Sibleyras 之可调 FX 构造的量子 Q1 安全性

The FX construction FX_k,k′[E](x) = E_k (x ⊕ k′) ⊕ k′ transforms a block cipher E: {0, 1}^κ ×{0, 1}ⁿ → {0, 1}ⁿ with κ-bit keys into a block cipher with (κ+n)-bit keys. It ensures^κ+n bits 2 security in the classical setting and^κ+n bits security in the quantum Q1 setting. Alagic et al. proposed 3 a so-called tweakable FX construction, which is defined as (Formula Presented). It constructs a tweakable block cipher from a (classical) block cipher and two auxiliary functions f₁ and f₂ . Alagic proved min{n/2, (κ + n)/3} bits quantum Q1 security for this construction. Interestingly, Sibleyras proposed another model of tweakable FX construction, which is defined as (Formula Presented). In Sibleyras’s construction, the block cipher E is invoked with a tweak-dependent key g(k_g, t). In the classical setting, Sibleyras’s construction was proved to ensure (κ + n)/2 bits security, and a natural question is whether it enjoys (κ + n)/3 bits quantum Q1 security. This study answers this question positively. By adapting a number of distributions in the proofs of Alagic et al. and Guo et al., it is proved that Sibleyras’s tweakable FX construction yields a tweakable block cipher with (κ + n)/3 bits quantum Q1 security. The gap between security bounds of Sibleyras’s and Alagic’s constructions indicates that minor modifications to cryptographic constructions may incur significant influences.