New answers tagged 3des
4
TL;DR: the official $2^{80}$-something theoretical security of 2-Key Triple DES w.r.t. key search¹ is still practically good enough in most of its many uses in 2020; but security authorities rightly do not condone it in new applications.
"3DES when $K_1=K_3$" is formally known as TDEA keying option 2 in FIPS 46-3 or 2TDEA or 2-Key Triple DES. It ...
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When two of the three keys with 3DES are the same, you are using a 2*56-bit keyspace that would need to be brute forced. So, when K1=K3, the brute force difficulty will be 2^112. As @hypatia points out though, a meet-in-the-middle attack exists though so you could run an attack in 2^80 time, which is faster than brute force.
Wikipedia has some more details ...
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If K1 = K3 and K1 and K2 are independent, your key length is 112 bits ($2*56$), but due to meet-in-the-middle attack, you have only 80 bits of security.
Note: don't use 3DES and any other 64-bit block ciphers
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3DES
What is described here is not 3DES (Triple DES or TDES and officially the Triple Data Encryption Algorithm (TDEA or Triple DEA)). Let us call the $E$ as DES encryption and $D$ as DES decryption. Then we can write 3DES encryption as
$$E(k_3,D(k_2,E(k_1,message)))$$ with independent keys $k_1,k_2,k_3$.
The provided security by 3DES with 3 key is not 192-...
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