International Association for Cryptologic Research (IACR)
Abstract
Censorship-circumvention tools are in an arms race against censors.
The censors study all traffic passing into and out of
their controlled sphere,
and try to disable censorship-circumvention tools
without completely shutting down the Internet.
Tools aim to shape their traffic patterns to match unblocked programs,
so that simple traffic profiling
cannot identify the tools within a reasonable number of traces;
the censors respond by deploying firewalls
with increasingly sophisticated deep-packet inspection.
Cryptography hides patterns in user data
but does not evade censorship
if the censor can recognize patterns in the cryptography itself.
In particular,
elliptic-curve cryptography
often transmits points on known elliptic curves,
and those points are easily distinguishable from uniform random strings of bits.
This paper introduces high-security high-speed elliptic-curve systems
in which elliptic-curve points are encoded so as to be indistinguishable
from uniform random strings.
At a lower level,
this paper introduces a new bijection
between strings and about half of all curve points;
this bijection is applicable to every odd-characteristic
elliptic curve with a point of order 2,
except for curves of j-invariant 1728.
This paper also presents guidelines to construct, and two examples of,
secure curves suitable for these encodings