Santa Claus' secret permutation
A solution is given by Peter Ryan, Crypto Santa.  In The New Codebreakers, vol. 9100 of Lecture Notes in Computer Science, pp. 543-549, Springer, 2016. http://dx.doi.org/10.1007/978-3-662-49301-4_33

An earlier version (with Sjouke Mauw and Sasa Radomirovic) can be found at http://hdl.handle.net/10993/25936 (Open access), Security protocols for Secret Santa.