Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents one main result to find balanced rotation symmetric Boolean functions with maximum algebraic immunity. Through swapping the values of two orbits of rotation class of the majority function, a class of 4k＋l variable Boolean functions with maximum algebraic immu- nity is constructed. The function f（x） we construct always has terms of degree n-2 independence of what ever n is. And the nonlinearity off（x） is relatively good for large n.
We investigate the lightweight block cipher KATAN family which consists of three variants with 32, 48 and 64-bit block sizes, called KATAN32, KATAN48 and KATAN64 respectively. However, three variants all have the same key length of 80 bits. On the basis of the bit-oriented faulty model and the differential analysis principle, we describe the attack that combines differential fault attack with the meet-in-the-middle (MITM) attack on the KATAN32. More precisely, inducing a fault at a bit, we can recover some linear differential fault equations on the key bits. During solving equations, without the help of computer, we need only algebraic deduction to obtain relations of some key bits. The complexity in this process is neglectable. The secret key of the full cipher can be recovered faster than exhaustive search for all three block sizes in the KATAN family. Our result describes that KATAN32 is vulnerable.
