Exposure-Resilient Functions and All-Or-Nothing Transforms
##
Exposure-Resilient Functions and All-Or-Nothing Transforms

Yevgeniy Dodis,
Shaih Halevi,
Eyal Kushilevitz and
Amit Sahai.

EUROCRYPT'00

### Abstract

We study the problem of *partial key exposure*. Standard
cryptographic definitions and constructions do not guarantee any
security even if a tiny fraction of the secret key is compromised. We
show how to build cryptographic primitives, in the standard model
(without random oracles), that remain secure even when an adversary is
able to learn *almost all* of the secret key.
The key to our approach is a new primitive of independent
interest, which we call an *Exposure-Resilient Function* (ERF) --
a deterministic function whose output appears random (in a perfect,
statistical or computational sense) even if *almost all* the bits
of the input are known. ERF's by themselves efficiently solve the
partial key exposure problem in the setting where the secret is simply
a random value, like in private-key cryptography. They can also be
viewed as very secure pseudorandom generators, and have many other
applications.

To solve the general partial key exposure problem, we use the
(generalized) notion of an *All-Or-Nothing Transform* (AONT), an
*invertible* (randomized) transformation T which, nevertheless,
reveals ``no information'' about x even if *almost all* the
bits of T(x) are known. By applying an AONT to the secret key of
any cryptographic system, we obtain security against partial key
exposure. To date, the only known security analyses of AONT
candidates were made in the random oracle model.

We show how to construct ERF's and AONT's with nearly optimal
parameters. Our computational constructions are based on any one-way
function. We also provide several applications and additional
properties concerning these notions.

[ postscript ]
[ back to Yevgeniy Dodis' research interests
]