The twisted modular multiplication and addition are two of the mixing operations of the block cipher IDEA. These are used to define so-called
Multiplication-Addition (MA) structure of IDEA. Several computer programs are used to study the nonlinearity properties of these mixing operations and MA
structure of IDEA in the sense of Nyberg and Matsui. Out of these calculations it is observed that the nonlinearities become zero for some key points. From this
observation, we change the MA structure slightly to remove these cases. This is given us to define a new structure, which is called RMA structure. In this thesis, we
have compared the nonlinearity values of MA, RMA and their compositions. In the light of these comparisons, we propose a slightly modified version of IDEA,
which we call RIDEA and this seems to give us a more secure block cipher than IDEA.
 

Keywords : Block Ciphers, Nonlinearity, Cryptanalysis