The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since more than tw...

In 2016, the National Institute of Standards and Technology (NIST) announced an open competition with goal finding standardizing suitable algorithms for quantum-resistant cryptography. This study presents a detailed, mathematically oriented overview round-three finalists NIST’s post-quantum cryptography standardization consisting lattice-based key encapsulation mechanisms (KEMs) CRYSTALS-Kyber,...

In this paper we report on our work to design, implement and evaluate a Fully Homomorphic Encryption (FHE) scheme. Our FHE scheme is an NTRU-like cryptosystem, with additional support for efficient key switching and modulus reduction operations to reduce the frequency of bootstrapping operations. Ciphertexts in our scheme are represented as matrices of 64-bit integers. The basis of our design i...

Nowadays, most smartphones come pre-equipped with location (GPS) sensing capabilities, allowing developers to create a wide variety of location-aware applications and services. While location awareness provides novel features and functionality, it opens the door to many privacy nightmares. In many occasions, however, users do not need to share their actual location, but to determine whether the...

NTRUEncrypt is a relatively new cryptosystem, introduced in 1996. The best known attacks on the cryptosystem are due to lattice basis reduction. In this Master’s project we have implemented lattice attacks using dimension-reduced and zero-forced lattices. Furthermore, we have reduced a modified version of the zero-forced lattice. This “non-lossy” zero-forced lattice performed better than the or...

In this paper, we show that the fundamental concepts behind the Ntrū cryptosystem can be extended to a broader algebra than Dedekind domains. Also, we present an abstract and generalized algorithm for constructing a Ntrū-like cryptosystem such that the underlying algebra can be non-commutative or even non-associative. To prove the main claim, we show that it is possible to generalize Ntrū over ...

We describe plausible lattice-based constructions with properties that approximate the soughtafter multilinear maps in hard-discrete-logarithm groups, and show that some applications of such multi-linear maps can be realized using our approximations. The security of our constructions relies on seemingly hard problems in ideal lattices, which can be viewed as extensions of the assumed hardness o...

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...

An identity-based encryption scheme enables the efficient distribution of keys in a multi-user system. Such schemes are particularly attractive in resource constrained environments where critical resources such as processing power, memory and bandwidth are severely limited. This research examines the first pragmatic lattice-based IBE scheme presented by Ducas, Lyubashevsky and Prest in 2014 and...

Abstract. The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since ov...