A pseudorandom code is a keyed error-correction scheme with the property that any polynomial number of encodings appear random to any computationally bounded adversary. We show that the pseudorandomness of any code tolerating a constant rate of random errors cannot be based on black-box reductions to almost any generic cryptographic primitive: for instance, anything that can be built from random oracles, generic multilinear groups, and virtual black-box obfuscation. Our result is optimal, as Ghentiyala and Guruswami (2024) observed that pseudorandom codes tolerating any sub-constant rate of random errors exist using a black-box reduction from one-way functions. The key technical ingredient in our proof is the hypercontractivity theorem for Boolean functions, which we use to prove our impossibility in the random oracle model. It turns out that this easily extends to an impossibility in the presence of ``crypto oracles,'' a notion recently introduced -- and shown to be capable of implementing all the primitives mentioned above -- by Lin, Mook, and Wichs (EUROCRYPT 2025).

翻译：伪随机码是一种带密钥的纠错方案，其特性是任何多项式数量的编码对任何计算受限的敌手而言都呈现随机性。我们证明，任何能容忍恒定随机错误率的码的伪随机性，都无法基于黑盒归约到几乎所有通用密码学原语：例如，任何可从随机预言机、通用多线性群和虚拟黑盒混淆构建的原语。我们的结果是最优的，因为Ghentiyala和Guruswami（2024）观察到，使用单向函数的黑盒归约可以构造出能容忍任何次恒定随机错误率的伪随机码。我们证明中的关键技术要素是布尔函数的超压缩性定理，我们用它来证明在随机预言机模型中的不可能性。事实证明，这很容易扩展到存在"密码预言机"时的不可能性——这一概念由Lin、Mook和Wichs（EUROCRYPT 2025）最近提出，并被证明能够实现上述所有原语。