Grants and Contracts Details
Description
This project concerns symmetric key cryptography. It includes continued collaboration between
the PI and M. Goresky and C. Carlet. Its goal is the development of new approaches in the design
and analysis of symmetric key cryptosystems - both block and stream ciphers. A major portion of
the funding is directed toward the education and training of graduate students in Kentucky.
Broader Impact. This grant will benefit society by helping design and implement high speed
cryptographic devices. It will advance science while promoting teaching, training and learning and
will broaden participation of an underrepresented group by supporting two female PhD students.
Block and stream ciphers are essential tools for sending all but the smallest amounts of data
securely. They are used for moderate to high volumes of data, such as JPEG files, video on demand,
and digital telephony. In such ciphers, linear components such as linear feedback shift registers and
bit permutations are used because they are extremely fast and can produce excellent randomness
properties. Yet these components are vulnerable to attacks exploiting linearity. To avoid this,
nonlinear Boolean functions are used as filters in various ways. The purpose of this grant is to find
new approaches to the design of block and stream ciphers and to study nonlinear functions and
pseudorandom sequence generators for cryptography.
History indicates the cryptosystems now used will need replacement at some point. We must
be ready with tools for designing new systems. The innovations from this grant will hasten the
development of those tools and will help provide a work force that has the knowledge to use them.
Pseudorandom sequence generators are used in other areas, for example as spreading codes in
spread spectrum systems, for frequency-hopping in radar and radio systems for protection against
jamming, as codewords in error-correcting codes, in large simulations and other quasi-Monte Carlo
applications. This work will likely have an impact in these areas as well as cryptography.
The principal investigator is one of only a few university faculty members in Kentucky actively
involved in cryptographic research. This grant will help support the education of young researchers
in this vital field, including graduate students from the underrepresented state of Kentucky.
Intellectual Merit.
In a block cipher, the input is modified through a series of rounds. Each round commonly
consists of linear mixing operations plus some highly nonlinear function applied to small blocks of
input symbols and a static key. Nonlinearity and statistical randomness properties of the functions
lead to resistance to various attacks, but the static key enables various types of attack.
In a typical stream cipher fast pseudorandom sequence generators are used. Their outputs are
inputs to a nonlinear combining function whose output is used as a keystream. The keystream is
then added symbol by symbol to the message to produce the cipher. The statistical randomness
of the keystream protects against attacks based on statistical bias, and the complexity of the
combining function, as measured by various nonlinearity measures, protects against known attacks.
We propose to (1) develop new designs of block ciphers with time varying keys using pseu-
dorandom sequence generators and new architectures of Feistel networks; (2) study the effect of
replacing LFSRs by FCSRs stream ciphers; (3) study measures of randomness of Boolean functions
(e.g., bentness, resilience, strict avalanche, and correlation immunity based on new generalizations
of the Walsh transform.); (4) further analyze AFSRs, e.g. the solution of the register synthesis
problem for more general classes of AFSRs, a step in understanding the security of a large class of
stream ciphers; and (5) develop more efficient implementations of sequence generators.
Status | Finished |
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Effective start/end date | 10/1/14 → 6/30/19 |
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