  In this paper, we initiate a study of asymmetric all-or-nothing transforms
(or asymmetric AONTs). A (symmetric) $t$-all-or-nothing transform is a
bijective mapping defined on the set of $s$-tuples over a specified finite
alphabet. It is required that knowledge of all but $t$ outputs leaves any $t$
inputs completely undetermined. There have been numerous papers developing the
theory of AONTs as well as presenting various applications of AONTs in
cryptography and information security.
  In this paper, we replace the parameter $t$ by two parameters $t_o$ and
$t_i$, where $t_i \leq t_o$. The requirement is that knowledge of all but $t_o$
outputs leaves any $t_i$ inputs completely undetermined. When $t_i < t_o$, we
refer to the AONT as asymmetric.
  We give several constructions and bounds for various classes of asymmetric
AONTs, especially those with $t_i = 1$ or $t_i = 2$. We pay particular
attention to linear transforms, where the alphabet is a finite field
$\mathbb{F}_q$ and the mapping is linear.
