How many weak-keys exists in T-310?

Abstract

T-310 is an important Cold War cipher. The cipher is extremely
complex and it outputs extremely few bits from the internal
state. A recent paper [6] shows an example of a highly anomalous key
such that T-310 can be broken by a slide attack with a decryption oracle.
In this paper we show that the same attacks are ALSO possible for
regular keys which satisfy all the ocial KT1 requirements. Tow other
recent papers [3, 5] show that some of the KT1 keys are very weak w.r.t
Linear Cryptanalysis. In this paper we show that a vast number of such
weak keys exist and study the exact pre-conditions which make them
weak. In addition we introduce a new third class of weak keys for RKDC
(Related-Key Dierential Cryptanalysis). We show that the original designers
in the 1970s have ensured that these RKDC properties cannot
happen for 4 rounds. We have discovered that these properties can happen
for as few as 5 rounds for some keys, and for 10 to 16 rounds they
become hard to avoid. The main reason why we study weak keys is to
show that none of these properties occur by accident, rather that they
are governed by precise pre-conditions which guarantee their existence,
and countless other keys with the same properties exist. Eventually this
is how interesting attacks can be found.