# Parameterizing adversaries with security parameters

In many cryptographic games, the adversary doesn't seem to be parameterized by the security parameter.‡ Are such games equivalent to variants in which the adversary is parameterized by the security parameter?‡‡

‡ E.g., Bellare et al.'s IND-CPA (Crypto'98) defines: $$(pk,sk) \leftarrow K(1^k)$$; $$(x_0,x_1,s) \leftarrow A_1(pk); ...$$, i.e., $$A_1$$ isn't taking $$1^k$$.

‡‡ E.g., is the game above equivalent to: $$(pk,sk) \leftarrow K(1^k)$$; $$(x_0,x_1,s) \leftarrow A_1(pk,1^k); ...$$.

• If you mean "making the adversary depend on the seu-curity parameter", you may want to look into the notion of non-uniformity. – fkraiem Jun 22 '16 at 16:10
• I meant is A(k) more powerful than A(), where k is a security parameter and A is the adversary. I suspect they are not, but I don't understand why. Perhaps A() can find k by brute force, thus k isn't needed. Or ... – user2768 Jun 22 '16 at 16:59
• What do you mean by "more powerful"? – fkraiem Jun 22 '16 at 17:13
• @user2768 Can you give an example of a scheme in which A() is not taking the security parameter as an input? – curious Jun 22 '16 at 20:31
• @fkraiem, "more powerful" as in can A() simulate A(k)'s challenger. – user2768 Jun 23 '16 at 7:36