Quantum Public-Key Encryption with Tamper-Resilient Public Keys

Explore the concept of Quantum Public-Key Encryption with Tamper-Resilient Public Keys from One-Way Functions. Learn about the essentials of Public-key Encryption (PKE), computational assumptions, and the implications of realizing PKE from OWFs in the quantum world. Delve into topics like statistical security, multiparty computation, and quantum-authenticated channels.

• Quantum
• Public-Key Encryption
• Tamper-Resilient
• Quantum Computing
• Cryptography

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1. Quantum Public-Key Encryption with Tamper-Resilient Public Keys from One-Way Functions Fuyuki Kitagawa (NTT), Tomoyuki Morimae (Kyoto Univ.), Ryo Nishimaki (NTT), Takashi Yamakawa (NTT & Kyoto Univ.) arXiv:2304.01800 1 Slides made by Tomoyuki Morimae

2. Public-key Encryption (PKE): (KeyGen, Enc, Dec) Receiver Sender ?? ??,?? ??????(1?) ???????:? ?? ?? ???(??,?) ?? ? ???(??,??) They do not need to share key in advance! 2

3. PKE needs computational assumption Cryptomania Multiparty computation Key exchange PKE [IR89] Zero knowledge PRGs Minicrypt OWFs Commitments SKE Digital signatures PKE needs stronger assumptions than OWFs 3 3

4. What happens in the Q world? Statistical security[BB84] ? Multiparty computation Cryptomania PKE Key exchange [BCKM21,GLSV21] Zero knowledge PRGs Minicrypt OWFs Commitments SKE Digital signatures Can we realize PKE from OWFs? 4 4

5. YES (Concurrent to [Malavolta, Walter, 2024]) 5

6. Quantum Public-key Encryption (QPKE) Receiver Sender Quantum ?? ?????(1?) ?? ?????(??) ?? ?? ???(??,?) Classical ?? ? ???(??,??) We construct QPKE from OWFs! 6

7. Subtle issue: authentication ?? should be authenticated Receiver Sender ?? ,?? ??????(1?) ??,?? ??????(1?) ?? ?? ?? ???(?? ,?) ?? ? ???(?? ,??) In classical PKE, pk is authenticated by, e.g., digital signatures 7

8. Quantum authenticated channel? Quantum authenticated channel Receiver Sender ?? ??,?? ??????(1?) However, quantum authentication channel quantum secure channel The problem becomes trivial! [Coladangelo 2023] and [Barooti, Grilo, Huguenin-Dumittan, Malavolta, Sattath, Vu, Walter, 2023] assume Q authenticated channel 8

9. In our QPKE, (1)Quantum channels are NOT authenticated (2)Classical channels are authenticated This is the same as the classical PKE 9

10. Construction 10

11. ?0,?1 0,1? ? {0,1} ?? = (?0,?1) ?? = 0 ?0 + 1 |?1 ???= 0 ?0+ 1?1 |?1 ? ???(??,??) If the adversary can distinguish ??0and ??1, it can get both ?0 and ?1. 11 [Aaronson, Atiya, Susskind, 2020] [Hhan, Morimae, Yamakawa, 2022] Q authenticated channel is necessary

12. ?? ????,?? ????.??????(1?) ? {0,1} ?? = ???? ?? = 0 ?(0) + 1 |?(1) Verify signature coherently ???= ? 0 ?(0) + 1?? 1 |?(1) If OK, the state is ? 0 ? 0 + ? 1 |? 1 12 If the adversary can distinguish ??0and ??1, it can get both ? 0 and ?(1). Many copies of ?? cannot be distributed

13. ????,?? ????.??????(1?) ? {0,1} ?? = ???? ? 0,1? ?? = (?, 0 ? 0? + 1 |?(1?)) + 1?1 |?(1?) ) ???= (?, 0 ? 0? 13 ?? is quantum

14. ????,?? ????.??????(1?) ? {0,1} ?? = ???? ? 0,1? ?? = (?, 0 ? 0? + 1 |?(1?)) Measure 0 ? 0? in the Hadamard basis to obtain ? + 1?1 |?(1?) ?? = (?,?) 14 ? = ? (0| ? 0? 1 |?(1?)) Can the receiver detect decryption error?

15. ??,?? ??????(1?) ?? ?? ???(??,?||?(?)) ?? 15

16. CCA security ?? ?? ??,?? ??????(1?) ?? ??( ?? ) Error oracle Decryption oracle / ???(??,??) 16 We give a generic compiler from CPA to CCA Such a general compiler is an open problem in classical PKE!

17. Open problems 17

18. Open problem 1: classical pk is possible? If pk is classical If pk is quantum |?? ?? ?? ?? ? |?? ?? ?? |?? ?? |?? Partial negative result shown by [Li, Li, Li, Liu, 2024] 18

19. Open problem 2: QPKE from weaker assumptions? PKE Cryptomania Multiparty computation ? Zero knowledge PRGs Minicrypt OWFs SKE Commitments Digital signatures Microcrypt OWSGs PRSGs EFI Pessiland No classical crypto 19 19

20. Thank you 20