Encrypting twice with same key gives back plain text

Question

I read in the answer here that when encrypting twice the plain text with same key could result in plain text as shown below

$encrypt_{key}((encrypt_{key}(plain)) = plain $

Which block-cipher algorithms are they? What is this property called in general? Is it considered weak?

Edit 1 : the question is about block ciphers, not block cipher modes of operation Edit 2 : added more clarity to the question through an equation

Answer 1

These block ciphers are called involutional ciphers, after the (mathematical) involution property of a function. This article shows a cryptographic analysis of two of them: Khazad and Anubis.

Neither Khazad nor Anubis seem to be broken at the time of writing, basically they use the same internal structure for normal block ciphers, replacing the inner components with involutional ones.

Answer 2

You're thinking of stream ciphers, not block ciphers. A stream cipher (like RC4, for example) is basically a pseudorandom number generator that produces a unique sequence of numbers for each key. These numbers are XORed with the raw data to produce an encrypted stream that can be decoded by generating the same sequence of numbers based on the same key. Repeating the XOR operations restores the original data.