## CryptoDB

### Richard Lindner

#### Publications

Year
Venue
Title
2010
EPRINT
We propose a new, efficient decoding algorithm for square-free (irreducible or otherwise) Goppa codes over $\F_p$ for any prime $p$. If the code in question has degree $t$ and its average code distance is at least $(4/p)t + 1$, the proposed decoder can uniquely correct up to $(2/p)t$ errors with high probability. The correction capability is higher if the distribution of error magnitudes is not uniform, approaching or reaching $t$ errors when any particular error value occurs much more often than others or exclusively. This makes the method interesting for (semantically secure) cryptosystems based on the decoding problem for permuted and punctured Goppa codes.
2008
EPRINT
Building upon a famous result due to Ajtai, we propose a sequence of lattice bases with growing dimension, which can be expected to be hard instances of the shortest vector problem (SVP) and which can therefore be used to benchmark lattice reduction algorithms. The SVP is the basis of security for potentially post-quantum cryptosystems. We use our sequence of lattice bases to create a challenge, which may be helpful in determining appropriate parameters for these schemes.
2008
EPRINT
Building upon a famous result due to Ajtai, we propose a sequence of lattice bases with growing dimension, which can be expected to be hard instances of the shortest vector problem (SVP) and which can therefore be used to benchmark lattice reduction algorithms. The SVP is the basis of security for potentially post-quantum cryptosystems. We use our sequence of lattice bases to create a challenge, which may be helpful in determining appropriate parameters for these schemes.
2007
EPRINT
The NTRU encryption scheme is an interesting alternative to well-established encryption schemes such as RSA, ElGamal, and ECIES. The security of NTRU relies on the hardness of computing short lattice vectors and thus is a promising candidate for being quantum computer resistant. There has been extensive research on efficient implementation of the NTRU encryption scheme. In this paper, we present a new algorithm for enhancing the performance of NTRU. The proposed method is between $11$\% and $23$\% faster on average than the best previously known method. We also present a highly efficient implementation of NTRU within the Java Cryptography Architecture.
2007
EPRINT
Micciancio defined a generalization of cyclic lattices, called ideal lattices. These lattices can be used in cryptosystems to decrease the number of parameters necessary to describe a lattice by a square root, making them more efficient. He proves that the computational intractability of classic lattice problems for these lattices gives rise to provably secure one-way and collision-resistant hash functions. This provable security relies on the assumption that reducing bases of ideal lattices is similar to reducing bases of random lattices. We give an indication that lattice problems in ideal lattices do not represent the general case by providing a distinguisher, which decides in time $O(n^4)$ whether a given basis of rank $n$ spans an ideal lattice or not. Using this algorithm we perform a statistical analysis for several dimensions and show that randomly generated lattices are practically never ideal.