## CryptoDB

### Jinhui Chao

#### Publications

Year
Venue
Title
2015
EPRINT
2008
EPRINT
In this paper, we present algorithms for implementation of the GHS attack to Elliptic curve cryptosystems (ECC). In particular, we consider two large classes of elliptic curves over cubic extension fields of odd characteristics which have weak covering curves against GHS attack, whose existence have been shown recently. We show an algorithm to find definition equation of the covering curve and an algorithm to transfer DLP of the elliptic curve to Jacobian of the covering curve. An algorithm to test if the covering curve is hyperelliptic is also shown in the appendix.
2006
EPRINT
In this paper, we show a general classification of cryptographically used elliptic and hyperelliptic curves which can be attacked by the Weil descent attack and index calculus algorithms. In particular, we classfy all the Weil restriction of these curves obtained by $(2,...,2)$ covering. Density analysis of these curves are shown. Explicit defintion equations of such weak curves are also provided.
2005
EPRINT
In this paper, we show explicitly the classes of elliptic and hyperelliptic curves of low genera defined over extension fields, which have weak coverings, i.e. their Weil restrictions can be attacked by either index calculus attacks to hyperelliptic curves or Diem's recent attack to non-hyperelliptic curves. In particular, we show how to construct such coverings from these curves and analyze density of the curves for them such construction is possible.
2000
ASIACRYPT
1998
ASIACRYPT
1994
CRYPTO
1991
CRYPTO