Linear cryptanalysis of NUSH block cipher

Abstract

NUSH is a block cipher as a candidate for NESSIE. NUSH is analyzed by linear crypt-analysis. The complexity δ=(ε, η) of the attack consists of data complexity ε and time complexity η. Three linear approximations are used to analyze NUSH with 64-bit block. When |K|=128 bits, the complexities of three attacks are (2⁵⁸, 2¹²⁴), (2⁶⁰, 2⁷⁸) and (2⁶², 2⁵⁵) respectively. When |K|=192 bits, the complexities of three attacks are (2⁵⁸, 2¹⁵⁷) (2⁶⁰, 2⁹⁶) and (2⁶², 2⁵⁸) respectively. When |K| =256 bits, the complexities of three attacks are (2⁵⁸, 2¹²⁵), (2⁶⁰, 2⁷⁸) and (2⁶², 2⁵³) respectively. Three linear approximations are used to analyze NUSH with 128-bit block. When |K|=128 bits, the complexities of three attacks are (2¹²², 2⁹⁵), (2¹²⁴, 2⁵⁷) and (2¹²⁶, 2⁵²) respectively. When |K|=192 bits, the complexities of three attacks are (2¹²², 2¹⁴²), (2¹²⁴, 2⁷⁵) and (2¹²⁶, 2⁵⁸) respectively. When |K|=256 bits, the complexities of three attacks are (2¹²², 2¹⁶⁸), (2¹²⁴, 2⁸¹) and (2¹²⁶, 2⁶⁴) respectively. Two linear approximations are used to analyze NUSH with 256-bit block. When |K|=128 bits, the complexities of two attacks are (2²⁵², 2¹²²) and (2²⁵⁴, 2¹¹⁹) respectively. When |K|=192 bits, the complexities of two attacks are (2²⁵², 2¹⁸¹) and (2²⁵⁴, 2¹⁷⁷) respectively. When |K|=256 bits, the complexities of two attacks are (2²⁵², 2²⁴⁰) and (2²⁵⁴, 2²¹⁹) respectively. These results show that NUSH is not immune to linear cryptanalysis, and longer key cannot enhance the security of NUSH.