Measuring cypher strength It fairly simple to measure the strength of a key space, largely it's just the number of possible keys. 

But how might I measure other properties, namely, a ciphers reliance to attacks such as: 


Frequency analysis
Differential Analysis 
Linear cryptanalysis


I was hoping for examples with DES or DES contrasted with something simple like Caesar Cipher.
There is no such thing as the "strength" of the key space, just the size of the key space.

For DES and RSA the key size differs from the encoded size of the key.

DES may also contain parity bits.

For RSA the key size is usually regarded the size of the modulus as the key strength depends on the size of the modulus. But you would also have to encode the exponents and in case of the private key, possibly the CRT parameters as well. Then it is still missing padding and overhead.



Generally we still show the strength after attacks in bits. For instance, the strongest attack requires about $2^{49}$ plaintexts. As a plaintext block is $2^3$ bits, the strength of the cipher - if this attack is possible - is about 52 bits instead of the promised 56 bits. As can be seen, DES is just insecure because of the small key size rather than cryptographic weaknesses. This allows it to be used for Triple DES which may still provide adequate security even nowadays.

The original Caesar cipher just has 25 keys (not counting the 0 key of course). So the key size is 4 to 5 bits. I think we can forgo cryptanalysis here; brute force will be fastest. DES is therefore at least 47 bits stronger than the Caesar cipher.



Key size and certainly key strength can be pretty good estimates of how strong a cipher is. But never forget that these values are just extrapolations from the known attacks. We use them to simplify the world; you'd have to look into the actual attacks possible for more detailed information.

And if you use the ciphers incorrectly, you may never ever get even near the security promised.