## CryptoDB

### Wen-Ai Jackson

#### Publications

Year
Venue
Title
2006
EPRINT
A linear $(q^d,q,t)$-perfect hash family of size $s$ in a vector space $V$ of order $q^d$ over a field $F$ of order $q$ consists of a sequence $\phi_1,\ldots,\phi_s$ of linear functions from $V$ to $F$ with the following property: for all $t$ subsets $X\subseteq V$ there exists $i\in\{1,\ldots,s\}$ such that $\phi_i$ is injective when restricted to $F$. A linear $(q^d,q,t)$-perfect hash family of minimal size $d(t-1)$ is said to be optimal. In this paper we use projective geometry techniques to completely determine the values of $q$ for which optimal linear $(q^3,q,3)$-perfect hash families exist and give constructions in these cases. We also give constructions of optimal linear $(q^2,q,5)$-perfect hash families.
2005
EPRINT
A linear $(q^d,q,t)$-perfect hash family of size $s$ in a vector space $V$ of order $q^d$ over a field $F$ of order $q$ consists of a set $\phi_1,\ldots,\phi_s$ of linear functionals from $V$ to $F$ with the following property: for all $t$ subsets $X\subseteq V$ there exists $i\in\{1,\ldots,s\}$ such that $\phi_i$ is injective when restricted to $F$. A linear $(q^d,q,t)$-perfect hash family of minimal size $d(t-1)$ is said to be {\em optimal}. In this paper we extend the theory for linear perfect hash families based on sequences developed by Blackburn and Wild. We develop techniques which we use to construct new optimal linear $(q^2,q,5)$-perfect hash families and $(q^4,q,3)$-perfect hash families. The sequence approach also explains a relationship between linear $(q^3,q,3)$-perfect hash families and linear $(q^2,q,4)$-perfect hash families.
2004
EPRINT
Threshold schemes allow secret data to be protected amongst a set of participants in such a way that only a pre-specified threshold of participants can reconstruct the secret from private information (shares) distributed to them on system setup using secure channels. We consider the general problem of designing unconditionally secure threshold schemes whose defining parameters (the threshold and the number of participants) can later be changed by using only public channel broadcast messages. In this paper we are interested in the efficiency of such threshold schemes, and seek to minimise storage costs (size of shares) as well as optimise performance in low bandwidth environments by minimising the size of necessary broadcast messages. We prove a number of lower bounds on the smallest size of broadcast message necessary to make general changes to the parameters of a threshold scheme in which each participant already holds shares of minimal size. We establish the tightness of these bounds by demonstrating optimal schemes.
2004
EPRINT
We consider the problem of changing the parameters of an established ideal $(k,n)$-threshold scheme without the use of secure channels. We identify the parameters $(k',n')$ to which such a scheme can be updated by means of a broadcast message and then prove a lower bound on the size of the relevant broadcast. The tightness of this bound is demonstrated by describing an optimal procedure for updating the parameters of an ideal scheme.
1997
JOFC
1996
JOFC
1995
EUROCRYPT
1994
ASIACRYPT
1993
CRYPTO
1992
AUSCRYPT

#### Coauthors

S. G. Barwick (4)
Keith M. Martin (8)
Christine M. O'Keefe (6)