From CryptoWiki

Bitcoin makes heavy use of the cryptographic hash function SHA-256, which stands for Secure Hash Algorithm 256-bit. Incidentally, the SHA algorithms were originally developed by the NSA. You might wonder how we can trust something that came from the NSA. That’s certainly cause to be suspicious, however, the algorithms are part of the public domain and have been vetted and analysed by cryptographers who know what they’re doing. The consensus is that they are secure.