Magic Numbers in MD5

I am curious where some of the magic numbers in MD5 originated.

First, we have the four chaining variables, A, B, C, and D which
are initialized with apparently random numbers.  Are they as
random as they look, or are they carefully chosen?

Second, we have the t_i values.  Schneier's first edition says this:

"In step i, t_i is the integer part of 4294967296xabs(sin(i)), when
i is in radians.  (Note that 4294967296 is 2^32.)"

Does abs(sin()) have some properties that are especially conducive to
strengthening MD5 or is it just a function to generate mildly random
numbers?  If the latter, wouldn't the algorithm be stronger if it was
used with completely random numbers?

Peter Hendrickson
ph@netcom.com

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On Fri, 13 Dec 1996, Peter Hendrickson wrote:

> I am curious where some of the magic numbers in MD5 originated.
> 
> First, we have the four chaining variables, A, B, C, and D which
> are initialized with apparently random numbers.  Are they as
> random as they look, or are they carefully chosen?

Random?

A = 0x01234567
B = 0x89abcdef
C = 0xfedcba98
D = 0x76543210

> Second, we have the t_i values.  Schneier's first edition says this:
> 
> "In step i, t_i is the integer part of 4294967296xabs(sin(i)), when
> i is in radians.  (Note that 4294967296 is 2^32.)"
> 
> Does abs(sin()) have some properties that are especially conducive to
> strengthening MD5 or is it just a function to generate mildly random
> numbers?  If the latter, wouldn't the algorithm be stronger if it was
> used with completely random numbers?

I am not sure of the properties of abs(sin()).  I know that the S-boxes in
Blowfish are initialized with pi.  I would guess that the purpose of using
such values is to use easily generated pseudo-random numbers.

Mark
- -- 
finger -l for PGP key
PGP encrypted mail prefered.
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At 9:15 PM -0800 12/13/96, Peter Hendrickson wrote:
>I am curious where some of the magic numbers in MD5 originated.
>
>First, we have the four chaining variables, A, B, C, and D which
>are initialized with apparently random numbers.  Are they as
>random as they look, or are they carefully chosen?
>
>Second, we have the t_i values.  Schneier's first edition says this:
>
>"In step i, t_i is the integer part of 4294967296xabs(sin(i)), when
>i is in radians.  (Note that 4294967296 is 2^32.)"
>
>Does abs(sin()) have some properties that are especially conducive to
>strengthening MD5 or is it just a function to generate mildly random
>numbers?  If the latter, wouldn't the algorithm be stronger if it was
>used with completely random numbers?
>
>Peter Hendrickson
>ph@netcom.com

Perhaps random numbers would be stronger but they would not be manifestly
random.
MD5's formula for t_i precludes the possibility that the definer of MD5
chose the numbers
accoriding to some undisclosed principles that would allow him a trap door.

The following code computes the magic numbers without requiring trig functions:

static word si[64];
static int md5init()
{double c1=0.5403023058681397, s1 = 0.8414709848078965;
int j; double a=1, b=0;
for(j=0; j<64; ++j)
 {double p = a*c1 - b*s1, q = a*s1 + b*c1;
  a=p; b=q;
  {union{double d; struct{int high; int low;} fx;} z;
   z.d=(fabs(b)-1.1e-10)+1048576;
   si[j] = z.fx.low;
 }}}

An alternative would have been to let t_i be MD4(i) or SHA(i).

Using SHA to define MD5 would have required collusion between Rivest
and NSA to allow for a trap door. Even then it would have been very difficult.