5th Assignment: Mesh Block Cipher

For this assignment I chose the Mesh Block Cipher to do some research. Because there are several variants are available (MESH-64, MESH-96, MESH-128, I'm going to focus on the MESH-64 variant.

The MESH block cipher

MESH is a block cipher designed in 2002 by Jorge Nakahara, Jr., Vincent Rijmen, Bart Preneel, and Joos Vandewalle. MESH is based directly on IDEA and uses the same basic operations.

The MESH block ciphers designs are based on the same group operations as the IDEA cipher, but with a number of novel features:

• Flexible block sizes in steps of 32 bits (the block size of IDEA is fixed at 64 bits)
• Larger MA-boxes
• Distinct key-mixing layers for odd and even rounds
• New key schedule algorithms that achieve fast avalanche and avoid the weak keys of IDEA.

The software performance of MESH ciphers are estimated to be better or comparable to that of triple-DES.

Main parameters

Mesh-64 Block Cipher


MESH-64 is a 64-bit block cipher with a 128-bit key and 8.5 rounds. The last 0.5 round is the output transformation. The key schedule for MESH-64 is:

• First, 16-bit constants ci are defined as: c0 = 1, and ci = 3 · ci−1 , i ≥ 1 with multiplication in GF(2)[x]/p(x), under the primitive polynomial p(x) = x^16 + x^5 + x^3 + x^2 + 1. The constant ‘3’ is represented by the polynomial x + 1 in GF(2).
• The 128-bit user key is partitioned into eight 16-bit words Ki , 0 ≤ i ≤ 7,  and assigned to Zj+1 = Kj ⊕ cj , 0 ≤ j ≤ 6, and Z1 = K7 ⊕ c7 .
• Finally, each subsequent 16-bit subkey is defined as follows:

for 8 ≤ i ≤ 59; ‘<<< 7' is left rotation by 7 bits; h(i) = i div 7 + 1, and l(i) = i mod 7 + 1.

Operations used:

• Bit-wise exclusive or ⊕
• Addition in Z216 
• Multiplications in GF(216 + 1)

Attacks

A number of attacks, such as truncated and impossible differentials, linear and Demirci’s attack, shows that more resources are required on the MESH ciphers than for IDEA, and indicates that both ciphers seem to have a large margin of security.

Main known attacks:

• Truncated  Differential Attack
• Linear Attack
• Impossible Differential Attack
• Demirci's Attack
• Biryukov-Demirci Attack

Performance

References:

• The MESH Block Ciphers - Jorge Nakahara Jr , Vincent Rijmen , Bart Preneel, Joos Vandewalle
• The Biryukov-Demirci Attack on IDEA and MESH Ciphers