RIM planned to pay $2.44 per outstanding share for Certicom, double what it bid in December. It eventually bowed out of that first offer, only to have VeriSign jump in and up the ante with a $1.67-per-share bid. That deal would have totaled $73 million.
VeriSign now will have a chance to exceed RIM's offer, according to the company.
"If the board of directors determines that the RIM offer does not continue to be a superior proposal, the board will promptly reaffirm its recommendation of the VeriSign arrangement," Certicom said in a news release.
Certicom makes elliptic curve cryptography technology, generally considered a highly efficient form of public-key encryption.
A VeriSign spokeswoman told SCMagazineUS.com that the company was not commenting on the news.
Both RIM and Certicom are based in Canada.