# Non-Expanding, Key-Minimal, Robustly-Perfect, Linear and Bilinear Ciphers

## James L. Massey and Ueli Maurer and Muzhong Wang

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```The purposes of this paper are: (1) to give appropriate definitions of
robustly-perfect ciphers, linear ciphers and bilinear ciphers; (2) to
give two general constructions of robustly-perfect bilinear block
ciphers that do not expand the plaintext and that have the smallest
possible amount of secret key; (3) to give some isolated examples of
robustly-perfect linear stream ciphers that use less key than had been
earlier conjectured to be necessary; and (4) to suggest some possible
useful applications for robustly-perfect linear and bilinear ciphers.

Section 2 introduces the notion of a robustly-perfect block cipher and
shows the connection of such ciphers to Latin squares. Linear and
bilinear block ciphers are defined in Sections 3 and 4, respectively.
Two general constructions of non-expanding, key-minimal
robustly-perfect bilinear ciphers are also given in Section 4, and some
as-yet-unanswered questions about such ciphers are raised. Section 5
gives a tentative general definition of a linear stream cipher, and
exhibits some counterexamples to a conjecture by Massey and Rueppel on
the amount of key required in such ciphers. Finally, Section 6 suggests
some possible practical applications for robustly-perfect linear and
bilinear ciphers and points out some further open questions about such
ciphers.