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NTRUSIGN: Digital Signatures Using the NTRU Lattice
TLDR
A mechanism to encrypt to an arbitrary collection of identities using a variant of the Boneh-Franklin identity based encryption scheme that enables a simple mechanism to drive access control to broadcast encrypted data using user identities as the public keys.
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Finding Small Roots of Univariate Modular Equations Revisited
TLDR
An alternative technique for finding small roots of univariate modular equations is described and it is compared with that taken in (Coppersmith, 1996), which links the concept of the dual lattice to the LLL algorithm.
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Approximate Integer Common Divisors
TLDR
As an application of the partial approximate common divisor algorithm, it is shown that a cryptosystem proposed by Okamoto actually leaks the private information directly from the public information in polynomial time.
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A Hybrid Lattice-Reduction and Meet-in-the-Middle Attack Against NTRU
TLDR
It is shown that by combining lattice reduction and a meet-in-the-middle strategy one can reduce the number of loops in attacking the NTRUEncrypt private key from 284.2 to 260.3, for the k = 80 parameter set.
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New Generic Algorithms for Hard Knapsacks
TLDR
This paper proposes here two new algorithms which improve on the current state-of-the-art algorithm by Schroeppel and Shamir and lowers the running time down to either $\tilde{O} (2^{0.385\, n})$ or ($2^{n/4})$ under a reasonable heuristic.
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Lattice Attacks on Digital Signature Schemes
We describe a lattice attack on the Digital Signature Algorithm (DSA) when used to sign many messages, mi, under the assumption that a proportion of the bits of each of the associated ephemeral keys,…
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The Modular Inversion Hidden Number Problem
TLDR
This work describes an algorithm for this MIHNP problem when k > (log2 p)/3 and conjecture that the problem is hard whenever k < ( log2 p/3) and shows that assuming hardness of some variants of this MIhNP problem leads to very efficient algebraic PRNGs and MACs.
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Choosing NTRUEncrypt Parameters in Light of Combined Lattice Reduction and MITM Approaches
We present the new NTRUEncrypt parameter generation algorithm, which is designed to be secure in light of recent attacks that combine lattice reduction and meet-in-the-middle (MITM) techniques. The…
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Effective LLL Reduction for Lattice Decoding
TLDR
The theoretic upper bound O(n3 log n) on the average complexity of effective LLL reduction for the i.i.d. Gaussian model of MIMO fading channels is established, which is an order lower than previously thought.
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Factoring N = prq for Large r
TLDR
An algorithm for factoring integers of the form N = prq for large r is presented and a new class of integers can be efficiently factored that is asymptotically faster than the Elliptic Curve Method.
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