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Symmetric Encryption

The start of modern cryptography is not a definite thing (obviously so, as the “eras” of cryptography are just labels people use to refer to them generally) but I decided to start my timeline for modern cryptography in the 1960s, as during this time, research projects at the American company IBM (International Business Machines) led to the creation of a cipher called the Lucifer cipher. 

This cipher was one of the first block ciphers to be made. A block cipher is a cipher that operates on blocks of 128 bits at a time. This is in contrast to a stream cipher, which encrypts 1 bit of data at a time. (In a way, you could consider classical ciphers stream ciphers) If the plaintext (un-encrypted data) is smaller than 128, padding schemes will add random data to it to make it up to 128. Modes of operation define how large amounts of data are encrypted. For example, the blocks of data can be encoded separately, or maybe the encryption of one block is affected by the previous encoded block of data.

The Lucifer cipher underwent a lot of alterations, and eventually the National Bureau of Standards adopted this altered version of Lucifer as the Data Encryption Standard, or DES, in 1977. Some of the alterations made that led to DES were actually quite controversial! For example, the key size in Lucifer was 128 bits, but only 56 in DES, which worried people who thought it would have been easier to brute force as it was shorter. It’s actually rumoured that the NSA (National Security Agency) did this so that the DES wasn’t too strong for them to break. Another change they added was the inclusion of something called S-boxes, which are effective at protecting against a form of attack called differential cryptanalysis. What I found really cool was that its effectiveness wasn’t talked about until much after, which suggests that the NSA knew about differential cryptanalysis 13 years before this information went public!

The DES is no longer secure enough for modern use, and in 2001 was replaced by the AES, or the Advanced Encryption Standard, which is its direct successor and is still used today. The reason that AES is more secure than DES is that the algorithm itself is more complex, but more importantly it uses longer key lengths. Using keys that are 128, 192, or 256-bit long means that the encryption is much stronger than using the 56-bit DES.

Lucifer, DES, and AES are all symmetric ciphers as well as being block ciphers. This means that the key used to encrypt the plaintext is the same key that is used to decrypt the data. Only some block ciphers are known publicly. DES and AES are the most famous of the lot, but other ones such as IDEA, Twofish, and Serpent exist too. 

As a whole, encrypting with block ciphers is slower as the entire block must be captured to encrypt or decrypt, and if just 1 mistake is made the whole block can be altered. But, they are stronger than other ciphers. Each mode of operation also has its own pros and cons. If each block is encoded by itself then they can be encrypted in parallel (which is faster), but it’s prone to cryptoanalysis as two identical blocks of plaintext would produce two identical blocks of ciphertext, therefore revealing patterns. The other ways are much more complex and take more time to encrypt but are more secure. 

For symmetric encryption to be used, both parties need to agree on the same key for the message to be shared secretly, which is a massive problem. How can the key be transferred securely?

Key Exchange

A year before the implementation of DES, in 1976, another massive breakthrough was made. Researchers Whitfield Hellman and Martin Diffie created the Diffie-Hellman key exchange, which was a method to share encryption and decryption keys safely across an unsecured network. The way it works depends on one-way functions. Typically in maths, most functions are two-way, as using a function on a number is pretty easy to undo. However, Hellman and Diffie found out that while multiplying two prime numbers was very easy, factorising the product down to its primes again was excruciatingly difficult, and the difficulty only increases as the numbers get bigger.

Say Alice and Bob are trying to share a key using the Diffie-Hellman exchange. Firstly, both of them need to execute a function in the form G^a mod P. P must be prime, and G and P are shared publicly so Alice and Bob can agree on them. The numbers are massive (usually 2048 bits) to make it harder to brute force, and they are generated randomly. Alice and Bob each choose different numbers for a, and run their functions. They will get different answers and they share their answers with each other publicly. (This is the public key) Then, Alice and Bob run another function in the form G^a mod P, but G is set to the other person’s answer. The value of a and P stay the same, and Alice and Bob arrive at the same secret answer. The secret answer can then be used to encrypt the message! (This is the private key)

Now, let’s say Eve wanted to find out what the key was. She intercepts their messages, but even though she has the exact information Alice and Bob shared with each other, she doesn’t know what the secret key is unless she solved the original equation, making this key exchange very secure! Modular arithmetic (the mod P part of the equation) is notoriously hard to reverse. If 2048-bit numbers are used, then brute forcing it requires 2^2048 numbers.

Asymmetric Encryption

The Diffie-Hellman key exchange was huge - I mean, any technology created 50 years ago that’s still in use must be pretty good, but it really only shone for sharing keys, not for encryption. For example, the issue with sending communication such as emails using Diffie-Hellman was that both parties needed to be online for a key to be generated as information needs to be mutually shared in the process, so you couldn’t just send an email using it whenever you wanted, which was a shame. However, one particular thing it did lead to was the invention of asymmetric encryption.

In 1977, the idea of public key cryptography (also invented by Diffie) came to fruition in the form of RSA. Named after its creators (Ron Rivest, Adi Shamir, and Leonard Adleman), the RSA works by all users having a public key, which is accessible by everyone, so anyone wanting to send that user a message just needed to search for it. The sender encrypts the message with the recipient’s public key, and then when the recipient comes online they are able to decrypt it with their own private key that’s not shared with anyone. It also uses an one-way function like the Diffie-Hellman exchange, albeit a more complex one. RSA is still used today for things like sending messages or visiting secure websites, and the keys tend to be 2048 or 4096 bits long so that they are hard to break. 1024-bit RSA was disallowed in 2013.

Encrypting via public key and decrypting via private key is great for keeping sensitive information safe, but what if you encrypted with your private key and the message was decrypted with your public key? The purpose of this encryption is to prove the sender is who they say they are - if the public key can’t decrypt the message then either the wrong key was used or the message has been meddled with in transit. To keep the message secure the sender could encrypt with their private key and also the recipient’s public key so only they could decrypt and read it. If the message is particularly long, the digital signature can be applied to a hash of the original message, rather than the whole thing. The RSA was the first to have this dual functionality.

So, there we go - the two main encryption types used today: symmetric and asymmetric. Symmetric encryption is useful for large amounts of data in particular, while asymmetric is more secure, but is slower and requires more resources and therefore can be more expensive. In practice, many secure systems will use both symmetric and asymmetric ciphers. Although, the actual security of a message comes down to the length of the key used - the longer or more complex it is, the more secure the encryption is. As the number of bits increases, the total number of arrangements for these bits increases exponentially. The IBM website states that a 56-bit key could be brute forced in around 400 seconds, a 128-bit key would take 1.872 x10^37 years, while a 256-bit key would take 3.31 x10^56 years.

Going Quantum

It goes without mention as to how important modern cryptography is. These encryption methods are used to keep confidential information such as credit card details, messages, and passwords safe for users like you and me, but also maintains government security on a national level. It’s also vital for cryptocurrency and digital signatures (as mentioned before), as well as browsing secure websites.

A big threat to current cryptographic standards is the development of quantum computing, which are computers based on principles of quantum mechanics. I won’t go into detail on how quantum computers work, but using quantum mechanics they are able to do massive numbers of calculations simultaneously. Although quantum computers already exist, they aren’t powerful or capable enough to threaten our current encryption algorithms yet. But, researchers suggest that they could be able to within a decade. People could use a technique called “store now, decrypt later”, where they keep currently encrypted messages so that they can decrypt them when quantum computers are available. This could cause many problems in the future, particularly if they involve secrets on an international level.

Quantum mechanics can also be used in cryptography as well! Quantum cryptography, originally theorised in 1984 by Charles Bennett and Gilles Brassard, can be used to exchange keys even more securely than Diffie-Hellman, and is called QKD, or Quantum Key Distribution. The reason it’s so incredible is that data that’s secured using it is immune to traditional cryptographic attacks. Now, I’m no quantum physicist (or any type of physicist!) but I will try my best to explain how it works. It works by sending photons, which are light particles, from the sender (eg. Alice) to the receiver (eg. Bob). These photons are sent at different orientations and Bob can measure the photon’s polarisation when he gets them.

Let’s say that photons can be in a vertical, horizontal, or one of the two diagonal orientations. We can pass them through a polarised filter to find out what orientation they are in. The filters are also specifically oriented. A vertical filter would let the vertical photons through, block the horizontal ones, and let the diagonal ones in 50% of the time but at the cost of the ones that pass through being reoriented. Therefore, when a particular photon successfully passes through, it’s impossible to know whether it was originally diagonal or vertical. This is important as it means that it’s possible to detect if someone else has been eavesdropping as the polarisations would have been changed.

Bob can use two measurement bases to receive the photons Alice sent. One will capture vertical and horizontal orientations, and one will capture diagonal ones. Bob has no idea what orientation Alice used for each photon, so he switches between his bases randomly, and will get it wrong some of the time. This is fine, as Alice and Bob then compare to see which ones Bob got right, and the ones he correctly guessed are used as a key (each photon representing 1 bit). The key can then be used for other encryption methods, such as AES.

The reason this works is that if Eve wanted to pry, she has to guess which base to use as well when she intercepts the photons (so she will also make mistakes), but she has no way of checking whether her records are correct or not, unlike Bob. It’s impossible for her to obtain the key as well. What’s more, when she guesses wrong she will change the photon polarisation, so Alice and Bob know that she’s eavesdropping.

Quantum cryptography would have huge security benefits if implemented on a wide scale due to its ability to prevent eavesdroppers, and the fact that it would be resistant to quantum computers. However, it is still in development. One key drawback is the specific infrastructure that is needed, and fiber optic cables have a limited range. This means that the number of destinations the data could be sent to is limited, and the signal cannot be sent to more than 1 recipient at any time.

As well as quantum cryptography, the NIST (The National Institute of Standards and Technology) and other cryptographers are working on other cryptographic algorithms that would stay secure even in the face of quantum computers. Ideas include lattice-based cryptography, hash-based cryptography, and code-based cryptography among others but none of them are at a point where they can actually be implemented yet.

However, one new idea that isn’t post-quantum but is gaining traction is Elliptic Curve Cryptography. Elliptic curve cryptography (ECC) is a form of asymmetric encryption that uses different points on an elliptic curve graph to generate keys in a more efficient manner than traditional methods. It creates shorter encryption keys, which means that less resources are needed while making the keys harder to break simultaneously. Improving the security of current systems just involves lengthening the keys, which slows down the encryption/decryption process, so the fact that ECC doesn’t need to do this gives it a big advantage. It is already used by the US government, iMessage, and Bitcoin, among others. 

Sidenotes

With the maths of these encryption methods being so strong, one key vulnerability is the people that utilise these methods, which is no surprise. Side channel attacks are a way to break cryptography by using information physically leaked from it. One attack, called a TEMPEST attack, is a technique that can pick up electromagnetic transmissions from a device as far as 300m away. These are often done by the FBI, but honestly can be done quite easily by some nerd who has some money to spare and can sit in a car outside your window. By monitoring the radiation emitted from your computer screen, the attacker can spy on you and your data. Another thing that can be monitored is your power consumption. Cryptography is energy intensive, and this attack has been able to recover RSA private keys in testing. Other forms of attacks include measuring amount of time required to encrypt data, which can perhaps be used to find factors or exponents. To combat this, encryption methods can add timing noise as a countermeasure. Or, an attacker can listen to someone type to find out their passwords, but to distinguish different key presses a sophisticated machine learning model is needed. Side channel attacks have actually been around for ages but its use has been severely limited in that the attacker needs to be physically close to the victim. They could get easier with time, however, as smartphones and drones can act as microphones remotely.

Another cool thing I haven’t covered yet are hash functions, which can take in an input and map it to a string of characters that’s random but unique to the original data. The output is called a hash digest or hash value. A good hash function will mean that no two different inputs will have the same hash value, and all outputs are the same length, making it hard to guess original text length. It’s vital for digital signatures and storing passwords securely.

Finally, if anyone managed to get to the end, then thank you! I really love cryptography and I find it astounding that we’ve been able to develop it into such a complex yet intrinsic part of daily life. Honestly, I had so much fun researching for this post! Encryption and cybersecurity and the future of computing is so interesting and I’m really glad I decided to write this :)