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Computational Certified Deletion Property of Magic Square Game and its Application to Classical Secure Key Leasing

Yuki Takeuchi, Duo Xu

TL;DR

The paper presents the first construction of a computational Certified Deletion Property (CDP) achieved with classical communication by compiling the non-local Magic Square Game (MSG) using the KLVY compiler into a two-round protocol. It proves that this compilation preserves the CDP and leverages it, together with the Kitagawa–Morimae–Yamakawa framework, to realize Secure Key Leasing with a classical Lessor (cSKL) for PKE, PRF, and DS, including the first realizations for PRF-cSKL and DS-cSKL and a reduction in assumptions via Claw-State Generators (CSGs). The work further provides a technical overview of the CDP construction, including the one-shot CDP, a NICD-MSG reduction, and a parallel-repetition argument (heuristic) to achieve negligible success probabilities for quantum adversaries. Overall, it advances practical cryptographic primitives (cSKL) powered by classical communication while integrating CDP with primal cryptographic tasks. The results have potential impact on cryptographic protocols where a classical party can lease and later verify deletion of quantum-protected keys, enabling more scalable, device-independent-style security with reduced quantum infrastructure requirements.

Abstract

We present the first construction of a computational Certified Deletion Property (CDP) achievable with classical communication, derived from the compilation of the non-local Magic Square Game (MSG). We leverage the KLVY compiler to transform the non-local MSG into a 2-round interactive protocol, rigorously demonstrating that this compilation preserves the game-specific CDP. Previously, the quantum value and rigidity of the compiled game were investigated. We emphasize that we are the first to investigate CDP (local randomness in [Fu and Miller, Phys. Rev. A 97, 032324 (2018)]) for the compiled game. Then, we combine this CDP with the framework [Kitagawa, Morimae, and Yamakawa, Eurocrypt 2025] to construct Secure Key Leasing with classical Lessor (cSKL). SKL enables the Lessor to lease the secret key to the Lessee and verify that a quantum Lessee has indeed deleted the key. In this paper, we realize cSKL for PKE, PRF, and digital signature. Compared to prior works for cSKL, we realize cSKL for PRF and digital signature for the first time. In addition, we succeed in weakening the assumption needed to construct cSKL.

Computational Certified Deletion Property of Magic Square Game and its Application to Classical Secure Key Leasing

TL;DR

The paper presents the first construction of a computational Certified Deletion Property (CDP) achieved with classical communication by compiling the non-local Magic Square Game (MSG) using the KLVY compiler into a two-round protocol. It proves that this compilation preserves the CDP and leverages it, together with the Kitagawa–Morimae–Yamakawa framework, to realize Secure Key Leasing with a classical Lessor (cSKL) for PKE, PRF, and DS, including the first realizations for PRF-cSKL and DS-cSKL and a reduction in assumptions via Claw-State Generators (CSGs). The work further provides a technical overview of the CDP construction, including the one-shot CDP, a NICD-MSG reduction, and a parallel-repetition argument (heuristic) to achieve negligible success probabilities for quantum adversaries. Overall, it advances practical cryptographic primitives (cSKL) powered by classical communication while integrating CDP with primal cryptographic tasks. The results have potential impact on cryptographic protocols where a classical party can lease and later verify deletion of quantum-protected keys, enabling more scalable, device-independent-style security with reduced quantum infrastructure requirements.

Abstract

We present the first construction of a computational Certified Deletion Property (CDP) achievable with classical communication, derived from the compilation of the non-local Magic Square Game (MSG). We leverage the KLVY compiler to transform the non-local MSG into a 2-round interactive protocol, rigorously demonstrating that this compilation preserves the game-specific CDP. Previously, the quantum value and rigidity of the compiled game were investigated. We emphasize that we are the first to investigate CDP (local randomness in [Fu and Miller, Phys. Rev. A 97, 032324 (2018)]) for the compiled game. Then, we combine this CDP with the framework [Kitagawa, Morimae, and Yamakawa, Eurocrypt 2025] to construct Secure Key Leasing with classical Lessor (cSKL). SKL enables the Lessor to lease the secret key to the Lessee and verify that a quantum Lessee has indeed deleted the key. In this paper, we realize cSKL for PKE, PRF, and digital signature. Compared to prior works for cSKL, we realize cSKL for PRF and digital signature for the first time. In addition, we succeed in weakening the assumption needed to construct cSKL.

Paper Structure

This paper contains 8 sections, 5 theorems, 1 equation, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. SKL with classical lessor
  3. Modular construction of SKL protocol
  4. Our Results
  5. The first computational certified deletion property
  6. New Classical Secure Key Leasing Protocols
  7. Technical Overview
  8. A computational certified deletion property

Key Result

lemma thmcounterlemma

Given the information of $r$ after the game is over, Alice cannot guess $b$ correctly with probability $1$.

Figures (1)

  • Figure 1: The magic square used in 3x3 magic square

Theorems & Definitions (5)

  • lemma thmcounterlemma: Informal, local randomnessFM18
  • lemma thmcounterlemma: Informal, one-shot computational certified deletion property
  • lemma thmcounterlemma: Informal, classical secure key leasing
  • lemma thmcounterlemma: Informal, one-shot computational certified deletion property
  • lemma thmcounterlemma: Theorem 6.1 from KMP+25