Quantum Asymmetric-Key Cryptosystem based on the Worst-Case Hardness of Graph Automorphism
Akinori Kawachi, Koshiba Takeshi, Harumichi Nishimura, Tomoyuki Yamakami · arXiv (Cornell University) · 2004
We introduce a notion of ``computational indistinguishability of quantum states,'' which is a natural extension of that of probability distributions, into the study of quantum computational cryptography, and exemplify two specific quantum states suitable for the construction of a certain cryptosystem. The two quantum states (1) can be generated easily, (2) seem to be hard to distinguish without certain hidden information, and (3) can be efficiently distinguished with help of the hidden information. Exploiting these two quantum states, we develop quantum asymmetric-key cryptosystems with provable computational security. We guarantee the security of our cryptosystem by showing a quantum polynomial-time reduction from the Graph Automorphism Problem to the hardness of distinguishing two distinct quantum states that correspond to ciphertext when we choose a decryption key uniformly at random. Namely, we prove that the average-case computational security of our cryptosystems is lower-bounded by the worst-case hardness of the Graph Automorphism Problem.