Use the mutable StringBuilder instead of String. Also there should be a way to know that you got the result from left one (if any) before searching right one. So I suggest following changes.
private static boolean encryptSearch(char c, BinaryNode curNode, StringBuilder result) {
char data = curNode.getData();
if (data != c) {
boolean found = false;
if (curNode.hasLeftChild()) {
found = encryptSearch(c, curNode.getLeftChild(), result);
if (found) {
result.insert(0, "0");
return true;
}
}
if (curNode.hasRightChild()) {
found = encryptSearch(c, curNode.getRightChild(), result);
if (found) {
result.insert(0, "1");
return true;
}
}
return false; //no result
}
return true;
}