Common cryptographic methods, especially Public Key Crypto Systems, PKCS based on difficulty to factor large integers or to compute the discrete logarithm, commonly deployed today will not resist attacks using quantum computers once these are operational. However, there are alternatives like hash based digital signature schemes, lattice based cryptography, or multivariatequadratic-equations pub...

Lattice-based cryptography has laid the foundation of various modern-day cryptosystems that cater to several applications, including post-quantum cryptography. For structured lattice-based schemes, polynomial arithmetic is a fundamental part. In instances, performance optimizations come from implementing compact multipliers due small range secret coefficients. However, this optimization does no...

Common cryptographic methods, especially Public Key Crypto Systems, PKCS based on difficulty to factor large integers or to compute the discrete logarithm, commonly deployed today will not resist attacks using quantum computers once these are operational. However, there are alternatives like hash based digital signature schemes, lattice based cryptography, or multivariate-quadratic-equations pu...

Ever since the appearance of quantum computers, prime factoring and discrete logarithm-based cryptography have been questioned, giving birth to so-called post-quantum cryptography. The most prominent field in is lattice-based cryptography, protocols that are proved be as difficult break certain hard lattice problems like Learning with Errors (LWE) or Ring (R-LWE). Furthermore, application crypt...

Lattice-based cryptography is a field of research that has been very active in the last decade. It offers expressiveness along with asymptotic efficiency and seems to the best of our knowledge to be resistant to quantum computers attacks. Advanced cryptography would then benefit from being designed from lattice assumptions. Along those primitives, there is one that grabs our interest: group sig...

The shortest vector problem (SVP) in lattices is related to problems in combinatorial optimization, algorithmic number theory, communication theory, and cryptography. In 1996, Ajtai published his breakthrough idea how to create lattice-based oneway functions based on the worst-case hardness of an approximate version of SVP. Worst-case hardness is one of the outstanding properties of all modern ...

A revocable identity-based encryption (RIBE) scheme, proposed by Boldyreva et al, provides a revocation functionality for managing a number of users dynamically and efficiently. To capture a realistic scenario, Seo and Emura introduced an additional important security notion, called decryption key exposure resistance (DKER), where an adversary is allowed to query short-term decryption keys. Alt...

The classic Leftover Hash Lemma (LHL) is often used to argue that certain distributions arising from modular subset-sums are close to uniform over their finite domain. Though very powerful, the applicability of the leftover hash lemma to lattice based cryptography is limited for two reasons. First, typically the distributions we care about in lattice-based cryptography are discrete Gaussians, n...

Goldreich-Goldwasser-Halevi (GGH) public key cryptosystem is an instance of lattice-based cryptosystems whose security is based on the hardness of lattice problems. In fact, GGH cryptosystem is the lattice version of the first code-based cryptosystem, proposed by McEliece. However, it has a number of drawbacks such as; large public key length and low security level. On the other hand, Low Densi...