Solving low-density subset sum problems
Journal of the ACM (JACM)
Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Solving simultaneous modular equations of low degree
SIAM Journal on Computing - Special issue on cryptography
Improved low-density subset sum algorithms
Computational Complexity
A course in computational algebraic number theory
A course in computational algebraic number theory
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
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
A linear space algorithm for computing the hermite normal form
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Complexity of Lattice Problems
Complexity of Lattice Problems
Random Lattices and a Conjectured 0 - 1 Law about Their Polynomial Time Computable Properties
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Extended Notions of Security for Multicast Public Key Cryptosystems
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
A Lattice-Based Public-Key Cryptosystem
SAC '98 Proceedings of the Selected Areas in Cryptography
Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto '97
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Quantum Public-Key Cryptosystems
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Eliminating Decryption Errors in the Ajtai-Dwork Cryptosystem
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the Ajtai-Dwork Cryptosystem
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Tensor-Based Trapdoors for CVP and Their Application to Public Key Cryptography
Proceedings of the 7th IMA International Conference on Cryptography and Coding
A Lattice Based Public Key Cryptosystem Using Polynomial Representations
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Improving Lattice Based Cryptosystems Using the Hermite Normal Form
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
The Two Faces of Lattices in Cryptology
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
On breaking generalized knapsack public key cryptosystems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Representing hard lattices with O(n log n) bits
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A knapsack-based probabilistic encryption scheme
Information Sciences: an International Journal
Fast LLL-type lattice reduction
Information and Computation
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
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
Public-key encryption in a multi-user setting: security proofs and improvements
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Cryptanalysis of the Paeng-Jung-Ha cryptosystem from PKC 2003
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Multi-bit cryptosystems based on lattice problems
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on 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
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
An algebraic broadcast attack against NTRU
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Broadcast attacks against code-based schemes
WEWoRC'11 Proceedings of the 4th Western European conference on Research in Cryptology
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In 1988, Håstad proposed the classical broadcast attack against public key cryptosystems. The scenario of a broadcast attack is as follows. A single message is encrypted by the sender directed for several recipients who have different public keys. By observing the ciphertexts only, an attacker can derive the plaintext without requiring any knowledge of any recipient's secret key. Håstad's attack was demonstrated on the RSA algorithm, where low exponents are used. In this paper, we consider the broadcast attack in the lattice-based cryptography, which interestingly has never been studied in the literature. We present a general method to rewrite lattice problems that have the same solution in one unique easier problem. Our method is obtained by intersecting lattices to gather the required knowledge. These problems are used in lattice based cryptography and to model attack on knapsack cryptosystems. In this work, we are able to present some attacks against both lattice and knapsack cryptosystems. Our attacks are heuristics. Nonetheless, these attacks are practical and extremely efficient. Interestingly, the merit of our attacks is not achieved by exploring the weakness of the trapdoor as usually studied in the literature, but we merely concentrate on the problem itself. As a result, our attacks have many security implications on most of the lattice-based or knapsack cryptosystems.