One-Wayness Intuition:hash should be hard to invert -"Preimage resistance" -Leth(x)=y∈{0，l}for a random x' -Given y,it should be hard to find x such that h(x)= ▣How hard? -Brute-force:try every possible x,see if h(x)=y -SHA-1 (common hash function)has 160-bit output .Assuming 264 trials per second,can do 289 trials per year Will take 271 years to invert SHA-1 on a random image 88 One-Wayness  Intuition: hash should be hard to invert ─ “Preimage resistance” ─ Let h(x’) = y ∈{0,1}n for a random x’ ─ Given y, it should be hard to find x such that h(x)=y  How hard? ─ Brute-force: try every possible x, see if h(x)=y ─ SHA-1 (common hash function) has 160-bit output ● Assuming 264 trials per second, can do 289 trials per year ● Will take 271 years to invert SHA-1 on a random image