Implement bit-wise matrix multiplication
APL, 28 characters
f←{2⊥,↑≠.×/{8 8⍴(64⍴2)⊤⍵}¨⍵}

Usage:
&gt; f 12345678 87654321
3977539

You can read it almost literally if you go right-to-left. (64⍴2)⊤ transforms each argument into 64 bit representation and 8 8⍴ makes an 8x8 matrix out of the results. ≠.×/ then applies the inner product to both arguments, where multiplication × and xor ≠ is used. The matrix is then transformed back to vector form ,↑, before 2⊥ undoes the basis transformation.