# What does 0...0 and 1...1 mean

I am very new to cryptography but can someone explain what exactly does 0...0 and 1...1 mean in general term. Is it that 1st and last bit can be 0,0 and 1,1 respectively and in-between bits can be anything $(0,1)$?

In case it helps… I stumbled upon this while trying to solve the following multiple choice question:

Let F be a block cipher with n-bit block length. Consider the message authentication code for 2n-bit messages defined by Mack(m1,m2)=Fk(m1⊕m2). Which of the following gives a valid attack on this scheme?

• Obtain tag t on message m,0…0 (with m≠0…0), and then output the tag t on the message 0…0,0…0.
• Obtain tag t on message m1,m2 (with m1≠m2), and then output the tag t on the message m2,m1.
• Obtain tag t on message m,0…,0, and then output the tag t⊕(1…1) on the message m,1…1.
• Obtain tag t on message m,m, and then output the tag 0…0 on the message 0…0,m.

Please note that I do not want an answer to the multiple choice question. I merely want to know how to interpret the notation 0...0 and 1...1`.

What exactly does $0...0$ and $1...1$ mean usually?

This simply means a (more or less) long string of $0$s or $1$s or more clearly $000000...000000$ and $111111...111111$.

Related notiational notes, you may have to use soon:

Sometimes the notation $0^n$ and $1^n$ is also used for these strings with exactly $n$ zeroes and ones.

Even more generally it's usually expected that people see the pattern, namely that nothing changes (or else there would be a note about this), for example $\lambda_0,...,\lambda_n$ is expected to be filled with $\lambda_i$ with $i\in \mathbb N_0, 0\leq i\leq n$ or relatedly $(\alpha,...,\alpha)\in \mathbb R^n, \alpha \in \mathbb R$ would be the same principle, that you'd have to fill the blanks with as many $\alpha$s as needed.

One last note: If you'd want to indicate that you want a leading string $0$ and a trailing string $0$ and stuff you don't care about in the middle you'd usually notate it as $n\in\{0,1\}^*$ and $0||n||0$ which means "place an arbitrary string of arbitrary length between the zeroes".

• Before anybody asks: No, there's no special reason why I used examples from standard math / linear algebra in the fourth paragraph.
– SEJPM
May 21 '16 at 18:56