In cryptography, security level is a measure of the strength that a cryptographic primitive — such as a cipher or hash function — achieves. Security level is usually expressed in "bits", where n-bit security means that the attacker would have to perform 2n operations to break it, but other methods have been proposed that more closely model the costs for an attacker. This allows for convenient comparison between algorithms and is useful when combining multiple primitives in a hybrid cryptosystem, so there is no clear weakest link. For example, AES-128 (key size 128 bits) is designed to offer a 128-bit security level, which is considered roughly equivalent to 3072-bit RSA.
In this context, security claim or target security level is the security level that a primitive was initially designed to achieve, although "security level" is also sometimes used in those contexts. When attacks are found that have lower cost than the security claim, the primitive is considered broken.
In symmetric cryptography
Symmetric algorithms usually have a strictly defined security claim. For symmetric ciphers, it is typically equal to the key size of the cipher — equivalent to the complexity of a brute-force attack. Cryptographic hash functions with output size of n bits usually have a collision resistance security level n/2 and a preimage resistance level n. This is because the general birthday attack can always find collisions in 2n/2 steps. For example, SHA-256 offers 128-bit collision resistance and 256-bit preimage resistance.
However, there are some exceptions to this. The Phelix and Helix are 256-bit ciphers offering a 128-bit security level. The SHAKE variants of SHA-3 are also different: for a 256-bit output size, SHAKE-128 provides 128-bit security level for both collision and preimage resistance.
In asymmetric cryptography
The design of most asymmetric algorithms (i.e. public-key cryptography) relies on neat mathematical problems that are efficient to compute in one direction, but inefficient to reverse by the attacker. However, attacks against current public-key systems are always faster than brute-force search of the key space. Their security level isn't set at design time, but represents a computational hardness assumption, which is adjusted to match the best currently known attack.
Various recommendations have been published that estimate the security level of asymmetric algorithms, which differ slightly due to different methodologies. For the RSA cryptosystem at 128-bit security level, NIST and ENISA recommend using 3072-bit keys and IETF 3253 bits. Elliptic curve cryptography requires shorter keys, so the recommendations are 256-383 (NIST), 256 (ENISA) and 242 bits (IETF).
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Meaning of "broken"
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