Solving low-density subset sum problems
Journal of the ACM (JACM)
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Improved low-density subset sum algorithms
Computational Complexity
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Generalized Birthday Problem
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Improving Implementable Meet-in-the-Middle Attacks by Orders of Magnitude
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
New generic algorithms for hard knapsacks
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Decoding random binary linear codes in 2n/20: how 1 + 1 = 0 improves information set decoding
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Tightly-Secure signatures from lossy identification schemes
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Faster algorithm for solving hard knapsacks for moderate message length
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Towards super-exponential side-channel security with efficient leakage-resilient PRFs
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Space---Time tradeoffs for subset sum: an improved worst case algorithm
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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At Eurocrypt 2010, Howgrave-Graham and Joux described an algorithm for solving hard knapsacks of density close to 1 in time Õ(20.337n) and memory Õ(20.256n), thereby improving a 30-year old algorithm by Shamir and Schroeppel. In this paper we extend the Howgrave-Graham-Joux technique to get an algorithm with running time down to Õ(20.291n). An implementation shows the practicability of the technique. Another challenge is to reduce the memory requirement. We describe a constant memory algorithm based on cycle finding with running time Õ(20.72n); we also show a time-memory tradeoff.