Solving low-density subset sum problems
Journal of the ACM (JACM)
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
A New Public-Key Cipher System Based Upon the Diophantine Equations
IEEE Transactions on Computers
Cryptanalysis of a Diophantine Equation Oriented Public Key Cryptosystem
IEEE Transactions on Computers
Non-injective knapsack public-key cryptosystems
Theoretical Computer Science
Quantum Public-Key Cryptosystems
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Designs, Codes and Cryptography
New schemes for sharing points on an elliptic curve
Computers & Mathematics with Applications
Security of the redefined Liaw's broadcasting cryptosystem
Computers & Mathematics with Applications
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
New definition of density on knapsack cryptosystems
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress 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
Diophantine approximation attack on a fast public key cryptosystem
ISPEC'06 Proceedings of the Second international conference on Information Security Practice and Experience
Hiding information and signatures in trapdoor knapsacks
IEEE Transactions on Information Theory
On the security of the Merkle- Hellman cryptographic scheme (Corresp.)
IEEE Transactions on Information Theory
A polynomial-time algorithm for breaking the basic Merkle - Hellman cryptosystem
IEEE Transactions on Information Theory
A Novel Combinatorial Public Key Cryptosystem
Informatica
Cryptanalysis of a quadratic knapsack cryptosystem
Computers & Mathematics with Applications
Cryptanalysis of a quadratic compact knapsack public-key cryptosystem
Computers & Mathematics with Applications
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Knapsack-type cryptosystems were among the first public-key cryptographic schemes to be invented. Their NP-completeness nature and the high speed in encryption/decryption made them very attractive. However, these cryptosystems were shown to be vulnerable to the low-density subset-sum attacks or some key-recovery attacks. In this paper, additive knapsack-type public-key cryptography is reconsidered. We propose a knapsack-type public-key cryptosystem by introducing an easy quadratic compact knapsack problem. The system uses the Chinese remainder theorem to disguise the easy knapsack sequence. The encryption function of the system is nonlinear about the message vector. Under the relinearization attack model, the system enjoys a high density. We show that the knapsack cryptosystem is secure against the low-density subset-sum attacks by observing that the underlying compact knapsack problem has exponentially many solutions. It is shown that the proposed cryptosystem is also secure against some brute-force attacks and some known key-recovery attacks including the simultaneous Diophantine approximation attack and the orthogonal lattice attack.