Quantum Analysis of AES Lowering Limit of Quantum Attack Complexity
TLDR
This work presents the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.Abstract:
. Quantum computing is considered among the next big leaps in the computer science. While a fully functional quantum computer is still in the future, there is an ever-growing need to evaluate the security of the secret-key ciphers against a potent quantum adversary. Keeping this in mind, our work explores the key recovery attack using the Grover’s search on the three variants of AES (-128, -192, -256) with respect to the quantum implementation and the quantum key search using the Grover’s algorithm. We develop a pool of implementations, by mostly reducing the circuit depth metrics. We consider various strategies for optimization, as well as make use of the state-of-the-art advancements in the relevant fields. In a nutshell, we present the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.’s Asiacrypt’20 paper by more than 98 percent for all variants of AES. Our qubit count - Toffoli depth product is improved from theirs by more than 75 percent. Furthermore, we analyze the Jaques et al.’s Eurocrypt’20 implementations in details, fix its bugs and report corrected benchmarks. To the best of our finding, our work improves from all the previous works (including the recent Eprint’22 paper by Huang and Sun) in terms of Toffoli/full depth and Toffoli depth - qubit count product.read more
Citations
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References
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Book
The Design of Rijndael: AES - The Advanced Encryption Standard
Joan Daemen,Vincent Rijmen +1 more
TL;DR: The underlying mathematics and the wide trail strategy as the basic design idea are explained in detail and the basics of differential and linear cryptanalysis are reworked.
Book
Quantum Computation and Quantum Information: 10th Anniversary Edition
TL;DR: Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.
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Grover’s quantum searching algorithm is optimal
TL;DR: It is shown that for any number of oracle lookups up to about {pi}/4thinsp{radical} (N) , Grover's quantum searching algorithm gives the maximal possible probability of finding the desired element.