MD4 steps 16-47: collision deltas

Each row is one register or message word, 32 columns = bits 31 ... 0. For a pair (A, B) the bitwise signed difference per bit is d = B bit - A bit.

• . bits equal (with "show equal-bit values": 0 / 1)
• + A bit 0, B bit 1 (Wang's +2^i)   - A bit 1, B bit 0 (-2^i). The digits sum to (B - A) mod 2^32.
• Second differential (1st delta - 2nd delta, per bit): . 0, + +1, - -1, ^ +2 (1st +, 2nd -), v -2 (1st -, 2nd +).
• Modular NAF view: the integer difference (B - A) mod 2^32 as a non-adjacent signed digit string: u = +2^i, n = -2^i, . = 0 (carry chains collapse into two digits). For the second differential the NAF of (D1 - D2) mod 2^32.
• Right columns: modular difference (hex) and number of nonzero digits (wt); hover the hex for the signed power-of-two sum. * in the third column: the word read at that step differs between A and B.
• Q[t+1] is the register produced by step t; Q13..Q16 are the IV (steps 16-47 start from the IV; feed-forward from the IV).
• Condition overlay: outline green = atom holds on the chosen copy, red = violated.