# how to break AES [duplicate]

why is breaking a (asymmetric) 1024 bit RSA key less difficult than breaking a 128 bit (symmetric) AES key? Breaking RSA key involves finding the prime factors of a large number. What is involved in breaking an AES key?

• I should say: Breaking RSA key involves finding the prime factors of a 1024-bit semi-prime. What is involved in breaking an 128-bit AES key? Nov 11, 2021 at 12:36
• You might think about the different ways an AES key can be created. Nov 11, 2021 at 13:31
• For AES, almost all are listed here: Has AES-128 been fully broken?. And, you are comparing apples and oranges. Nov 11, 2021 at 16:39

• The most efficient attack on RSA is factoring the modulus with the General Number Field Sieve. The complexity is $$L_n\left[1/3, \sqrt{64/9} \right]$$, for a number of length $$log(n)$$. For large numbers, this is super-polynomial, but much, much less than exponential in the number of bits of $$n$$.
• For AES, the most efficient attacks are quite close to the actual bitlength of the key. The best known attack on AES 128 has complexity $$2^{126}$$, which is usually called "126 bits" of security.