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Lattice Based Group Key Exchange Protocol in the Standard Model

Parhat Abla

Published Jul 24, 2021• 1 citation
Publisher

Abstract

Group key exchange schemes allow group members to agree on a session key. Although there are many works on constructing group key exchange schemes, but most of them are based on algebraic problems which can be solved by quantum algorithms in polynomial time. Even if several works considered lattice based group key exchange schemes, believed to be post-quantum secure, but only in the random oracle model. In this work, we propose a group key exchange scheme based on ring learning with errors problem. On contrast to existing schemes, our scheme is proved to be secure in the standard model. To achieve this, we define and instantiate multi-party key reconciliation mechanism. Furthermore, using known compiler with lattice based signature schemes, we can achieve authenticated group key exchange with postquantum security.

DOI
10.5121/csit.2021.111113

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Group key exchange schemes allow group members to agree on a session key. Although there are many works on constructing group key exchange schemes, but most of them are based on algebraic problems which can be solved by quantum algorithms in polynomial time. Even if several works considered lattice based group key exchange schemes, believed to be post-quantum secure, but only in the random oracle model. In this work, we propose a group key exchange scheme based on ring learning with errors problem. On contrast to existing schemes, our scheme is proved to be secure in the standard model. To achieve this, we define and instantiate multi-party key reconciliation mechanism. Furthermore, using known compiler with lattice based signature schemes, we can achieve authenticated group key exchange with postquantum security.
An authenticated mobile key exchange is necessary for post quantum secure communication over a public channel. It allows two entities to create a secure and unique session key for every communication session. We feel a need to design two party efficient and secure authenticated key agreement. We have also observed all the protocols given above are based on learning with error assumption over a finite ring. The ”Module Learning with Errors” assumption is the more appropriate choice among ”Learning with Errors” and ”Ring Learning with Errors” for designing practical password-authenticated key exchange protocols. With the help of ”Module Learning with Errors” assumption, and by lowering the number of ring polynomials, several implementations of the protocols can be realized. Therefore, this paper contains quantum safe, efficient, and practical ”Module Learning with Errors” assumption based authenticated key agreement protocol. The protocol’s security analysis is presented within the framework of the random oracle model.
A three-party authenticated key exchange protocol enables two entities to agree on a session key with the help of a dedicated server through an insecure channel. Lattice based cryptography plays a very important role in authentication and key exchanges that protects against the threat of quantum attacks. However, it is not easy to design quantum resistant password based three-party protocol due to the high demand for security requirements and the limited resources nature of mobile devices. In this article, we have proposed a new post quantum three party key exchange based on a variant of lattice assumption, the ring learning errors. The protocol ensures security against impersonation attack, stolen smartcard attack, password guessing attack, and other existing attacks. In authentication phase, the protocol have used lattice based cryptography that plays a very important role in authentication and key exchanges that protects against the threat of quantum attacks. The proposed protocol ensures both securities against quantum attacks and efficiency due to simple algebraic operations that are polynomial addition and multiplications.
Using the hard assumption of Ring-Decision Learning With Errors (Ring-DLWE) in the lattice, a new Authenticated Key Exchange (AKE) scheme is proposed, which is based on the Peikert's reconciliation technique. Under the standard model, the proposed scheme is provably secure in the CK model, which is additionally achieves weak Perfect Forward Secrecy (wPFS). Compared with the current Key Exchange (KE) schemes based on the LWE, the proposed scheme not only protects the shared session key with balanced key derivation function but also resists quantum attacks because of the hard assumption on lattice problem.
Using the hard assumption of Ring-Decision Learning With Errors (DLWE) in the lattice, we propose a new authenticated key exchange (AKE) scheme which is based on Peikert’s reconciliation technique. Under the CK+ model, the proposed scheme is provably secure. Compared with the traditional Diffie-Hellman (DH) authenticated key exchange (AKE) schemes, the proposed scheme not only has better efficiency and stronger security but also resists quantum attacks because of the hard assumption on lattice problem. The comparisons between Ring-LWE based ones shows that the proposed scheme protects the shared session key with balanced key derivation function (KDF) compared with those current AKE schemes from LWE.
A three-party authenticated key exchange protocol enables two entities to agree on a session key with the help of a dedicated server over public channel. Shor’s algorithm is a big threat for existing authenticated key exchange protocols. Lattice based cryptography plays a very important role in designing authentication and key agreement secure against the threat of quantum attacks. However, it is not easy job to design quantum resistant password based three party protocol due to the high demand for security requirements and the limited resources nature of mobile devices. In this article, we have proposed a new post quantum three party key exchange based on ring learning with errors assumption. This protocol is motivated from Islam et al.’s authenticated key exchange protocol. Their protocol is not secure against stolen smartcard attack, password guessing attack, and can’t provide user anonymity. The anonymous communication is a big requirement for practical applications like e-healthcare services/smart vehicular communication. This paper also contains the performance analysis of the proposed protocol along with other relevant protocols.
This note describes a key exchange method based on the ring-LWE (RLWE) assumption. It builds upon several results, including Regev's landmark quantum reduction from certain worst case lattice problems (approx. GapSVP and SIVP) to random instances of the search variant of a particular learning problem (LWE). It also builds on the follow on work of Lyubashevsky, Peikert and Regev on the average case hardness of the RLWE search variant for polynomially bounded numbers of RLWE samples, along with novel applications of automorphism groups in number fields for a RLWE search to decision reduction (thereby demonstrating pseudorandomness of RLWE in these number fields). Subsequently, these results were adopted for the construction of Diffie-Hellman like key exchange methods by Peikert, and then by Lindner and Peikert followed by Ding and then by Ding, Xie and Lin who proposed efficient variants of such protocols. Subsequent work by Peikert proposed another efficient variant, phrased as a key encapsulation method, incorporating a low bandwidth reconciliation technique allowing two parties to exactly agree on a uniformly distributed secret value from noisy RLWE instances. This was followed by a concrete instantiation with parameter sets by Bos, Costello, Naehrig, Stebila, followed by another instantiation by Alkim, Ducas, Poppelmann and Schwabe with the same ring polynomial but a smaller modulus and a different reconciliation method. Unlike most other public key cryptography based key exchange methods, it is believed that RLWE based key exchange would remain secure in the event that an adversary is able to build a quantum computer. This document is a product of the Crypto Forum Research Group (CFRG).