Sh-Boom was written by The Chords, a doo-wop group from The Bronx, New York. It was actually the B-side of their first single, but it received much more attention than the A-side and became a nationwide hit in the US in 1954. It was quickly covered by a white Canadian vocal quartet called The Crew Cuts, who made it into more of a vocal show-piece and had an even bigger hit with their version in the same year.
The Gurt Lush arrangement is based on the Crew Cuts version, but The Chords' more R&B-styled original is well worth a listen. There's also a short video of The Chords talking about the song's genesis.
Sadly, The Chords never managed another hit record, but The Crew Cuts had plenty more, mainly with covers of originally R&B songs. Catchy arrangements and clean vocal delivery were clearly their strongest suits.