll try to explain the basics. The principle behind it concerns Heisenberg’s uncertainty principle; the idea that attempting to observe a quantum effect or system will change it in some way (just go with it). The two parties sending a message to one another communicate in two ways; one via a ‘quantum link’ with which to send the secret message, and another via an open channel (e.g. the internet). The first party (who convention dictates is called Alice) sends her message via the quantum channel, polarising each bit of quantum data in one of two types of direction (just go with it). The receiving party (traditionally called Bob) receives this polarised quantum data, but since he doesn’t know which type of polarisation Alice has uses he just picks one at random each time (just go with it). About half of the time, therefore, he’ll get the right answer. Alice then tells him over the open channel which polarisation she used for each bit (usually, for reasons of speed, this is all done automatically via computer), and Bob tells her which type of polarisation he checked for each bit. They both discard the ones where they did it a different way around, and keep the ones where they did it the same way as a shared key- thus is the key exchanged.

However, if somebody (Eve, conventionally) has been eavesdropping on this little conversation and has measured the polarisation of the quantum bits, then the polarisation of the bits will have been changed by this process (just go with it). This introduces error into Bob’s reading, some of which can just be put down to the mechanics of the process; if, however, more than p bits show an error (p is picked to be a suitable number- I couldn’t give you an example), then the line and key is presumed to be insecure and the whole process is started again. Simple, isn’t it?

Despite all the bother and complexity about these processes however, it is still acknowledged that perhaps the best way to conceal a message’s content is to simply hide the thing very, very well. The Egyptians would frequently tattoo a message into a slave’s head, send him to the recipient and then let him shave his head afterwards, but a more advanced version was employed during WW2 as a direct link between Franklin D. Roosevelt and Winston Churchill. Both had a set of identical tracks of white noise (ie random sound), which they would ‘add’ to a recorded audio message and their counterpart would ‘subtract’ when it got to the other end. The random nature of white noise made the link impossible to break (well, at the time; I don’t know what a computer might be able to do to with it) without access to the original track. The code was used throughout the war, and was never broken.