Strassen's 1969 algorithm for fast matrix multiplication 2] is based on the possibility to multiply two 2 2 matrices A and B by using 7 multiplications instead of the usual 8. The corresponding formulas are an important part of any algorithms course, but, unfortunately, even in the best textbook expositions (see, e.g., 1]), they look very ad hoc. In this paper, we show that the use of natural s...

Verifiable computing (VC) uses cryptography to delegate computation to untrusted workers. But in most VC schemes, the delegated program must first be arithmetized – expressed as a circuit with multiplication and addition over a finite field. Previous work has compiled subsets of languages like C, LLVM, and bespoke assembly to arithmetic circuits. In this paper, we report on a new DSL for VC, ca...

A key recovery attack allows an attacker to recover the private key of an underlying encryption scheme when given a number of decryption oracle accesses. Previous research has shown that most existing Somewhat Homomorphic Encryption (SHE) schemes suffer from this attack. In this paper, we propose efficient key recovery attacks against two NTRU-based SHE schemes, which have not gained much atten...

Sweden has adopted a somewhat different approach to handle the corona pandemic, which been widely debated both on national and international levels. The Swedish model involves more individual responsibility reliance voluntary civic liability than law enforcement, while common measures in other countries are based controlling strategies, such as restrictive lockdowns, quarantines, closed borders...

a. csaszar introduced and extensively studied the notion of generalized opensets. following csazar, we introduce a new notion hyperconnected. we study some specicproperties about connected and hyperconnected in generalized topological spaces. finally, wecharacterize the connected component in generalized topological spaces.

Designing efficient cryptographic protocols tolerating adaptive adversaries, who are able to corrupt parties on the fly as the computation proceeds, has been an elusive task. In this paper we make progress in this area. First, we introduce a new notion called semi-adaptive security which is slightly stronger than static security but significantly weaker than fully adaptive security. The main di...

The purpose of this paper is to compare side-by-side the NTRU and BGV schemes in their non-scale invariant (messages in the lower bits), and their scale invariant (message in the upper bits) forms. The scale invariant versions are often called the FV and YASHE schemes. As an additional optimization, we also investigate the affect of modulus reduction on the scale-invariant schemes. We compare t...

We present a hardware architecture for all building blocks required in polynomial ring based fully homomorphic schemes and use it to instantiate the somewhat homomorphic encryption scheme YASHE. Our implementation is the first FPGA implementation that is designed for evaluating functions on homomorphically encrypted data (up to a certain multiplicative depth) and we illustrate this capability b...