A fundamental research challenge in modern cryptography is understanding the necessary hardness assumptions
required to build different cryptographic primitives. Attempts to answer this question have gained
tremendous success in the last 20-30 years. Most notably, it was shown that many highly complicated primitives
can be based on the mere existence of one-way functions (i.e. easy to compute and hard to invert),
while other primitives cannot be based on such functions. This research has yielded fundamental tools
and concepts such as randomness extractors and computational notions of entropy. Yet many of the most
fundamental questions remain unanswered.
Our first goal is to answer the fundamental question of whether cryptography can be based on the
assumption that P not equak NP. Our second and third goals are to build a more efficient symmetric-key cryptographic
primitives from one-way functions, and to establish effective methods for security amplification of
cryptographic primitives. Success in the second and third goals is likely to have great bearing on the way
that we construct the very basic cryptographic primitives. A positive answer for the first question will be
considered a dramatic result in the cryptography and computational complexity communities.
To address these goals, it is very useful to understand the relationship between different types and
quantities of cryptographic hardness. Such understanding typically involves defining and manipulating
different types of computational entropy, and comprehending the power of security reductions. We believe
that this research will yield new concepts and techniques, with ramification beyond the realm of foundational
cryptography.
