Editing RC5 (section)

==Algorithm==

RC5 encryption and decryption both expand the random key into 2(r+1) words that will be used sequentially (and only once each) during the encryption and decryption processes. All of the below comes from Rivest's revised paper on RC5.<ref>{{Cite web|url=http://people.csail.mit.edu/rivest/Rivest-rc5rev.pdf|archiveurl=https://web.archive.org/web/20180921234702/http://people.csail.mit.edu/rivest/Rivest-rc5rev.pdf|url-status=dead |title=The RC5 Encryption Algorithm|archivedate=September 21, 2018|website=people.csail.mit.edu}}</ref>

===Key expansion===

The key expansion algorithm is illustrated below, first in [[pseudocode]], then example [[C (programming language)|C code]] copied directly from the reference paper's appendix.

Following the naming scheme of the paper, the following variable names are used:
* {{math|{{var|w}}}} – The length of a word in bits, typically 16, 32 or 64. Encryption is done in 2-word blocks.
* {{math|1={{var|u}} = {{var|w}}/8}} – The length of a word in bytes.
* {{math|{{var|b}}}} – The length of the key in bytes.
* {{math|K[]}} – The key, considered as an array of bytes (using 0-based indexing).
* {{math|{{var|c}}}} – The length of the key in words (or 1, if b = 0).
* {{math|L[]}} – A temporary working array used during key scheduling, initialized to the key in words.
* {{math|{{var|r}}}} – The number of rounds to use when encrypting data.
* {{math|1={{var|t}} = 2({{var|r}}+1)}} – the number of round subkeys required.
* {{math|S[]}} – The round subkey words.
* {{math|P{{sub|{{var|w}}}}}} – The first magic constant, defined as {{math|Odd(({{var|e}} − 2) {{times}} 2{{sup|{{var|w}}}})}}, where {{math|Odd}} is the nearest odd integer to the given input, {{math|{{var|e}}}} is the [[e (mathematical constant)|base of the natural logarithm]], and {{math|{{var|w}}}} is defined above. For common values of {{math|{{var|w}}}}, the associated values of {{math|P{{sub|{{var|w}}}}}} are given here in hexadecimal:
** For ''w'' = 16: 0xB7E1
** For ''w'' = 32: 0xB7E15163
** For ''w'' = 64: 0xB7E151628AED2A6B
* {{math|Q{{sub|{{var|w}}}}}} – The second magic constant, defined as {{math|Odd(({{phi}} − 1) {{times}} 2{{sup|{{var|w}}}})}}, where {{math|Odd}} is the nearest odd integer to the given input, where {{math|{{phi}}}} is the [[golden ratio]], and {{math|{{var|w}}}} is defined above. For common values of {{math|{{var|w}}}}, the associated values of {{math|Q{{sub|{{var|w}}}}}} are given here in hexadecimal:
** For ''w'' = 16: 0x9E37
** For ''w'' = 32: 0x9E3779B9
** For ''w'' = 64: 0x9E3779B97F4A7C15

<syntaxhighlight lang="python">
# Break K into words
# u = w / 8
c = ceiling(max(b, 1) / u)
# L is initially a c-length list of 0-valued w-length words
for i = b-1 down to 0 do:
    L[i / u] = (L[i / u] <<< 8) + K[i]
     
# Initialize key-independent pseudorandom S array
# S is initially a t=2(r+1) length list of undefined w-length words
S[0] = P_w
for i = 1 to t-1 do:
    S[i] = S[i - 1] + Q_w
    
# The main key scheduling loop
i = j = 0
A = B = 0
do 3 * max(t, c) times:
    A = S[i] = (S[i] + A + B) <<< 3
    B = L[j] = (L[j] + A + B) <<< (A + B)
    i = (i + 1) % t
    j = (j + 1) % c

# return S
</syntaxhighlight>

The example source code is provided from the appendix of Rivest's paper on RC5. The implementation is designed to work with w = 32, r = 12, and b = 16.

<syntaxhighlight lang="c">
void RC5_SETUP(unsigned char *K)
{
   // w = 32, r = 12, b = 16
   // c = max(1, ceil(8 * b/w))
   // t = 2 * (r+1)
   WORD i, j, k, u = w/8, A, B, L[c];
   
   for (i = b-1, L[c-1] = 0; i != -1; i--)
      L[i/u] = (L[i/u] << 8) + K[i];
   
   for (S[0] = P, i = 1; i < t; i++)
      S[i] = S[i-1] + Q;
   
   for (A = B = i = j = k = 0; k < 3 * t; k++, i = (i+1) % t, j = (j+1) % c)
   {
      A = S[i] = ROTL(S[i] + (A + B), 3);
      B = L[j] = ROTL(L[j] + (A + B), (A + B));
   }
}
</syntaxhighlight>

===Encryption===

Encryption involved several rounds of a simple function, with 12 or 20 rounds seemingly recommended, depending on security needs and time considerations. Beyond the variables used above, the following variables are used in this algorithm:

* A, B - The two words composing the block of [[plaintext]] to be encrypted.

<syntaxhighlight lang="python">
A = A + S[0]
B = B + S[1]
for i = 1 to r do:
    A = ((A ^ B) <<< B) + S[2 * i]
    B = ((B ^ A) <<< A) + S[2 * i + 1]

# The ciphertext block consists of the two-word wide block composed of A and B, in that order.
return A, B
</syntaxhighlight>

The example C code given by Rivest is this.

<syntaxhighlight lang="c">
void RC5_ENCRYPT(WORD *pt, WORD *ct)
{
   WORD i, A = pt[0] + S[0], B = pt[1] + S[1];
   
   for (i = 1; i <= r; i++)
   {
      A = ROTL(A ^ B, B) + S[2*i];
      B = ROTL(B ^ A, A) + S[2*i + 1];
   }
   ct[0] = A; ct[1] = B;
}
</syntaxhighlight>

===Decryption===

Decryption is a fairly straightforward reversal of the encryption process. The below pseudocode shows the process.

<syntaxhighlight lang="python">
for i = r down to 1 do:
    B = ((B - S[2 * i + 1]) >>> A) ^ A
    A = ((A - S[2 * i]) >>> B) ^ B
B = B - S[1]
A = A - S[0]

return A, B
</syntaxhighlight>

The example C code given by Rivest is this.

<syntaxhighlight lang="c">
void RC5_DECRYPT(WORD *ct, WORD *pt)
{
   WORD i, B=ct[1], A=ct[0];
   
   for (i = r; i > 0; i--)
   {
      B = ROTR(B - S[2*i + 1], A) ^ A;
      A = ROTR(A - S[2*i], B) ^ B;
   }
   
   pt[1] = B - S[1]; pt[0] = A - S[0];
}
</syntaxhighlight>