The first amendment

Prohibiting CP is a violotation of the first amendment of the US.

Interestingly, Japan allowed for legal possession of CP until June 2014. The article regarding freedom of expression in their constitution is also analogous to the First Amendment in the USA.
http://japan.kantei.go.jp/constitution_and_government_of_japan/constitution_e.html

Article 21. Freedom of assembly and association as well as speech, press and all other forms of expression are guaranteed.
No censorship shall be maintained, nor shall the secrecy of any means of communication be violated.

Compare with the USA's First Amendment:
https://www.law.cornell.edu/constitution/first_amendment

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.