In its current form, for example, the encryption process generates an encoded message that is considerably longer than the original message. Ajtai and Dwork are also checking for loopholes and exploring ways to fine-tune their scheme. Other researchers are studying the cryptographic implications of these and related findings. For one thing, some key mathematical results obtained by Ajtai last year may help revive interest in knapsack cryptosystems by suggesting ways to bulletproof those schemes. Until that happens, the best we can do is to show that randomly generated instances of the new cryptosystem are as hard to crack as the hardest instances of the underlying problem.
Cryptographers now have a new mathematical field on which to exercise their schemes.
Ajtai, M., and C. Dwork. Cipra, B. 1996. Lattices may put security codes on a firmer footing. Peterson, I. 1997. Chinks in digital armor .