Преимущество противника в криптографии: анализ и оценка безопасности шифров.

In cryptography, an adversary's advantage is a measure of how successfully it can attack a cryptographic algorithm, by distinguishing it from an idealized version of that type of algorithm. Note that in this context, the "adversary" is itself an algorithm and not a person. A cryptographic algorithm is considered secure if no adversary has a non negligible advantage, subject to specified bounds on the adversary's computational resources (see concrete security). "Negligible" usually means "within O(2−p)" where p is a security parameter associated with the algorithm. For example, p might be the number of bits in a block cipher's key.

Let F be an oracle for the function being studied, and let G be an oracle for an idealized function of that type. The adversary A is a probabilistic algorithm, given F or G as input, and which outputs 1 or 0. A's job is to distinguish F from G, based on making queries to the oracle that it's given. We say:

Let F be a random instance of the DES block cipher. This cipher has 64 bit blocks and a 56 bit key. The key therefore selects one of a family of 256 permutations on the 264 possible 64 bit blocks. A "random DES instance" means our oracle F computes DES using some key K (which is unknown to the adversary) where K is selected from the 256 possible keys with equal probability. We want to compare the DES instance with an idealized 64 bit block cipher, meaning a permutation selected at random from the (264)! possible permutations on 64 bit blocks. Call this randomly selected permutation G. Note from Stirling's approximation that (264)! is around , so even specifying which permutation is selected requires writing down a number too large to represent exactly in any real computer. Viewed another way, G is an instance of a "cipher" whose "key length" is about 1021 bits, which again is too large to fit in a computer. (We can, however, implement G with storage space proportional to the number of queries, using a random oracle). Note that because the oracles we're given encrypt any plaintext of our choosing, we're modelling a chosen plaintext attack or CPA, and the advantage we're calculating can be called the CPA advantage of a given adversary. If we also had decryption oracles available, we'd be doing a chosen ciphertext attack or CCA and finding the CCA advantage of the adversary.

Call this adversary A0. It simply flips a coin and returns 1 or 0 with equal probability and without making any oracle calls. Thus, Pr[A0(F)=1] and Pr[A0(G)=1] are both 0.5. The difference between these probabilities is zero, so Adv(A0) is zero. The same thing applies if we always return 0, or always return 1: the probability is the same for both F and G, so the advantage is zero. This adversary can't tell F and G apart. If we're cipher designers, our desire (maybe not achievable) is to make it so that it's computationally infeasible for any adversary to do significantly better than this. We will have succeeded if we can make a cipher for which there's no distinguisher faster than brute force search.