Brute force attacks on cryptography could take billions of years, which no one has to spare. Maybe you live in a country where rubber hose cryptography is, shall we say, frowned upon. Hacking a target's endpoint is an option, but what if you get caught? Better to use an attack that leaves no forensic traces behind.
Enter side channel attacks. A side channel attack breaks cryptography by using information leaked by cryptography, such as monitoring the electromagnetic field (EMF) radiation emitted by a computer screen to view information before it's encrypted in a van Eck phreaking attack, aka Transient Electromagnetic Pulse Emanation STandard (TEMPEST). Other well-known side channel attacks include spying on the power consumption of an electronic device to steal an encryption key, or acoustic attacks that record the sound of a user's key strokes to steal their passphrase.