Password Security Calculator

Pre-Algebra · Axiom Academy

LESSON Password Security Calculator Why a longer, more varied password is safer comes down to one idea: combinations grow as a power, . 1. Each Character Multiplies the Count Build a password one slot at a time. If b different characters can go in each slot, then a 1-slot password has b choices. Adding a second slot gives b new choices for every first choice — so the count multiplies by b again . This is the multiplication principle . Each new slot multiplies the running count by the pool size 2. Combinations = Pool to the Length Repeated multiplication by the pool size, once per slot, is a power. With a pool of b characters and a length of L slots: Two separate levers drive this number, and they are not equal: Lowercase only is b = 26 . Adding uppercase, the 10 digits, and about 32 symbols brings the pool to 26+26+10+32 = 94 . Every extra character is one more factor of b . Length sits in the exponent, so it compounds the hardest. Per character, the 94-pool beats the 26-pool by a factor of . Adding just one lowercase character multiplies the total by a full 26 — and the gap explodes from there. A 6-character lowercase password has 26^6 = 308 , 915 , 776 possibilities — about 309 million. Stretch the same alphabet to 12 characters and it becomes : from hundreds of millions to tens of quadrillions, just from length. 3. Turning the Count Into Time

This is the written version of the interactive lesson above. See the full Pre-Algebra course.