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Implementing Grover's on AES-based AEAD schemes.

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Area of Science:

  • Cryptography and Quantum Computing Security
  • Symmetric Key Cryptography Analysis
  • Post-Quantum Cryptography (PQC) Evaluation

Background:

  • Advancements in quantum computing necessitate evaluating the security of existing cryptographic algorithms.
  • Grover's search algorithm presents a significant threat to symmetric key cryptography by reducing search costs.
  • Embedding ciphers into quantum circuits is crucial for assessing quantum attack feasibility.

Purpose of the Study:

  • To provide the first cost estimation of Grover's key search attack against AES-based Authenticated Encryption with Associated Data (AEAD) schemes: Rocca-S, AEGIS-128, and Tiaoxin-346.
  • To analyze these attacks considering the circuit depth restrictions set by the National Institute of Standards and Technology (NIST) Post-Quantum Cryptography (PQC) standardization process.
  • To determine the security of these AEAD schemes against Grover's algorithm under specified constraints.

Main Methods:

  • Quantum circuit implementation of Rocca-S, AEGIS-128, and Tiaoxin-346 using QISKIT.
  • Estimation of attack costs using gate count and depth-times-width metrics.
  • Analysis conducted under NIST's maximum quantum circuit depth constraints.

Main Results:

  • Estimated gate counts for Grover's attack: Rocca-S (1.09 × 2^253), AEGIS-128 (1.14 × 2^124), and Tiaoxin-346 (1.22 × 2^124).
  • Under NIST's depth constraints, the analyzed AEAD schemes demonstrate security against Grover's key recovery attack.
  • The quantum circuits were successfully implemented and analyzed using the QISKIT SDK.

Conclusions:

  • The evaluated AES-based AEAD schemes (Rocca-S, AEGIS-128, Tiaoxin-346) are currently secure against Grover's search algorithm for key recovery, considering NIST's PQC depth limitations.
  • The research provides crucial insights into the practical quantum security of widely used symmetric ciphers.
  • Further research in quantum algorithm implementation and cost analysis is essential for future cryptographic security.