高阶密码学（英语：Higher Order Cryptography）（Long Version）
On Higher-Order Cryptography (Long Version)
摘要：
第二类构造在密码学中大量存在：加密和认证方案的对手，如果活跃的话，被建模为可以访问预言机的算法，即二阶算法。但是，如何使密码方案本身更高阶呢？本文回答了这个问题，首先描述了为什么高阶密码学作为一个有趣的研究对象，然后展示了概率多项式时间算法的概念如何可以推广到严格高于2阶的算法，最后证明了一些关于高阶密码学原语，即认证方案和伪随机函数存在性的肯定和否定结果。
英文摘要：
Type-two constructions abound in cryptography: adversaries for encryption and authentication schemes, if active, are modeled as algorithms having access to oracles, i.e. as second-order algorithms. But how about making cryptographic schemes themselves higher-order? This paper gives an answer to this question, by first describing why higher-order cryptography is interesting as an object of study, then showing how the concept of probabilistic polynomial time algorithm can be generalized so as to encompass algorithms of order strictly higher than two, and finally proving some positive and negative results about the existence of higher-order cryptographic primitives, namely authentication schemes and pseudorandom functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
