I was looking at solutions for a problem but I noticed it said $\langle2\rangle$ and was unsure of what that meant.

screenshot of relevant part

From Homework 5 (PDF)

  • $\begingroup$ That's a very strange notation to be used here. But the instructor as noted at the top corner of the paper, @chris-peikert who happens to be a member here, maybe we should ask him? $\endgroup$
    – DannyNiu
    Commented Mar 13, 2018 at 7:32
  • $\begingroup$ I've started a chat room with him, I'm not sure if you could join. $\endgroup$
    – DannyNiu
    Commented Mar 13, 2018 at 7:40
  • 2
    $\begingroup$ It appears from context that $\langle x \rangle$ is a canonical representation of the integer $x$ as an $n$- bit bitstring. Otherwise those inputs and outputs are not in the correct donation/range. $\endgroup$
    – Maeher
    Commented Mar 13, 2018 at 7:44
  • $\begingroup$ @Maeher So basically the solution demonstrated an attack on a artifical hash compression function that is collision resistant but not pseudo-random? $\endgroup$
    – DannyNiu
    Commented Mar 13, 2018 at 7:51
  • $\begingroup$ You also see this notation in quantum mechanics, as in part 1 of Why should one model an entropy source in order to build a TRNG?. Don't ask me, I just copied it but you see if often in photonic TRNG papers. It may have multiple meanings subject to domain. $\endgroup$
    – Paul Uszak
    Commented Mar 22, 2019 at 16:59

1 Answer 1


From the context of the exercise, it appears that $\langle x\rangle$ is meant to denote a canonical representation of the integer $x$ as a bitstring of length $n$.

If this were not the case, those inputs and outputs would not be in the correct domain and range respectively.

Likely this notation was defined somewhere in the lecture notes, but I cannot find them at the moment.

  • $\begingroup$ Sounds like a very logical answer, in that case it is likely defined as I2OSP as defined in RSA (a statically sized, unsigned big endian / network order integer representation. $\endgroup$
    – Maarten Bodewes
    Commented Mar 22, 2019 at 22:04

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