## example of Collision resistance and one-way function

**Collision Resistant fun:**

from Definition, if f(.) is a collision resistant function, then it is hard to hard find different x and x’ such that f(x)=f(x’).

Lets see some example:

let, f(x) = x*x.

For this function we can find f(-2) = f(2) = 4. So, we find two different x and x’ such that f(x) = f(x’). So, given f(x)=x*x is not collision resistant.

Again, if f(x) = x, then this is collision resistant because, we cannot find two different x such that f(x)=f(x’).

Likewise, there are lots of examples for collision resistant and non collision resistant function.

**One-way function:**

given a function y=f(x), it is hard to find x when y is given.

for example, f(x)=x*x, is trivially not one-way function because given y=x^2, we can readily find sqrt(y) to find x.

There is an excellent example at [1] about one-way function which I excerpt verbose.

Alice and Bob procure the same edition of the white pages book for a particular town, say Cambridge. For each letter Alice wants to encrypt, she finds a person in the book whose last name starts with this letter and uses his/her phone number as the encryption of that letter.

```
```To decrypt the message Bob has to read through the whole book to find all the numbers. The decryption will take a lot more time than the encryption. If the book increases in size the time it takes Alice to do the encryption almost doesn’t increase, but the decryption process becomes more and more draining.

`This example is very good for teaching one-way functions to non-mathematicians.`

....

## How to approach a professor for funding/ Assistantship / Admission / supervison

**How to address Prof:**

By full Name or By Last name (EX: Dr. / Prof. Dakai Zhu).

**How to start :**

Its good to start with a greeting (Like Good morning or Good Day ).

**What to day :**

1. Your identity.

2. Your Interest.

3. Why you pick him… ( for your interest in his research).

4. How you know him… (through webpage, or while reading one of this paper.. etc)

5. How much you know his work/research (mention If you have some knowledge about his work).

6. Some (if any) of your contribution in the same field.

7. Mention your publication (if any) with title and one copy of each attached with the mail.

8. Mention your specific Strong points( Like From you are, your result, Admission test result).

9. Mention work Experience if it really fit with his work(but if does not match then do not prolong it).

**Attachments :**

1. Academic Transcript.

2. CV

3. GRE / TOEFL Score

4.Papers(if have)

**Remember:**

The prof will not pick you for your benefit. He will pick you for his own benefit. Think How you can let him think that you are important and he needs you . This may take reading his paper, talk show, presentation, so on.

**Important:**

Try to be as much different as possible. Prof generally receives ton of email daily. Let him feel you are special. It is not using some good adjective rather showing interest/familiarity in his work / research work.

Try to make a high estimation about yourself which really you are. You may share some of your ideas with him.

## E-mail courtesy….

Yesterday, I composed a mail to my friend and he did not reply me any word. It really hurts me. She did the same thing once more. I don’t know why she does not follow the email courtesy. I hope and wish, she and some one like her will read my post.

something I feel should be regarded as communication courtesy over email .

They are :

1. If some one write you a mail , don’t forget to send him at least an acknowledgement / thank you mail in return. Every time, I get no reply for some mail I sent to somebody , it really hurts me… 😦 I believe the feeling is same for others who writes mails.

2. If you need some time (even day / week ) to compose the mail , at least let him/her know that you will write to him/her at the possible quickest time.

3. If you are on leave (for some days) set auto reply features so that some one who have sent you mail can know your status.

Posted by :

Prosunjit Biswas