Computational Indistinguishability Between Quantum States and Its Cryptographic Application

We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is “secure” against any polynomial-time quantum adversary. Our problem QSCDff is to distinguish between two types of random coset states with a hidden permutation over the symmetric group of finite degree. This naturally generalizes the commonly-used distinction problem between two probability distributions in computational cryptography. As our major contribution, we show three cryptographic properties: (i) QSCDff has the trapdoor property; (ii) the average-case hardness of QSCDff coincides with its worst-case hardness; and (iii) QSCDff is computationally at least as hard in the worst case as the graph automorphism problem. These cryptographic properties enable us to construct a quantum public-key cryptosystem, which is likely to withstand any chosen plaintext attack of a polynomialtime quantum adversary. We f...

• Type: Conference
• Year: 2005
• Where: EUROCRYPT
• Authors: Akinori Kawachi, Takeshi Koshiba, Harumichi Nishimura, Tomoyuki Yamakami
• Keywords: Cryptographic Properties, Cryptography, EUROCRYPT 2005, Quantum Adversary, Quantum Cryptographic Scheme