(Reuters) - A federal judge denied Apple Inc’s bid to set aside or reduce a $502.8 million patent infringement verdict favoring VirnetX Holding Corp, and awarded interest and royalties that could boost Apple’s total payout in two lawsuits above $1.1 billion. In a decision issued on Friday, U.S. District Judge Robert Schroeder in Tyler, Texas rejected Apple’s request for a new trial and several other claims. These included that VirnetX’s award should not exceed $113.7 million, and that jurors should have been told the U.S. Patent and Trademark Office had deemed VirnetX’s claims “unpatentable.” Jurors in October found that Apple infringed two VirnetX patents related to secure networks, known as virtual private networks, to which owners of various iPhones and iPads may connect. Schroeder also awarded royalties of 84 cents per unit for future infringements, mirroring the rate set by the jury. Apple had said future royalties should be zero, or else no more than 19 cents per unit. Apple and VirnetX did not immediately respond to requests for comment. In afternoon trading, VirnetX shares were up 54 cents, or 10.8%, at $5.63. Apple, based in Cupertino, California, and VirnetX, based in Zephyr Cove, Nevada, have battled in patent litigation for more than a decade. Last March, Apple paid VirnetX $454 million after the U.S. Supreme Court refused to hear the iPhone maker’s appeal in an earlier patent case. In a Dec. 18 court filing, Apple said the latest award could boost its payout in both cases to $1.116 billion. The case is VirnetX Inc v. Apple Inc, U.S. District Court, Eastern District of Texas, No. 12-00855.