regular expression matching on encrypted data using secure multiparty computation Lets consider Secure Multiparty Computation based on Secret Sharing schemes (rather than Garbled Circuits approach). If we have to do regular expression matching on secret shares of words of texts. Trivial solution is to secret share each letter of the word and distribute to different parties and later each party executes the regular expression on the secret shares of each letter. 

For example : $SERVER\_01\_LAB$ could be secret shared on each letter "S,E,R,V,E,R,0,1,_,L,A,B" . and for the regular expression $SERVER.*LAB$,  we build secret shares of each letter and send the regex of respective shares to individuals for matching.

But this is too trivial and breaks all the security because if we create secret shares of individual letters then adversary can perform simple frequency analysis on shares and break it . 

Can we do this better ?  Any better approaches exist ?
there are some special constructions that could be used. for example see this paper of florain kerschbaum (freely available version).
also, you can use some secure DFA evaluation protocols, as any regex can be represented as a DFA.

what you have proposed is not secure and the servers can learn lots of information.