How Many Passwords Does A Cellphone Have?

By+Gao+Yanqing

Nowadays, as the popularization of smart phones, practically everyone has such a phone. It is not only a communication tool , but an inalienable part of our daily life, work and study. It is said that modern people have to take three things before going out: phone, purse and keys. Many people are said to take their phone even when they go to toilets, which shows the magic power of phones.

As our intimidate partner, there are a lot of private information stored in our phones. If the information has been lost or transmitted outside unconsciously, how awkward it will be ? and even worse, is there a high possibility that bad person will have an access to those accout information stored in the phones? Fortunatelly, we can set password for our phones, in this case, even our phones fall into the hands of bad people unsciously and we will not be afraid of privacy disclosure. But there is one question, is our phone code safe, and will it be decoded easily? How many passwords can we set ?

A basic permutation and combination formula

First I want to present you some basic mathematic knowledge. Take three numbers to form a combination from 1,2,3,4, and how many combinations can you get? The answer is 24, if we make a list of it, they are

Then how to get the total combinations in a faster approach. The answer is this: let us suppose the final combination is ABC, and ABC must be selected among 1234, then how many possibilities for the position of letter A? obviously, A can be anyone of 1,2,3,4, therefore, there are 4 possibilities. How about B, let us assume that the value of A is 2, then B can only be anyone among 1,3,4,so B has 3 choices. And in this way, C can be selected from the left two numbers. Thus, the total combination of ABC is 4*3*2=24. it is a basic permutation in maths indeed and we can express it by A(4,3), then a formula can be derived like this:

which means that taking the number of m from the total number of n to make the number of combination that formed by these numbers.

iPhone has a number of 10000 passwords

Let us return to the subject, now we will annalyze how many combinations of smart phone. Currently, there are two strategies of phones, one is based on Iphone operation system which is targeted for iPhone; the other is based on Android.

First let us have a look at iPhone which catches the most attention of the public. iPhone is known to have four fixed password, each of which can be any number from 0 to 9, then the number of the total combination is 10*10*10*10=10000. Code of this kind is still to easy to computer, but it is defensive enough to defend our code will be decoded through handcraft. But then if the number of the fixed password can not be repeated, how many combination can we have , the answer is A(10,4)=5040, almost half of the previous. In this way, Jobs way of setting code is reasonable.

Android has a number of 389112 of pattern codes

Codes of this strategy is one path on the 3*3 dot matrix, and the path connect four dotsat least, nine at most. So, the number of required path at most can be A(9,4)+A(9,5)+A(9,6)+ A(9,7)+A(9,8)+A(9,9)=985824, which is nearly 98 times that of iPhone. But, the nubmer is an upper limit that Android can set, moreover, there is a limit in setting the password for Android, namely, when setting, the necessary dots on the path must be connected. For the sake of analysis, we adopt Sudoku to display the above patterns, and marked nine dots of the matrix with the number from one to nine.

Follow the above rules, the number 2178 and 1987 is abnormal, but 15987 is ok. It seems that things are more complicated and strong combinatorial mathematics will not work here. The what can we do, luckily, we have computer by writing programme to solve the problem.

First we should generate 985824 combination without limitation:

And then we need to delete invalid pair in assemblage A, and we will delete any pair like *13*2*, among which the * stands for zero or more numbers, as for the pair <9,1>, we need remove all elements like *91*5*. Keep on doing like this, then the remaining of elements in assemblage A are legal, thus, we can get the number of pattern code for Android, then how many passwords can be set eventually? The answer is 389112, nearly one third of the total. If one tries to decode one password within a second, it probably takes 108 hours to break the passwords, namely, four days and a half, it is believed that no one can get himself involved in decoding so many passwords without even a short rest within four days and nights.

Through the above analysis, I think most of you have a basic understanding of the password safety of your smart phone. One may ask what if we lost our code? Here, I will show you one knack: you can open an account, so when you forget the password, then registered account will be resetted, such service is provided by most cellphone operators.