JavaScript search function works great in Chrome, Safari, and Opera, but takes forever in IE and Firefox

I'm working on an online dictionary that has to be executed completely client-side and can't use any external libraries, so I'm loading the dictionary entries as a series of JavaScript arrays and then passing them to the webpage. I use a search function that iterates through an index of each entry and checks it for matches against a search string, then returns all matching entries. (This is actually done by hiding non-matching entries with CSS to avoid having to re-draw up to 30,000 entries in HTML with each search.)

elen = Entries.length;
for (j=0;j<elen;j++) {
    shh_cypher = ShoshoniIndex[j]; //These search indexes are created from the JS array by an earlier function
    eng_cypher = EnglishIndex[j];

    //displays results and hides all other dictionary entries
    if(shh_cypher.match(search_term)) {
        document.getElementsByTagName("dt")[j].style.display = "";
    }
    else if(eng_cypher.match(search_term)) {
        document.getElementsByTagName("dt")[j].style.display = "";
    }
    else document.getElementsByTagName("dt")[j].style.display = "none";
        
    document.title = "Search is " + Math.round((j/elen)*100) + "% complete…";
}

There's a small delay on the search in Chrome, Opera, and Safari, but it's acceptable. In IE and Firefox it takes a really long time to return any results for the first search, and then works great (almost no delay) for any subsequent searches, but the initial delay makes it unusable. With a shortened version of the database, everything works fine across the board, so I know it's just a matter of timing, and not that it doesn't work in those browsers.

Any ideas on how to whip through a 30,000-entry array faster in JavaScript, or ideas about why Firefox and IE would be causing problems, but not the others?

Maybe by caching your DOM elements, instead of going through the DOM in every iteration, this would be faster.

var dt_elements = document.getElementsByTagName("dt");
...
dt_elements[j].style.display = "";