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Adaptive precision LLL and Potential-LLL reductions with Interval arithmetic
Lattice reduction lattice techniques
2016/5/30
Lattice reduction is fundamental in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra–Lenstra–Lovász reduction algorithm (called LLL or L3) has be...
Efficient Interval Check in the Presence of Malicious Adversaries
private interval check secure integer comparison malicious model
2016/1/7
We consider the following problem: Assuming that Alice and
Bob have an integer interval [a, e] and an integer b respectively, for a
commitment c to b, Alice and Bob jointly check whether b is within...
Computing Discrete Logarithms in an Interval
discrete logarithm problem (DLP) Discrete Logarithms
2010/12/9
We present two new low-storage algorithms for the discrete logarithm problem in an interval of size $N$. The first algorithm is based on the Pollard kangaroo method, but uses 4 kangaroos instead of th...
Using Equivalence Classes to Accelerate Solving the Discrete Logarithm Problem in a Short Interval
discrete logarithm problem (DLP) elliptic curves negation map efficiently computable group homomorphisms
2010/12/9
The Pollard kangaroo method solves the discrete logarithm problem (DLP) in an interval of size $N$ with heuristic average case expected running time approximately $2 \sqrt{N}$ group operations. A rece...
On Optimal Hash Tree Traversal for Interval Time-Stamping
analysis of algorithms implementation complexity interval time-stamping
2009/4/15
Skewed trees constitute a two-parameter family of recursively constructed
trees. Recently, Willemson proved that suitably picked skewed trees are
space-optimal for interval time-stamping. At the sam...