 
Summary: Fast Cryptographic Primitives Based on the Hardness of
Decoding Random Linear Code
PRELIMINARY TECHNICAL REPORT
Benny Applebaum #
Abstract
Current cryptographic constructions typically involve a large multiplicative computational
overhead that grows with the desired level of security. Recently, at STOC 2008, Ishai, Kushile
vitz, Ostrovsky, and Sahai (IKOS) suggested the possibility of implementing cryptographic
primitives, while incurring only a constant computational overhead compared to insecure im
plementations of the same tasks. Surprisingly, Ishai et al showed that such highly efficient
cryptographic constructions can be realized, under plausible, yet nonstandard, intractability
assumptions.
In this paper, we show that if one is willing to accept polylogarithmic computational over
head, many constructions can be achieved under standard assumptions. Specifically, assuming
the hardness of decoding random linear code (or equivalently, hardness of learning parity with
noise), we get the following results.
1. A pseudorandom generator G : {0, 1} n
# {0, 1} 2n which doubles its input length and
can be computed in quasilinear time ”
O(n) = n · polylog(n). By plugging G in the
