Carlos Tafoya and John Kaplar

Block ciphers (a primitive of cryptography) require heavy use of bit manipulation (i.e. permutation of bits, extraction of bits, rotation of bits). This is easy in hardware, but in software this requires custom functions that are tedious to code and test.

Free, formal cryptographic languages are nonexistent.

A simple language called LIMP (Logical Imperative)

LIMP will simplify the bit manipulation that block ciphers require

Limp has a C-like syntax Currently Limp Can fully support the DES

block cipher The interpreter for LIMP is written in Java

Cryptographic languages are rare Only commercial one is called Cryptol Cryptol is a domain specific programming

language for cryptography Developed for the NSA and heavily used in

the aerospace and defense industries. Cryptol is not free! Cryptol has ML-like syntax (Yuck!! or

Yeah!!) http://www.galois.com/

Block Ciphers Definition for a Block Cipher B

◦

◦ B is a function that takes an n-bit plaintext (i.e. the message), a k-bit key and produces an n-bit cipher-text (i.e. the encrypted message)

N = {0,1} , the set of all n-bit binary strings

{0,1} , the set of all k-bit binary strings

B:N K N, where B is 1-to-1 for a fixed element e K

n

k

let

K

DES (Data Encryption Standard)

Limp Data Types Bit-Vector

◦ A Bit vector is an n-bit twos complement integer.◦ The number of bits, or Bit-Vector Width, can be

fully controlled by the programmer◦ Bit-Vectors can be declared in binary(0b), hex(0x)

or decimal Arrays

◦ Arrays of Bit-Vectors

•Limp Expression Operators Expression Operators

◦ Limp Contains the normal expression operators +,-,*,/,&,|,^,!,<<,>>

Limp also has 4 special operators <<< (rotate a bit vector left)

0b0110 <<< 2 = 0b1001 >>> (rotate a bit vector right)

0b0110 >>> 1 = 0b0011 @ (Bit Vector Concatenation)

0b000 @ 0b111 = 0b000111 # (Bit Vector Width restrictor)

3 # (0b0111+0b0111) =110 (not 01110)

Limp Built-in Functions permute(vector, permArray)

◦ This functions takes a Bit-Vector (vector) and an array that specifies how the bits of the vector are to be permuted (permArray) and returns a new bit vector containing the permutation.

◦ The Permutation may be smaller, larger or the same size as the Bit-Vector being permuted (i.e. compression, expansion, and permutation)

◦ Example v = 0b0011 permute(v, [3,2,1,0]) = 0b1100 permute(v, [2,1]) = 0b10 Permute(v, [3,2,1,0,3]) = 0b11001

Limp Built-in Functions extract(vector, start, end)

◦ This function takes a Bit-Vector (vector), a start index (start), and an end index (end) and returns a new Bit-Vector whose value is the bit range [start,end] from the passed in Bit-Vector

◦ Example v = 0b000111 extract(v, 1,3) = 0b001

Limp Commands e (expression evaluation) r = e (assignment) c1;c2 (sequencing) loop e c (looping) print e (printing values)

Limp Example (Key Schedule)

keySchedule(masterKey) { p1 = [ 56, 48, 40, 32, 24, 16, 8, 0, 57, 49, 41, 33, 25, 17, 9, 1, 58, 50, 42, 34, 26, 18, 10, 2, 59, 51, 43, 35, 62, 54, 46, 38, 30, 22, 14, 6, 61, 53, 45, 37, 29, 21, 13, 5, 60, 52, 44, 36, 28, 20, 12, 4, 27, 19, 11, 3 ];

p2 = [ 13, 16, 10, 23, 0, 4, 2, 27, 14, 5, 20, 9, 22, 18, 11, 3, 25, 7, 15, 6, 26, 19, 12, 1, 40, 51, 30, 36, 46, 54, 29, 39, 50, 44, 32, 47, 43, 48, 38, 55, 33, 52, 45, 41, 49, 35, 28, 31 ];

rotate = [1,1,2,2,2,2,2,2,1,2,2,2,2,2,2,1];

permKey = permute(masterKey, p1); left = extract(permKey,0,27); right = extract(permKey,28,55);

keys = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; count = 0; loop 16 { left = left <<< rotate[count]; right = right <<< rotate[count]; keys[count] = permute(left@right,p2); count = count + 1; } return keys;}

Same Functionality in Cstatic void des_key_schedule(const char * _rawkey, uint32_t * subkey){ const unsigned char *rawkey = (const unsigned char *) _rawkey; uint32_t left, right, work; int round;

READ_64BIT_DATA (rawkey, left, right) DO_PERMUTATION (right, work, left, 4, 0x0f0f0f0f) DO_PERMUTATION (right, work, left, 0, 0x10101010) left = ((leftkey_swap[(left >> 0) & 0xf] << 3) | (leftkey_swap[(left >> 8) & 0xf] << 2) | (leftkey_swap[(left >> 16) & 0xf] << 1) | (leftkey_swap[(left >> 24) & 0xf]) | (leftkey_swap[(left >> 5) & 0xf] << 7) | (leftkey_swap[(left >> 13) & 0xf] << 6) | (leftkey_swap[(left >> 21) & 0xf] << 5) | (leftkey_swap[(left >> 29) & 0xf] << 4));

left &= 0x0fffffff;

right = ((rightkey_swap[(right >> 1) & 0xf] << 3) | (rightkey_swap[(right >> 9) & 0xf] << 2) | (rightkey_swap[(right >> 17) & 0xf] << 1) | (rightkey_swap[(right >> 25) & 0xf]) | (rightkey_swap[(right >> 4) & 0xf] << 7) | (rightkey_swap[(right >> 12) & 0xf] << 6) | (rightkey_swap[(right >> 20) & 0xf] << 5) | (rightkey_swap[(right >> 28) & 0xf] << 4));

right &= 0x0fffffff;

for (round = 0; round < 16; ++round) { left = ((left << encrypt_rotate_tab[round]) | (left >> (28 - encrypt_rotate_tab[round]))) & 0x0fffffff; right = ((right << encrypt_rotate_tab[round]) | (right >> (28 - encrypt_rotate_tab[round]))) & 0x0fffffff;

*subkey++ = (((left << 4) & 0x24000000) | ((left << 28) & 0x10000000) | ((left << 14) & 0x08000000) | ((left << 18) & 0x02080000) | ((left << 6) & 0x01000000) | ((left << 9) & 0x00200000) | ((left >> 1) & 0x00100000) | ((left << 10) & 0x00040000) | ((left << 2) & 0x00020000) | ((left >> 10) & 0x00010000) | ((right >> 13) & 0x00002000) | ((right >> 4) & 0x00001000) | ((right << 6) & 0x00000800) | ((right >> 1) & 0x00000400) | ((right >> 14) & 0x00000200) | (right & 0x00000100) | ((right >> 5) & 0x00000020) | ((right >> 10) & 0x00000010) | ((right >> 3) & 0x00000008) | ((right >> 18) & 0x00000004) | ((right >> 26) & 0x00000002) | ((right >> 24) & 0x00000001));

*subkey++ = (((left << 15) & 0x20000000) | ((left << 17) & 0x10000000) | ((left << 10) & 0x08000000) | ((left << 22) & 0x04000000) | ((left >> 2) & 0x02000000) | ((left << 1) & 0x01000000) | ((left << 16) & 0x00200000) | ((left << 11) & 0x00100000) | ((left << 3) & 0x00080000) | ((left >> 6) & 0x00040000) | ((left << 15) & 0x00020000) | ((left >> 4) & 0x00010000) | ((right >> 2) & 0x00002000) | ((right << 8) & 0x00001000) | ((right >> 14) & 0x00000808) | ((right >> 9) & 0x00000400) | ((right) & 0x00000200) | ((right << 7) & 0x00000100) | ((right >> 7) & 0x00000020) | ((right >> 3) & 0x00000011) | ((right << 2) & 0x00000004) | ((right >> 21) & 0x00000002)); }}

LIMP removes the complexity of dealing with bit manipulation in software.

Provides an easy and free alternative to Cryptol.

Do you have questions, concerns, or comments?