At 8:30 PM -0600 1/18/98, Jim Choate wrote:
Hi,
It has been proposed to compress the keys from 100 cypherpunks down to a 64 character add in the NYT. Let's consider the math a moment to determine if this is realizable.
Each key will require some sort of identifier, to make it simple lets assume 8 characters to identify the cypherpunks and 8 bytes to represent their key (64-bits). This mean that each line will contain 16 bytes. With a hundred entries that is 1600 bytes or 12800 bits.
Now 64 characters of text in a newspaper represents approx. 64 6-bit characters (we can't use a full 8-bit because the paper doesn't normaly support that many characters in normal text). This provides us with 384 bits.
The proposal leads to a requirement for an algorithm with an average compression factor of:
12800/384 or 33.33:1 with no data loss.
That's a pretty hefty compression factor for average responce.
Is there a loss-less algorithm which provides this level?
Compression efficiency depends upon 1) the entropy of the input data, 2) the allowable losses and 3) finding an efficient algorithm to code for that entropy. For example, text rarely compress w/o loss beyond 4-5 to 1 (and 2-3 is more typical) using LZW (the defacto standard algorithm). Images have much more correlation in their data (and therfore can be compressed more readily), but even so lossless compression beyond 3-5 to 1 is uncommon (e.g., TIFF). JPG and other lossy algorithms need no apply. I think I'm on fairly firm ground assuming that key data entropy is very high and therefore little or no compressible is feasible. --Steve