Linear Approximation Analysis: an improved technique for linear cryptanalysis of 4-bit Bijective Crypto S-Boxes

4-bit Linear Relations play an important role in Cryptanalysis of 4-bit Bijective S-Boxes. Count of existence of all 4-bit Linear Relations, for all of 16 input and output 4-bit bit patterns of 4-bit Bijective S-Boxes said as S-Boxes has been reported in Linear Cryptanalysis of 4-bit S-Boxes. In this paper a brief review of this cryptanalytic method for 4-bit S-Boxes has been introduced in a very lucid and conceptual manner. A new Analysis to search for the existing Linear Approximations among the input Boolean Functions (BFs) and output BFs of a particular 4-bit S-Box has also been introduced in this paper. The search is limited to find the existing Linear Relations or Approximations in the contrary to count the number existence among all 16 4-bit input and output bit patterns for all possible linear approximations.