There is more than one artist with this name:

1) CONSPIRACY was a progressive rock band founded by Billy Sherwood (formerly of Yes) and Chris Squire (bassist in Yes). The band released two albums: Conspiracy (2000) and The Unknown (2003), and a live DVD (2006). It is currently inactive. The Unknown was re-released digitally in 2010 by Inside Out Records.
Squire and Sherwood share lead vocals on the album, with Squire playing most of the bass parts and Sherwood playing most of the guitar and keyboard parts, plus contributing some drumming. The name Conspiracy represented Squire and Sherwood's desire to collaborate with different musicians. The album included appearances from White, Haun and World Trade drummers Jay Schellen and Mark T Williams. Conspiracy also included one track based on a set of jam sessions involving Squire, Steve Stevens and Michael Bland called "Violet Purple Rose", consisting of a recording from the sessions with overdubs from Sherwood.
https://en.wikipedia.org/wiki/Conspiracy_%28band%29

2) Conspiracy is a Black Metal project, currently residing in Amsterdam, The Netherlands.
Created in 1994 by Carpathian Wolf (in 1996-2008 member of the band MELECHESH ).
After signing in 2005 with Pulverised Records, CONSPIRACY (NL) has released 3 full length albums : "Reincarnated" 2006, "Concordat" 2009, "Irremediable" 2010.
http://www.myspace.com/metalconspiracy

3) Conspiracy is also a hip-hop/psychadelic producer from Atlanta, GA. He is the producer for King Robot (with Reid Richards) and Lee Harvey Oswald (with DJ Spytek):
http://www.myspace.com/weknowthedeal

4) Conspiracy was a hardcore band

5) Conspiracy is also a rock band from the Netherlands: http://www.conspiracyontheweb.com/

6) Conspiracy was also a death metal band from Apeldoorn, the Netherlands.

7) Conspiracy is also a Death/Thrash Metal band from Upper Austria: http://www.conspiracynet.at

8) Conspiracy is also an EBM band from Leicester, UK. They had one single release called Electric Bitch.

9) Also there is also a Thrash band from Thessaloniki/Greece http://www.myspace.com/conspiracygreece

10) There is also a band formed in Enschede Holland. They changed there name in Innosin. Read more on Last.fm. User-contributed text is available under the Creative Commons By-SA License; additional terms may apply.