We initiate the cryptographic study of order-preserving symmetric encryption (OPE), a primitive suggested in the database community by Agrawal et al. (SIGMOD '04) for allowing efficient range queries on encrypted data. Interestingly, we first show that a straightforward relaxation of standard security notions for encryption such as indistinguishability against chosen-plaintext attack (IND-CPA) is unachievable by a practical OPE scheme. Instead, we propose a security notion in the spirit of pseudorandom functions (PRFs) and related primitives asking that an OPE scheme look "as-random-as-possible" subject to the order-preserving constraint. We then design an efficient OPE scheme and prove its security under our notion based on pseudorandomness of an underlying blockcipher. Our construction is based on a natural relation we uncover between a random order-preserving function and the hypergeometric probability distribution. In particular, it makes black-box use of an efficient sampling algorithm for the latter.

Fully Homomorphic encryption (FHE) has been gaining in popularity as an emerging means of enabling an unlimited number of operations in an encrypted message without decryption. A major drawback of FHE is its high computational cost. Specifically, a bootstrapping step that refreshes the noise accumulated through consequent FHE operations on the ciphertext can even take minutes of time. This significantly limits the practical use of FHE in numerous real applications.By exploiting the massive parallelism available in FHE, we demonstrate the first instance of the implementation of a GPU for bootstrapping CKKS, one of the most promising FHE schemes supporting the arithmetic of approximate numbers. Through analyzing CKKS operations, we discover that the major performance bottleneck is their high main-memory bandwidth requirement, which is exacerbated by leveraging existing optimizations targeted to reduce the required computation. These observations motivate us to utilize memory-centric optimizations such as kernel fusion and reordering primary functions extensively.Our GPU implementation shows a 7.02× speedup for a single CKKS multiplication compared to the state-of-the-art GPU implementation and an amortized bootstrapping time of 0.423us per bit, which corresponds to a speedup of 257× over a single-threaded CPU implementation. By applying this to logistic regression model training, we achieved a 40.0× speedup compared to the previous 8-thread CPU implementation with the same data.

Transglutaminase 2 (TGase 2) catalyzes a crosslink between protein bound-glutamine and -lysine. We proposed the mechanism of TGase 2 activation depends on conformation change from unfolded monomer to unfolded dimer. We found that TGase 2 has temperature-sensitive conformation change system at 30 °C. Small-angle X-ray scattering analysis showed that the enzyme was maintained as an unfolded monomer at temperatures below 30 °C, but changed to an unfolded dimer at over 30 °C. Mass analysis revealed that the C-terminus of TGase 2 was the critical region for dimerization. Furthermore, this conformational switch creates new biochemical reactivity that catalyzed inter-molecular crosslink at above 30 °C as an unfolded dimer of TGase 2 while catalyzed intra-molecular crosslink at below 30 °C as an unfolded monomer of TGase 2. The mechanism of TGase 2 activation depends on temperature-sensitive conformation change from unfolded monomer to unfolded dimer at over 30 °C. Furthermore, inter-molecular crosslinking activity is generated by the dimeric form of TGase 2. TGase 2 switches its conformation from a monomer to a dimer following a change in temperature, which engendered unique catalytic function of enzyme as inter-molecular crosslinking activity with calcium.

Osm1 and Frd1 are soluble fumarate reductases from yeast that are critical for allowing survival under anaerobic conditions. Although they maintain redox balance during anaerobiosis, the underlying mechanism is not understood. Here, we report the crystal structure of a eukaryotic soluble fumarate reductase, which is unique among soluble fumarate reductases as it lacks a heme domain. Structural and enzymatic analyses indicate that Osm1 has a specific binding pocket for flavin molecules, including FAD, FMN, and riboflavin, catalyzing their oxidation while reducing fumarate to succinate. Moreover, ER-resident Osm1 can transfer electrons from the Ero1 FAD cofactor to fumarate either by free FAD or by a direct interaction, allowing de novo disulfide bond formation in the absence of oxygen. We conclude that soluble eukaryotic fumarate reductases can maintain an oxidizing environment under anaerobic conditions, either by oxidizing cellular flavin cofactors or by a direct interaction with flavoenzymes such as Ero1.

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