Boosting Crypto-1's Defense Against Math Attacks

In recent years, researchers have been working hard to fix a big problem with data security in Mifare Classic. One of the issues is that it doesn't create random numbers very well. This makes it easier for attackers to use something called a SAT solver to break the security. To make Crypto-1 stronger against these attacks, experts suggested changing the way the feedback function works. They used something called a primitive polynomial companion matrix. This change makes it much harder for SAT solvers to attack.When they tested this new and improved Crypto-1, they found that it took the most memory and computer time to break. This meant the attackers would have a tougher time. There was also another version of Crypto-1 that had the best results. It used both the improved feedback function and an improved filter function. This version revealed the least amount of important information to attackers. So, the modified Crypto-1 that uses both the improved feedback function and filter function is much stronger and performs better than the original Crypto-1.