gcd 𝑎, 𝑁
== 1
Pick random a < N
No
gcd 𝑎, 𝑁 is
a factor of N
Yes
Find the period r of
𝑎 𝑥 𝑚𝑜𝑑𝑁
Done
Yes
𝑟 == 𝑜𝑑𝑑
No
Yes
𝑎𝑟/2
== −1
(𝑚𝑜𝑑𝑁)
No
gcd 𝑎𝑟/2 + 1, 𝑁 or
gcd 𝑎𝑟/2 − 1, 𝑁 is
a factor of N