IDEA is a block cipher which
uses a 128-bit length key to encrypt successive 64-bit blocks of plaintext. The procedure
is quite complicated using subkeys generated from the key to carry out a series of modular
arithmetic and XOR operations on segments of the 64-bit plaintext block. The encryption
scheme uses a total of fifty-two 16-bit subkeys. These are generated from the 128-bit
subkey as follows:
- The 128-bit key is split into eight 16-bit keys which are the
first eight subkeys.
- The digits of the 128-bit key are shifted 25 bits to the left
to make a new key which is split into the next eight 16-bit subkeys.
The second step is repeated until the fifty two subkeys have
been generated.
The encryption involves modular multiplication with a modulus
of ((2^16)+1) and addition with a modulus of (2^16). The 64-bit plaintext block is split
into four 16-bit segment which we'll call p1, p2, p3 and p4. The subkeys are s1, s2, s3,
s4 ....s52.
The encryption consists of eight rounds with each round
involving the following steps:
p1 x s1 --> d1
p2 + s2 --> d2
p3 + s3 --> d3
p4 x s4 --> d4
d1 XOR d3 --> d5
d2 XOR d4 --> d6
d5 x s5 --> d7
d6 + d7 --> d8
d8 x s6 --> d9
d7 + d9 --> d10
d1 XOR d9 --> d11
d3 XOR d9 --> d12
d2 XOR d10 --> d13
d4 XOR d10 --> d14
After this process the output blocks d12, d13 are exchanged
so that d11, d13, d12 and d14 are used as input to the next round (in that order) along
with the next 6 subkeys, s7 to s12. This procedure is followed for eight rounds in total
giving four output blocks which we'll call e1, e2, e3 and e4. Four more steps using the
last four subkeys complete the encryption:
e1 x s49 --> c1
e2 + s50 --> c2
e3 + s51 --> c3
e4 x s52 --> c4
Note: for the purposes of the algorithm, a key of all zeros
is defined as being equal to 2^16 for modular multiplication steps. The final four
output blocks, c1 to c4, are re-attached to form a 64-bit block of the ciphertext. The
whole process is repeated for successive 64-bit blocks of plaintext until all of the
plaintext has been encrypted. Decryption uses exactly the same sequence of operations of
successive 64-bit blocks of the ciphertext, but with a different set of subkeys. The
decryption subkeys are worked out from the encryption subkeys being either multiplicative
or additive inverses of them. The decryption subkeys (relative to the encryption subkeys
s1 to s52) are shown in the table below:
1st round s49* s50# s51# s52* s47 s48
2nd round s43* s45# s44# s46* s41 s42
3rd round s37* s39# s38# s39* s35 s36
4th round s31* s33# s32# s34* s29 s30
5th round s25* s27# s26# s28* s23 s24
6th round s19* s21# s20# s22* s17 s18
7th round s13* s15# s14# s16* s11 s12
8th round s7* s9# s8# s10* s5 s6
Final transformation.....s1* s2# s3# s4*
sXX* = multiplicative inverse of sXX modulus ((2^16)+1)
sXX# = additive inverse of sXX modulus (2^16)
[NOTE: A subkey with all bits zero is its own multiplicative
inverse in this algorithm] |
