In cryptography, the branch number is a numerical value that characterizes the amount of diffusion introduced by a vectorial Boolean function F that maps an input vector a to output vector . For the (usual [1]) case of a linear F the value of the differential branch number is produced by:
If both a and have s components, the result is obviously limited on the high side by the value (this "perfect" result is achieved when any single nonzero component in a makes all components of to be non-zero). A high branch number suggests higher resistance to the differential cryptanalysis: the small variations of input will produce large changes on the output and in order to obtain small variations of the output, large changes of the input value will be required. [2]
The term was introduced by Daemen and Rijmen in early 2000s and quickly became a typical tool to assess the diffusion properties of the transformations. [1]
The branch number concept is not limited to the linear transformations, Daemen and Rijmen provided two general metrics: [3]
In cryptography, the branch number is a numerical value that characterizes the amount of diffusion introduced by a vectorial Boolean function F that maps an input vector a to output vector . For the (usual [1]) case of a linear F the value of the differential branch number is produced by:
If both a and have s components, the result is obviously limited on the high side by the value (this "perfect" result is achieved when any single nonzero component in a makes all components of to be non-zero). A high branch number suggests higher resistance to the differential cryptanalysis: the small variations of input will produce large changes on the output and in order to obtain small variations of the output, large changes of the input value will be required. [2]
The term was introduced by Daemen and Rijmen in early 2000s and quickly became a typical tool to assess the diffusion properties of the transformations. [1]
The branch number concept is not limited to the linear transformations, Daemen and Rijmen provided two general metrics: [3]