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EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
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SIAM Journal on Computing
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Information Processing Letters
Approximating Good Simultaneous Diophantine Approximations Is Almost NP-Hard
MFCS '96 Proceedings of the 21st International Symposium on Mathematical Foundations of Computer Science
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Journal of the ACM (JACM)
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ACM Transactions on Mathematical Software (TOMS)
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SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
The LLL Algorithm: Survey and Applications
The LLL Algorithm: Survey and Applications
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EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
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EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
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We introduce the Inhomogeneous Simultaneous Approximation Problem (ISAP), an old problem from the field of analytic number theory. Although the Simultaneous Approximation Problem (SAP) is already known in cryptography, it has mainly been considered in its homogeneous instantiation for attacking schemes. We take a look at the hardness and applicability of ISAP, i. e., the inhomogeneous variant, for designing schemes. More precisely, we define a decisional problem related to ISAP, called DISAP, and show that it is NP-complete. With respect to its hardness, we review existing approaches for solving related problems and give suggestions for the efficient generation of hard instances. Regarding the applicability, we describe as a proof of concept a bit commitment scheme where the hiding property is directly reducible to DISAP. An implementation confirms its usability in principle (e. g., size of one commitment is 6273 bits and execution time is in the milliseconds).