The computational complexity of simultaneous diophantine approximation problems
SIAM Journal on Computing
A Fortran Multiple-Precision Arithmetic Package
ACM Transactions on Mathematical Software (TOMS)
ACM Computing Surveys (CSUR)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the complexity of finding short vectors in integer lattices
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
On breaking generalized knapsack public key cryptosystems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
IEEE Transactions on Information Theory
On generating solved instances of computational problems
CRYPTO '88 Proceedings on Advances in cryptology
Cryptographic lower bounds for learnability of Boolean functions on the uniform distribution
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Parallel lattice basis reduction
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Weakness of a public-key cryptosystem based on factorizations of finite groups
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A New Identification Scheme Based on Syndrome Decoding
CRYPTO '93 Proceedings of the 13th Annual International Cryptology Conference on Advances in Cryptology
Approximating SVPinfty to within Almost-Polynomial Factors Is NP-Hard
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
The Two Faces of Lattices in Cryptology
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Non-standard approaches to integer programming
Discrete Applied Mathematics
The optimal LLL algorithm is still polynomial in fixed dimension
Theoretical Computer Science - Latin American theoretical informatics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A Measure for the Non-Orthogonality of a Lattice Basis
Combinatorics, Probability and Computing
Hardness of approximating the shortest vector problem in lattices
Journal of the ACM (JACM)
Hardness of Approximating the Closest Vector Problem with Pre-Processing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Lattice problems and norm embeddings
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Hardness of approximating the Shortest Vector Problem in high ℓp norms
Journal of Computer and System Sciences - Special issue on FOCS 2003
Designs, Codes and Cryptography
Web Intelligence and Agent Systems
A knapsack-based probabilistic encryption scheme
Information Sciences: an International Journal
Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions
Computational Complexity
Solving Medium-Density Subset Sum Problems in Expected Polynomial Time: An Enumeration Approach
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Safer parameters for the Chor-Rivest cryptosystem
Computers & Mathematics with Applications
Security of a Class of Knapsack Public-Key Cryptosystems against Low-Density Attack
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Broadcast Attacks against Lattice-Based Cryptosystems
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
From approximate to optimal solutions: constructing pruning and propagation rules
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Analysis of the efficiency of the Chor-Rivest cryptosystem implementation in a safe-parameter range
Information Sciences: an International Journal
Relationship between weight of plaintext and successful attacks in knapsack cryptosystems
Proceedings of the 2nd International Conference on Interaction Sciences: Information Technology, Culture and Human
Quadratic compact knapsack public-key cryptosystem
Computers & Mathematics with Applications
An improved low-density subset sum algorithm
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Attacking the Chor-Rivest cryptosystem by improved lattice reduction
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Noisy polynomial interpolation and noisy chinese remaindering
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Toward non-parallelizable client puzzles
CANS'07 Proceedings of the 6th international conference on Cryptology and network security
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
New definition of density on knapsack cryptosystems
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
An improved multi-set algorithm for the dense subset sum problem
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
A new construction of knapsack PKC by using a random sequence
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Basis reduction and the complexity of branch-and-bound
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
Improved generic algorithms for hard knapsacks
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Adapting density attacks to low-weight knapsacks
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Zero-knowledge proof of generalized compact knapsacks (or a novel identification/signature scheme)
ATC'06 Proceedings of the Third international conference on Autonomic and Trusted Computing
Public-key cryptographic primitives provably as secure as subset sum
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Solving medium-density subset sum problems in expected polynomial time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
New generic algorithms for hard knapsacks
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Parallel shortest lattice vector enumeration on graphics cards
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
Lower bounds of shortest vector lengths in random NTRU lattices
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Faster algorithm for solving hard knapsacks for moderate message length
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Asymmetric multi-path division communications in underwater acoustic networks with fading channels
Journal of Computer and System Sciences
New attacks for knapsack based cryptosystems
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
A note on BDD problems with λ2 -gap
Information Processing Letters
Automated simplification of large symbolic expressions
Journal of Symbolic Computation
| Hi-index | 0.02 |
The subset sum problem is to decide whether or not the 0-l integer programming problem &Sgr;ni=l aixi = M, ∀I, xI = 0 or 1, has a solution, where the ai and M are given positive integers. This problem is NP-complete, and the difficulty of solving it is the basis of public-key cryptosystems of knapsack type. An algorithm is proposed that searches for a solution when given an instance of the subset sum problem. This algorithm always halts in polynomial time but does not always find a solution when one exists. It converts the problem to one of finding a particular short vector v in a lattice, and then uses a lattice basis reduction algorithm due to A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovasz to attempt to find v. The performance of the proposed algorithm is analyzed. Let the density d of a subset sum problem be defined by d = n/log2(maxi ai). Then for “almost all” problems of density d d n, it is proved that the lattice basis reduction algorithm locates v. Extensive computational tests of the algorithm suggest that it works for densities d dc(n), where dc(n) is a cutoff value that is substantially larger than 1/n. This method gives a polynomial time attack on knapsack public-key cryptosystems that can be expected to break them if they transmit information at rates below dc(n), as n → ∞.