Adapting Density Attacks to Low-Weight Knapsacks

Cryptosystems based on the knapsack problem were among the first public-key systems to be invented. Their high encryption/decryption rate attracted considerable interest until it was noticed that the underlying knapsacks often had a low density, which made them vulnerable to lattice attacks, both in theory and practice. To prevent low-density attacks, several designers found a subtle way to increase the density beyond the critical density by decreasing the weight of the knapsack, and possibly allowing non-binary coefficients. This approach is actually a bit misleading: we show that low-weight knapsacks do not prevent efficient reductions to lattice problems like the shortest vector problem, they even make reductions more likely. To measure the resistance of low-weight knapsacks, we introduce the novel notion of pseudo-density, and we apply the new notion to the Okamoto-Tanaka-Uchiyama (OTU) cryptosystem from Crypto ’00. We do not claim to break OTU and we actually believe that this ...

• Type: Conference
• Year: 2005
• Where: ASIACRYPT
• Authors: Phong Q. Nguyen, Jacques Stern
• Keywords: ASIACRYPT 2005, Cryptology, Low Density, Low-weight Knapsacks, first Public-key Systems