Foundations of Single-Decryptor Encryption

2026
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Authors: Fuyuki Kitagawa; Takashi Yamakawa
Published in: Theory of Cryptography
Publisher: Springer Nature Switzerland

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Abstract

This chapter delves into the foundations of single-decryptor encryption (SDE), a quantum cryptographic primitive that ensures decryption keys cannot be cloned. It introduces a new security notion called CPA anti-piracy security, which unifies and strengthens existing definitions. The text explores the relationships among different security notions, demonstrating that CPA anti-piracy security implies most of them. It also presents a new construction of SDE based on polynomially secure indistinguishability obfuscation (iO) and one-way functions (OWFs), which is simpler and more efficient than previous constructions. The chapter concludes with a discussion of the implications of CPA anti-piracy security for other security notions and the potential for future research in quantum cryptography.

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Abstract

Single decryptor encryption (SDE) is public key encryption (PKE) where the decryption key is an unclonable quantum state. Coladangelo, Liu, Liu, and Zhandry (CRYPTO 2021) realized the first SDE assuming subexponentially secure indistinguishability obfuscation (iO) and one-way functions (OWFs), along with the polynomial hardness of the learning with errors (LWE) assumption. Since then, SDE has played a pivotal role in recent advances in quantum cryptography. However, despite its central importance in unclonable cryptography, many fundamental questions about SDE remain unanswered. For example, a line of works has proposed various security notions for SDE, but their relationships have hardly been discussed. Moreover, while many subsequent works have adopted the construction methodology of Coladangelo et al., none have explored its improvement, leaving the possibility of a more efficient approach to SDE.

In this work, we address these fundamental questions concerning SDE. Our contributions are threefold.

New security notion: We introduce a strengthened indistinguishability-based security notion for SDE, which we call CPA\(^+\)anti-piracy security. We show that CPA\(^+\)security unifies the existing security notions for SDE, as detailed in the third item.
New construction: We present an SDE scheme that satisfies CPA\(^+\)anti-piracy security, based solely on polynomially secure iO and OWFs. In addition to relying on weaker and more general assumptions, our SDE scheme offers a significant advantage over the scheme of Coladangelo et al., as both the construction and its security proof are much simpler.
Relationships among security notions: We demonstrate that CPA\(^+\)anti-piracy security implies all existing security notions for SDE, with the sole exception of identical challenge ciphertext security proposed by Georgiou and Zhandry (EPRINT 2020). Although we do not establish a direct implication from CPA\(^+\)anti-piracy security to identical challenge ciphertext security, we provide a generic transformation from an SDE scheme satisfying the former to one achieving the latter in the quantum random oracle model. Additionally, we establish various relationships among different security notions for SDE. By combining these results with our SDE construction, we derive several new feasibility results.

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Title: Foundations of Single-Decryptor Encryption
Authors: Fuyuki Kitagawa
Takashi Yamakawa
Publisher: Springer Nature Switzerland
Book: Theory of Cryptography
Print ISBN: 978-3-032-12295-7

Electronic ISBN: 978-3-032-12296-4

Copyright Year: 2026
DOI: https://doi.org/10.1007/978-3-032-12296-4_6

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