SHAIKH SAMIUDDIN NIZAMI

SIMPLIFIED IDEA ALGORITHM SHAIKH SAMIUDDIN NIZAMI SIMPLIFIED IDEA ALGORITHM BY SHAIKH SAMIUDDIN NIZAMI BETL / F07 / 0106

SIMPLIFIED IDEA IDEA stand for The International Data Encryption Algorithm It was published in 1991 by Lai, Massey, and Murphy IDEA is a modification of the Proposed Encryption Standard (PES) The algebraic idea behind IDEA is the mixing of three incompatible algebraic operations on 16-bit blocks: bitwise XOR, addition modulo 216, and multiplication modulo 216 + 1.

SIMPLIFIED IDEA vs IDEA Plain text size = 64 bits Plain text size = 16bits Key size = 128 bits Key size = 32bits Total rounds = 8.5 Total rounds = 4.5

KEY GENERATION

SHAIKH SAMIUDDIN NIZAMI ENCRYPTION KEY Key size = 32 bits Total rounds= 4.5 we use 24 bits key for each 4 round For 5th round we use 16 bits key The bits are shifted cyclically 6 places to the left

SHAIKH SAMIUDDIN NIZAMI ENCRYPTION KEY The 32-bit key is 1101 1100 0110 1111 0011 1111 0101 1001. the bits are shifted cyclically 6 places to the left 32-bit key = 1st Shifted 6 places = 2nd Shifted 6 places = 3rd Shifted 6 places = 1101 1100 0110 1111 0011 1111 0101 1001 1101 11 0001 1011 1100 1111 1101 0110 0111 0111 00 0110 1111 0011 1111 0101 1001 0001 10 1111 0011 1111 0101 1001 1101 1100 0110 11 1100 1111 1101 0110 0111 0111 1111 00 1111 1101 0110 0111 0111 0001 1011 1100 11 1111 0101 1001 1101 1100 0110 Z1 Z2 Z3 Z4 Z5 Z6 Round 1 1101 1100 0110 1111 0011 Round 2 0101 1001* 0001 1011 Round 3 0111 0111* Round 4 1001 0110* Round 5 * denotes a shift of bits

DECRYPTION KEY Kij denotes the j-th decryption key of decryption round i. Zij denotes the jth encryption key of encryption round i. For the first decryption round: K11 =(Z51 )−1, where (Z51 )−1 denotes the multiplicative inverse of the first encryption key of encryption round 5 – the “half round” final transformation – modulo 17; K12 = −Z52 , where −Z52 denotes the additive inverse of the second encryption key of encryption round 5 modulo 16; K13 = −Z53 ; K14 = (Z54 )−1; K15 = Z45 ; and K16 = Z46 .

SHAIKH SAMIUDDIN NIZAMI DECRYPTION KEY Inverses of nibbles for addition modulo 16 Inverses of nibbles for multiplication modulo 17 Number in binary Integer Inverse in binary Inverse in integer 0000 0001 1 1111 15 0010 2 1110 14 0011 3 1101 13 0100 4 1100 12 0101 5 1011 11 0110 6 1010 10 0111 7 1001 9 1000 8 Number in binary Integer Inverse in binary Inverse in integer 0001 1 0010 2 1001 9 0011 3 0110 6 0100 4 1101 13 0101 5 0111 7 1000 8 1111 15 1010 10 1100 12 1011 11 1110 14 0000

DECRYPTION KEY Encryption key Decryption key Inverses of nibbles for multiplication modulo 17 Inverses of nibbles for addition modulo 16 Encryption key Number in binary Integer Inverse in binary Inverse in integer 0000 0001 1 1111 15 0010 2 1110 14 0011 3 1101 13 0100 4 1100 12 0101 5 1011 11 0110 6 1010 10 0111 7 1001 9 1000 8 Z1 Z2 Z3 Z4 Z5 Z6 Round 1 1101 1100 0110 1111 0011 Round 2 0101 1001* 0001 1011 Round 3 0111 0111* Round 4 1001 0110* Round 5 Number in binary Integer Inverse in binary Inverse in integer 0001 1 0010 2 1001 9 0011 3 0110 6 0100 4 1101 13 0101 5 0111 7 1000 8 1111 15 1010 10 1100 12 1011 11 1110 14 0000 * denotes a shift of bits Decryption key K1 K2 K3 K4 K5 K6 Round 1 1000 0011 1010 0101 1100 0110 Round 2 1011 0111 0100 1111 Round 3 1001 Round 4 1110 Round 5

ENCRYPTION

MULTIPLICATION 1 0 0 1 1 1 0 1 1 1 1 1 Multiplication modulo 216 + 1. 9 1 0 0 1 = 9 x 13 117 1 1 0 1 = 13 1 1 1 1 117 / 17 = 6.88 6 x 17 = 102 117 - 102 = 15 1111

ADDITION 1 1 1 0 0 1 1 0 0 1 1 Addition modulo 216 Rules: Just take starting 4 bits 1 1 0 0 1 1

BITWISE XOR 1 0 0 0 Rules: Same = 0 Diff = 1 1 0 1 0 1

BLOCK DIAGRAM X1 X2 X3 X4 Z1 Z2 Z3 Z4 Z5 Round 1 Multiply Z6 Add Bitwise XOR Three more Round Z1 Z2 Z3 Z4 Round 5 Y1 Y2 Y3 Y4

Round 1 X1 X2 X3 X4 Message = 1001 1100 1010 1100 1001 X1 1100 X2 1010 X3 1100 X4 1101 Z1 1100 Z2 0110 Z3 1111 Z4 1111 1000 0000 1010 1111 0000 1111 1000 1010 0010 1111 0011 Z5 0010 1011 1011 1101 1101 1111 Z6 1011 1000 1000 0011 1111 0000 1000 1000 0111 1000 1000 1010 0011 0011 1011 1001 0111 1011 1000 1001

Round 2 0111 X1 1011 X2 1000 X3 1001 X4 0101 Z1 1001 Z2 0001 Z3 1011 Z4 0001 0100 1001 1110 0001 1001 1000 0100 1110 1010 1000 1100 Z5 1010 1011 1011 0101 0101 1111 Z6 1011 0111 0111 0010 0001 1001 0111 0111 0110 1110 0100 1110 0010 0010 0110 1100 0110 0110 1110 1100

Round 3 0110 X1 0110 X2 1110 X3 1100 X4 1101 Z1 0110 Z2 0111 Z3 0111 Z4 1010 1100 0101 0000 1010 0101 1111 1100 0000 1100 1111 1111 Z5 1100 0100 0100 0000 0000 0011 Z6 0100 1110 1110 0010 1010 0101 1110 1110 0100 1011 1100 0000 0010 0010 1110 0010 0100 1110 1011 0010

Round 4 0100 X1 1110 X2 1011 X3 0010 X4 1111 Z1 0101 Z2 1001 Z3 1101 Z4 1001 0011 0100 1001 1001 0100 1101 0011 1001 1010 1101 1100 Z5 1010 0011 0011 1101 1101 0110 Z6 0011 1010 1010 1101 1001 0100 1010 1010 0011 1110 0011 1001 1101 1101 1110 0100 0011 1110 1110 0100

Round 5 0011 X1 1110 X2 1110 X3 0100 X4 1111 Z1 1101 Z2 0110 Z3 0111 Z4 1011 1011 0100 1011 1011 1011 0100 1011 Cipher = 1011 1011 0100 1011

DECRYPTION

BLOCK DIAGRAM X1 X2 X3 X4 K1 K2 K3 K4 K5 Round 1 Multiply K6 Add Bitwise XOR Three more Round K1 K2 K3 K4 Round 5 Y1 Y2 Y3 Y4

X1 X2 X3 X4 Round 1 Cipher = 1011 1011 0100 1011 1011 X1 1011 X2 0100 X3 1011 X4 1000 K1 0011 K2 1010 K3 0101 K4 0011 1110 1110 0100 0011 1110 1101 1110 0100 1010 1101 1100 K5 1010 0011 0011 1101 1101 0110 K6 0011 1010 1010 1101 0011 1110 1010 1010 1001 0100 1110 0100 1101 1101 0011 1001 1001 0011 0100 1001

Round 2 1001 X1 0011 X2 0100 X3 1001 X4 1000 K1 1011 K2 0111 K3 0100 K4 0100 1110 1011 0010 0100 1011 1111 1110 0010 1100 1111 1111 K5 1100 0100 0100 0000 0000 0011 K6 0100 1110 1110 0010 0100 1011 1110 1110 1010 0101 1110 0010 0010 0010 1100 0000 1010 1100 0101 0000

Round 3 1010 X1 1100 X2 0101 X3 0000 X4 0100 K1 1010 K2 1001 K3 0101 K4 0110 0110 1110 1100 0110 1110 1000 0110 1100 1010 1000 1100 K5 1010 1011 1011 0101 0101 1111 K6 1011 0111 0111 0010 0110 1110 0111 0111 0001 1001 0110 1100 0010 0010 0100 1110 0001 0100 1001 1110

Round 4 0001 X1 0100 X2 1001 X3 1110 X4 0111 K1 0111 K2 1111 K3 1110 K4 0111 1011 1000 1001 0111 1000 1111 1011 1001 0010 1111 0011 K5 0010 1011 1011 1101 1101 1111 K6 1011 1000 1000 0011 0111 1000 1000 1000 1111 0000 1011 1001 0011 0011 1000 1010 1111 1000 0000 1010

Round 5 1111 X1 1000 X2 0000 X3 1010 X4 0100 K1 0100 K2 1010 K3 1000 K4 1001 1100 1010 1100 1001 1100 1010 1100 Message = 1001 1100 1010 1100

REFERENCES A simplified idea algorithm by nick hoffman International data encryption algorithm by how-shen chang http://en.wikipedia.org/wiki/International_Data_Encryption_Algorithm

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