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Confusion

A cryptographic design goal where the relationship between the key and the ciphertext is complex, making cryptanalysis difficult.
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The statement of the theorem

Let E:{0,1}n×{0,1}k→{0,1}mE: \{0, 1\}^n \times \{0, 1\}^k \to \{0, 1\}^m be the cryptographic function mapping plaintext MM and key KK to ciphertext CC. Confusion dictates that the relationship between CC and KK must be highly complex, ideally resisting algebraic analysis. This is formalized by requiring that the function C=E(M,K)C = E(M, K) cannot be accurately approximated by a low-degree polynomial over a finite field Fq\mathbb{F}_q:\nFor any polynomial P∈Fq[x1,…,xm] of degree d≪m, the probability P(C)=0 must be negligible.\text{For any polynomial } P \in \mathbb{F}_q[x_1, \dots, x_m] \text{ of degree } d \ll m, \text{ the probability } P(C) = 0 \text{ must be negligible.}