An Efficient Quantum Collision Search Algorithm and Implications on Symmetric Cryptography
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The CNS algorithm has O(N^{2/5}) query complexity using O(N^{1/5}) classical memory.
“In ASIACRYPT 2017, Chailloux, Naya-Plasencia, and Schrottenloher suggested a new quantum collision finding algorithm, called CNS algorithm, of O(N 2/5 ) query complexity using O(N 1/5 ) classical memory [11].”
From Time–space complexity of quantum search algorithms in symmetric cryptanalysis: applying to AES and SHA-2 (2018) · cites this paper as [11]
With optimal parameters l=d/2 and d=2n/5, the CNS algorithm finds a collision in T_q=O(N^{2/5}) with S_c=O(N^{1/5}).
“With the optimal parameters l = d/2 and d = 2n/5, a collision is found in T q = O(N 2/5 ) with S c = O(N 1/5 ).”
From Time–space complexity of quantum search algorithms in symmetric cryptanalysis: applying to AES and SHA-2 (2018) · cites this paper as [11]
If S_q=2^s, the CNS time complexity becomes O(2^{(n-d-l-s)/2}(2^{d/2}+2^l)+2^{l+d/2-s}) for s≤min(l,n-d-l); when l=d/2 and d=2/5(n+s), the complexities satisfy (T_q)^5(S_q)^3=O(N^2) and T_q(S_c)^3=O(N).
“If S q = 2 s , time complexity becomes O(2 (n-d-l-s)/2 (2 d/2 + 2 l ) + 2 l+d/2-s ) for s ≤ min(l, ndl).When l = d/2 and d = 2/5{n + s}, the complexities satisfy (T q ) 5 (S q ) 3 = O(N 2 ) and T q (S c ) 3 = O(N ).”
From Time–space complexity of quantum search algorithms in symmetric cryptanalysis: applying to AES and SHA-2 (2018) · cites this paper as [11]
Cites
A fast quantum mechanical algorithm for database search
Grover, L. K. (1996) · Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 · doi:10.1145/237814.237866 · Cited by 8,830 · see citing works
Algorithms for quantum computation: discrete logarithms and factoring
Shor, P. W. (2002) · Proceedings 35th Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1994.365700 · Cited by 8,713 · see citing works
Applying Grover’s Algorithm to AES: Quantum Resource Estimates
Grassl, M., Langenberg, B., Roetteler, M., & Steinwandt, R. (2016) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-29360-8_3 · Cited by 299 · see citing works
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Kim, P., Han, D., & Jeong, K. C. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-2107-3 · Cited by 80 · see citing works
Quantum reversible circuit of AES-128
Almazrooie, M., Samsudin, A., Abdullah, R., & Mutter, K. N. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-1864-3 · Cited by 75 · see citing works
- Authors
- Chailloux, A., Naya-Plasencia, M., & Schrottenloher, A.
- Affiliations
- Institut national de recherche en sciences et technologies du numérique (FR)
- Corresponding author
- Chailloux, André
- Venue
- Lecture Notes in Computer Science
- Publisher
- Springer International Publishing
- Published
- 2017
- Volume
- 10625
- Pages
- 211-240
- ISSN
- 0302-9743 (ISSN-L)
- 1611-3349
- OpenAlex
- W2768789137
- Cited by
- 106
- References
- 3
- Citations by year
- 2026: 5 · 2025: 10 · 2024: 13 · 2023: 13 · 2022: 18 · 2021: 19 · 2020: 11 · 2019: 8 · 2018: 7 · 2017: 2
- FWCI
- 3.49
- Type
- conference paper
- Language
- en
- Open access
- closed
- Licence
- Locations
- Lecture notes in computer science (publishedVersion)
- HAL (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Cryptographic Implementations and Security
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- amplitude amplification, Grover's algorithm, symmetric encryption, block cipher modes of operation, quantum cryptanalysis, post-quantum security, query complexity, time complexity, parallelization, SHA-3
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