New Linear Trails and Linear Hulls of CHAM

Abstract

CHAM is a family of lightweight block ciphers with block sizes of 64 bits and 128 bits. CHAM performs very well in lightweight environments and is known to be one of the block ciphers that can be implemented with the smallest hardware area. In this paper, we evaluate the security of CHAM against linear cryptanalysis. Linear cryptanalysis is a cryptanalytic attack technique used to analyze the security of block ciphers by exploiting linear approximations of the cipher’s operations to deduce information about the secret key. We present a 36-round linear trail with correlation 2−31 of CHAM with 64-bit blocks and a 50-round linear trail with correlation 2−63 of CHAM with 128-bit blocks. Up to now, they are the best linear trails of CHAM. Furthermore, we present a 42-round linear hull with potential greater than 2−61.793 of CHAM with 64-bit blocks and a 54-round linear hull with potential greater than 2−126.394 of CHAM with 128-bit blocks. To the best of our knowledge, they are the first known linear hulls of CHAM.

Keywords

• Block cipher
• CHAM
• linear approximation
• linear cryptanalysis
• linear hull
• linear trail