Abstract
We introduce a new construction method of diffusion layers for
Substitution Permutation Network (SPN) structures along with its
security proofs. The new method can be used in block ciphers, stream
ciphers, hash functions, and sponge constructions. Moreover, we define a
new stream cipher mode of operation through a fixed pseudorandom
permutation and provide its security proofs in the indistinguishability
model. We refer to a stream cipher as a Small Internal State Stream
(SISS) cipher if its internal state size is less than twice its key
size. There are not many studies about how to design and analyze SISS
ciphers due to the criterion on the internal state sizes, resulting from
the classical tradeoff attacks. We utilize our new mode and diffusion
layer construction to design an SISS cipher having two versions, which
we call DIZY. We further provide security analyses and hardware
implementations  of DIZY. In terms of area cost, power, and energy
consumption, the hardware performance is among the best when compared to
some prominent stream ciphers, especially for frame-based encryptions
that need frequent initialization. Unlike recent SISS ciphers such as
Sprout, Plantlet, LILLE, and Fruit; DIZY does not have a keyed update
function, enabling efficient key changing.Â