## CryptoDB

### Dong Hoon Lee

#### Publications

Year
Venue
Title
2008
ASIACRYPT
2007
EPRINT
In this paper, we revisit the variant of the self-shrinking generator(SSG) proposed by Chang et al. at ICISC 2006. This variant, which we call SSG-XOR was claimed to have better cryptographic properties than SSG in a practical setting. But we show that SSG-XOR has no advantage over SSG from the viewpoint of practical cryptanalysis.
2005
FSE
2005
EPRINT
Modular exponentiation in an abelian group is one of the most frequently used mathematical primitives in modern cryptography. {\em Batch verification} is to verify many exponentiations simultaneously. We propose two fast batch verification algorithms. The first one makes use of exponents with small weight, called {\em sparse exponents}, which is asymptotically 10 times faster than the individual verification and twice faster than the previous works without security loss. The second one is applied only to elliptic curves defined over small finite fields. Using sparse Frobenius expansion with small integer coefficients, we propose a complex exponent test which is four times faster than the previous works. For example, each exponentiation in one batch requires asymptotically 9 elliptic curve additions in some elliptic curves for $2^{80}$ security.
2004
FSE
2004
FSE
2004
FSE
2003
EPRINT
We apply the algebraic attacks on stream ciphers with memories to the summation generator. For a summation generator that uses $n$ LFSRs, the algebraic equation relating the key stream bits and LFSR output bits can be made to be of degree less than or equal to $2^{\lceil\log_2 n \rceil}$, using $\lceil\log_2 n \rceil + 1$ consecutive key stream bits. This is much lower than the upper bound given by previous general results.
2002
EPRINT
We investigate relations among the discrete logarithm (DL) problem, the Diffie-Hellman (DH) problem and the bilinear Diffie-Hellman (BDH) problem when we have an efficient computable non-degenerate bilinear map $e:G\times G \rightarrow H$. Under a certain assumption on the order of $G$, we show that the DH problem on $H$ implies the DH problem on $G$, and both of them are equivalent to the BDH problem when $e$ is {\it weak-invertible}. Moreover, we show that given the bilinear map $e$ an injective homomorphism $f:H\rightarrow G$ enables us to solve the DH problem on $G$ efficiently, which implies the non-existence a {\it self-bilinear} map $e:G\times G \rightarrow G$ when the DH problem on $G$ is hard. Finally we introduce a sequence of bilinear maps and its applications.