![]() A computer running through all the possibilities for your 12-character password one by one would take 62 trillion times longer. That is more than 62 trillion times the size of the first space. If you are told to select a 12-character password that can include uppercase and lowercase letters, the 10 digits and 10 symbols (say, !, #, $, %, ^, &, ?, / and +), you would have 72 possibilities for each of the 12 characters of the password. For example, if you were told to use six lowercase letters-such as, afzjxd, auntie, secret, These choices are independent: you do not have to use different letters, so the size of the password space is the product of the possibilities, or 26 x 26 x 26 x 26 x 26 x 26 = 26 6. When you are asked to create a password of a certain length and combination of elements, your choice will fit into the realm of all unique options that conform to that rule-into the “space” of possibilities. I will also explain how hackers can uncover passwords even when stolen data sets lack is the logic behind setting hack-resistant passwords. I will explain the mathematical rationale for some standard advice, including clarifying why six characters are not enough for a good password and why you should never use only lowercase letters. Obviously such measures add safety, but how exactly? ![]() We are also told to change our choices regularly. At one time or another, we have all been frustrated by trying to set a password, only to have it rejected as too weak. ![]()
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December 2022
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