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Theoretical Computer Science
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STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
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EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
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FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
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Cryptography and Communications
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In this paper, we introduce a new lattice reduction technique applicable to the narrow, but important class of Hypercubic lattices, (L ≅ ZN). Hypercubic lattices arise during transcript analysis of certain GGH, and NTRUSign signature schemes. After a few thousand signatures, key recovery amounts to discovering a hidden unitary matrix U, from its Gram matrix G = UUT. This case of the Gram Matrix Factorization Problem is equivalent to finding the shortest vectors in the hypercubic lattice, LG, defined by the quadratic form G. Our main result is a polynomial-time reduction to a conjecturally easier problem: the Lattice Distinguishing Problem. Additionally, we propose a heuristic solution to this distinguishing problem with a distributed computation of many "relatively short" vectors.