Lattice Based Group Signatures: Achieving Anonymity in Post Quantum World

International Journal of Research and Scientific Innovation (IJRSI) | Volume V, Issue III, March 2018 | ISSN 2321–2705

Lattice Based Group Signatures: Achieving Anonymity in Post Quantum World

Jayadev C.O Sekhar, Sangeetha Jose

 Dept. of Information Technology, Government Engineering College Idukki, Kerala, India

Abstract—Group signature, as the name specifies is a special kind of signature scheme which allows a group of users to sign a message by preserving the constraints of anonymity and traceability. There are a lot of such schemes proposed by using number theoretic concepts. The emergence of quantum computers in the near future is making the existence of number theory based cryptographic constructions under scrutiny. Since lattice based cryptography overcomes the drawbacks of number theory based constructions, the post quantum world is interested in the lattice theory based constructions. This paper discusses about different lattice based group signatures.

Keywords—Group signatures; lattice based crypto; post quantum crypto; quantum computers; number theory

I. INTRODUCTION

Lattice based cryptography [10] finds its importance in the post quantum world, where the computational power is exponentially increased. Present world crypto systems does not consider the threat posed by the quantum computational power. The chances of breaking such systems using quantum computational power is very high. This is because of the fact that such systems are depending on hard problems which are breakable with quantum computational power. This raises the need for a good alternative, lattice based cryptography. It is making use of the hardness of some problems characterized by taking specific vector distances in the lattices. Quantum computational power seems to be insufficient for solving these problems. This feature of lattice problems can be used for the construction of post quantum crypto systems.

The algorithms that provide solution to the lattice problems takes exponential computational time. But the same algorithms, once given with quantum power can break the conventional number theoretic constructions in polynomial time, making them vulnerable to attacks by quantum computers [8]. So, lattice based cryptography seems to be the most attractive alternative for the post quantum world which is not so far away. The importance of lattice based cryptography also relies on the factors like worst case hardness, efficient implementations and relatively simple constructions. The research on the field of lattices have shown that there exist no polynomial time algorithm that approximates lattice problems to within polynomial factors. The security of all lattice based cryptographic constructions depends on this conjecture. Also, the development of lattice algorithms for solving these problems does not see any progress from the early 1980s.

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