Exploring Unclonable Cryptography: Definitions and Limitations
Delve into the world of unclonable cryptography, understanding new definitions, constructions, and limitations. Discover the unique properties that set unclonable encryption apart from classical cryptography and explore its practical applications.
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One-out-of-Many Unclonable Cryptography: Definitions, Constructions, and More Fuyuki Kitagawa Ryo Nishimaki NTT SIL NTT SIL Some icons from Freepik www.flaticon.com
What we propose New definitions for unclonable cryptography Relaxed indistinguishability-based unclonability 1 Unclonable crypto schemes in the standard model SKE and predicate encryption Copy-protection for single-bit output point function Single-decryptor encryption Standard Def. 2 Under the new Def.
What is Unclonable Crypto? (Focusing on unclonable encryption)
Limitation of Classical Cryptography Can copy classical information as much as you want Keep a copy Store Download Copy-protection is impossible by classical cryptography Copy protection using quantum power!
Unclonable Encryption (Security) [BL20] ?? ?? ?? Pr ? = ?1= ?2 1 ?1 ?2 2+ ???? 5
Prior Works One-way secure in the standard model Broadbent-Lord (TQC 2020) Ananth-Kaleoglu (TCC 2021) 1 Indistinguishable secure in the QROM 2 Ananth-Kaleoglu-Li-Liu-Zhandry (CRYPTO 2022) Ananth-Kaleoglu-Liu (CRYPTO 2023)
Question & Main Result Q. Indistinguishable secure UE in the standard model? Big open question! This work: achieving UE in the standard model Under a relaxed definition Based on the LWE assumption
One-out-of-Many Unclonability
If n copies with prob. 1 breaking at least 1 ?+ ? 1 + 1 1 =1 2+ ?+ ?, One-out-of-Many Unclonability ? ? 1 2 2?+? 1 2 ?? ? [?] ?? ? 1 ? 1 +? 1 1 2 ? Pr ? = ? 1 1 2+ 2?+ ???? ? 9
Interpretation of New Definition ??? #???????_???????_?????? 1 See ? = 2 case Assume checking ?1and ?2answers, but looking at only one answer ??? 2???+ ??? ??? 2???+ ???+ ??? 1 +1 Both correct ?1is incorrect, ?2is correct 1 2???+ ??? +1 1 2+1 4+ ???? 2+ ???? Standard Def. says ??? ??? 1 2+ ???? expected #correct answer [Behera-Sataath20]: similar security for quantum money [Aaronson09]: focusing on expected #successful copies (given multiple instances) for copy-protection
Construction Overview [AKL23]: 1-bit scheme w/o assumptions Same as [GZ20] Multi-bit plaintext One-time strong anti-piracy SDE OM-UE OM-SDE [GZ20] s SDE is different from [CLLZ21] s SDE Watermarking extraction technique [KN22] Hash Encryption & Garbled Circuits 1-key succinct-key Ciphertext-Policy FE LWE OM: One-out-of-Many SDE: Single-Decryptor Encryption (Copy-protected decryption key)
SDE from 1-key succinct-key CPFE Derived from ? ?-dependant part is short KeyGen: ?? = ??= ??1?1 ???|?? , ?? = (?,??.??) Enc: ??.?? = ??.???(??.??,?[?]), ? ? : output ? for any input ?? = ??.??,? Dec: Recover ? from ??and ? ??.???= ? (succinct-key property) Recover ? ? ? = ? from ??.?? and ??.??? BB84 state Extracting ? from decryptor via watermarking technique [KN22] Breaking monogamy property of BB84
Other Results (One-out-of-many) copy-protection for 1-bit point function From (one-out-of-many) UE, QFHE, and tools instantiated with LWE (One-out-of-many) unclonable predicate encryption From (one-out-of-many) UE, QFHE, and tools instantiated with LWE
One-out-of-Many Unclonable Cryptography Definitions UE, Copy-protection for point functions, Unclonable PE 1 ia.cr/2023/229 Thank you! Constructions One-time secret-key multi-bit SDE and OM UE from LWE Copy-protection for 1-bit point functions and unclonable UE from UE 2
