All About Cryptographic Bit Lengths

You’re evaluating cryptographic solutions and you come across the term bit length for various security parameters. So, what is a bit length? And what size is sufficient to secure your data? The most common bit length refers to the encryption algorithm, and another important length refers to key management.

Algorithms

In a digital system, data is represented as a sequence of bits. That is, a sequence of 0’s and 1’s. A cryptographic algorithm is the means by which an encryption device scrambles data. It is a mathematical function which converts unencrypted data (called plaintext) into encrypted data (called ciphertext). 

Most commonly encountered algorithms are block algorithms. This means that they operate on blocks of data of a fixed size, encrypting one block after another. An example is the Advanced Encryption Standard (AES) algorithm, which takes 128 consecutive bits of plaintext and transforms it into 128 bits of ciphertext. The block size of AES is said to be 128-bits. AES can be thought of as a permutation on 128-bit blocks, mapping every 128-bit sequence to a unique, seemingly unrelated 128-bit output sequence. Note: The block size does not bear directly on the encryption strength.

Cryptographic Key

Now, if the permutation is known, ciphertext can be reversed to its original plaintext state. A cryptographic algorithm prevents unauthorized parties from reversing the ciphertext by use of a key. A cryptographic key for an algorithm is a string of bits (0’s and 1’s) of a defined length called the key length. An algorithm that uses keys of length “n” is often called an n-bit algorithm. The key is used in the definition of the algorithm itself, and each distinct choice of key turns the algorithm into a distinct permutation. Without the key, the permutation is not known and the ciphertext cannot be reversed.

An adversary may attempt to decrypt ciphertext by guessing the key and using it to see if the ciphertext decrypts into something that looks like plaintext. In practice, this means testing every possible key until the one that was used is found. A key search can be time-consuming if not impossible, even with modern computers. The reason is the mathematics of exponentiation.

Inside the Math

An n-bit key is a sequence of 0’s and 1’s of length n. Since there are two possibilities for each bit in the key, there are 2ⁿ different n-bit keys. Thus, if an algorithm used an 8-bit key, there would be 2⁸ = different 256 keys to try. The number of keys grows exponentially. A 16-bit algorithm has 2¹⁶ = 65,536 keys to try, and a 32-bit algorithm has 2³² = 4,294,967,296 keys. Modern algorithms use length of 128 or 256 bits.  2²⁵⁶ is roughly the same as the estimated number of particles in the universe.

Examples of algorithms include DES (64-bit blocks, 56-bit keys), IDEA (64-bit blocks, 128-bit keys), and AES (128-bit blocks, and implementations supporting 128-, 192-, and 256-bit keys).

What Key Size is Sufficient?

How large of a key is large enough to prevent a successful key search? Computers can search through possibilities very quickly, but even they are eventually overwhelmed by the task. The following table estimates the  amount of time it would take to find the correct key on a computer capable of trying one key every microsecond (ms, a millionth of a second), as well as on a parallelized network (one in which the search is split among many computers) capable of testing a million keys every microsecond.

Length of Key	Number of Keys	Testing 1 key per ms	Testing 106 keys per ms
32 bits	232 = 4.3 x 109	231ms = 35.8 minutes	2.15 milliseconds
56 bits	256 = 7.2 x 1016	255ms = 1142 years	10 hours
128 bits	2128 = 3.4 x 1038	2127ms = 5.4 x 1024 years	5.4 x 1018 years
256 bits	2255 = 5.8 x 1076	2255ms = 1.8 x 1063 years	1.8 x 1057 years

Summing It Up

Certain things stand out from the table above. First, a 56-bit algorithm such as DES is still secure against anything except an organized parallelized effort. Second, the key space of a 128-bit algorithm is sufficiently large to resist a key search from even national-scale efforts. And finally, even if the available computing power and speed doubles every year, 128-bit keys will remain secure over our lifetimes. No computer or network of computers will be able to search every 128-bit key. For this reason, 128- and 256-bit algorithms are recommended, and bit-sizes beyond these are considered superfluous.   

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