The function of the Internet proxy is to check and convert the data exchanged between client and server. In fact, the two-party secure communication protocol with good security is turned into an unsafe multiparty protocol. At present, there are relatively few proxy protocols that can be applied in practice. This paper analyzes the classic agent protocol mcTLS and pointed out the security issues. We focus on the security of TLS 1.3 and proposed a lattice-based multi-party proxy protocol: LaTLS. LaTLS can be proved secure in the eCK model, it can resist key-sharing attacks, counterfeiting attacks, replay attacks, and achieve forward security. Compared with traditional DH and ECDH schemes, LaTLS is more effcient. Its security is based on the shortest vector problem, therefor it has anti-quantum attack properties.
The function of the Internet proxy is to check and convert the data exchanged between client and server. In fact, the two-party secure communication protocol with good security is turned into an unsafe multiparty protocol. At present, there are relatively few proxy protocols that can be applied in practice. This paper analyzes the classic agent protocol mcTLS and pointed out the security issues. We focus on the security of TLS 1.3 and proposed a lattice-based multi-party proxy protocol: LaTLS. LaTLS can be proved secure in the eCK model, it can resist key-sharing attacks, counterfeiting attacks, replay attacks, and achieve forward security. Compared with traditional DH and ECDH schemes, LaTLS is more effcient. Its security is based on the shortest vector problem, therefor it has anti-quantum attack properties.
In this paper, we have proposed a two-party authenticated key establishment (AKE), and authenticated key transport protocols based on lattice-based cryptography, aiming to provide security against quantum attacks for secure communication. This protocol enables two parties, who may share long-term public keys, to securely establish a shared session key, and transportation of the session key from the server while achieving mutual authentication. Our construction leverages the hardness of lattice problems Ring Learning With Errors (Ring-LWE), ensuring robustness against quantum and classical adversaries. Unlike traditional schemes whose security depends upon number-theoretic assumptions being vulnerable to quantum attacks, our protocol ensures security in the post-quantum era. The proposed protocol ensures forward secrecy, and provides security even if the long-term key is compromised. This protocol also provides essential property key freshness and resistance against man-in-the-middle attacks, impersonation attacks, replay attacks, and key mismatch attacks. On the other hand, the proposed key transport protocol provides essential property key freshness, anonymity, and resistance against man-in-the-middle attacks, impersonation attacks, replay attacks, and key mismatch attacks. A two-party key transport protocol is a cryptographic protocol in which one party (typically a trusted key distribution center or sender) securely generates and sends a session key to another party. Unlike key exchange protocols (where both parties contribute to key generation), key transport protocols rely on one party to generate the key and deliver it securely. The protocol possesses a minimum number of exchanged messages and can reduce the number of communication rounds to help minimize the communication overhead.
ABSTRACT A three‐party post‐quantum key agreement protocol involves server with two communicating parties securely agreeing on a shared secret key in a way that is resistant to quantum attacks. Once the shared secret key is shared using authenticated key agreement protocol, then user (A), and user (B) can use it for securing communication channel using symmetric‐key encryption AES‐256 algorithm. Although there are few third‐party post‐quantum authenticated and key agreement schemes exist, but the recent studies in this paper illustrates that they are not satisfying properties like unlinkability, anonymity, perfect forward secrecy, and signal leakage attacks. Therefore, the proposed protocol ensures anonymity, unlinkablity, perfect forward secrecy, and resistant against signal leakage attacks. The proposed protocol uses different random numbers for each of sessions and ensures freshness of the session key to maintain forward secrecy. In this protocol, the user (A) only communicates with server, and establish an authenticated session key with user (B) which avoids server overheads. The use of ring learning with errors (RLWE) instead of the simpler learning with errors (LWE) is primarily motivated by the need for efficiency, compactness, and scalability in cryptographic applications. A comparative study, including both performance and security assessments, demonstrates that the proposed design is more secure and efficient.
Proxy re-encryption plays an important role for data security in cloud computing and big data, but the traditional re-encryption scheme based on the classical number theory problem cannot resist quantum attack, and the lattice-based cryptosystem has been proved to have the ability to resist quantum attack, so the lattice-based re-encryption scheme has always been a research hotspot. In view of the problem that collusion-resistance and multi-hop cannot be satisfied at the same time in existing schemes, this paper proposes a new identity-based proxy re-encryption scheme on lattice. Firstly, the scheme uses trapdoors as private keys to achieve one-way anti-collusion. In addition, we construct a variant of Learning with Errors (LWE), which uses a convert algorithm to transform the user matrix and replace the vector with a uniform matrix, so that the scheme can meet the requirements of multi-hop and encrypt multiple bits of messages at one time. Theoretical analysis and experimental simulation prove that the security of the new scheme can be reduced to a decision LWE problem, which can reach the IND-sID-CPA security in the standard model and can improve the encryption efficiency while ensuring the security.
With the advancement of quantum computing, the utilization of quantum algorithms such as Shor’s algorithm enables the efficient resolution of problems that are intractable in classical computing paradigms, posing a significant threat to traditional signature schemes. Lattice-based cryptography is considered one of the most promising post-quantum cryptographic algorithms due to its computational advantages and potential resistance to quantum attacks. Proxy signature is an authorization mechanism that allows the original signer to delegate the signing power to a proxy. The security of existing proxy signature schemes is mostly based on classical hard problems, which cannot guarantee security under quantum attacks. Therefore, this paper combines lattice-based cryptography with proxy signatures to propose a new lattice-based proxy signature scheme (NLBPS). NLBPS constructs signatures using lattice-based trapdoor sampling algorithms and preimage sampling algorithms. Comparative analysis shows that the proposed scheme has relatively smaller key and signature sizes compared to some existing lattice-based proxy signature schemes, and it also offers a certain improvement in computational efficiency.
This thesis is about lattices. Much of the cryptography that is being used today, can be broken by (large) quantum computers in the future! There are multiple computational problems involving lattices that are easy in dimension 2 or 3 but are hard in high dimensions. These problems are, as far as we know, difficult for both classical computers and quantum computers. Therefore, we can use lattices to build so-called post-quantum cryptography, which will remain secure even when large quantum computers are built. A goal of cryptography is to make secure communication between two or more parties possible. There are two important cryptographic protocols: encryption and signature schemes. Encryption makes the content of messages incomprehensible for eavesdroppers. A signature scheme enables one to verify whether a message was really sent by some party. The two parties hold different keys in a signature scheme, just like in the real world: one party writes signatures with a special pen, while the other knows the precise colour composition of the ink in the pen. Encryption is similar: everyone can encrypt a message using a public key, while deciphering is only possible for one owning the private key. Lattices can be used to generate such a public/private key pair. The private key is a description of the lattice, that consists of the shortest lattice points. This key is private because it is difficult in high dimensions, to even compute a somewhat short lattice point. The public key is an arbitrary description of the lattice, which usually consists of long lattice points. The fastest algorithm that upon input a public key, computes the private key associated to it, requires time and memory that grows exponentially as a function of the dimension. Part II concerns the dual attack. This is an algorithm that, upon input a description of a lattice and a point, outputs the lattice point that is the closest to the point while making use of the dual lattice. Every dual lattice point corresponds with a wave function (in fact, character) that is maximal at every lattice point. Using this wave function, one can decide whether a point is close to the lattice or not. By subdividing the lattice like a chess board into a black sublattice and a white coset, you can determine whether the black sublattice is closer to the point than the white coset. If this method is repeatedly sufficiently many times, one can determine which lattice point is closest to the point. Chapter 3 shows that an assumption that was used in literature to analyse the so-called dual-sieve attack is incorrect, because it produces contradictions in multiple theoretic regimes, and experiments show that it leads to wrong predictions. Chapter 4 contains an alternative assumption for the dual-sieve attack. This assumption leads to accurate predictions for multiple important probability distributions of points. Part III concerns the lattice isomorphism problem (LIP). Special lattices with good properties are convenient when building a signature scheme, because they make a signature scheme very efficient. Because every cryptology researcher knows a good description of such a lattice, the lattice has to be hidden differently. Using LIP we can hide the lattice by randomly rotating it. The specific rotation now becomes the private key. Chapter 5 is dedicated to the construction of the signature scheme Hawk, which is based on LIP. To find the private key of Hawk, one needs to solve smLIP, a module variant of LIP for the simple lattice Z^n, the lattice consisting of all integer vectors. Security of Hawk is based on the new one more shortest vector problem (omSVP). In Chapter 6 we study automorphisms of the module lattice: a rotation that maps the lattice to itself. Theorem 6.2 states that, using a nontrivial automorphism, it becomes much easier to find a short vector, and to solve smLIP. An automorphism sends a short lattice point to a (possibly different) short lattice point, and therefore may easily solve omSVP. If smLIP is a difficult computational problem, then it will be difficult to find a nontrivial automorphism, and thus, it will be difficult to solve omSVP by ‘just’ finding a nontrivial automorphism.
A key exchange protocol is an important primitive in the field of information and network security and is used to exchange a common secret key among various parties. A number of key exchange protocols exist in the literature and most of them are based on the Diffie-Hellman (DH) problem. But, these DH type protocols cannot resist to the modern computing technologies like quantum computing, grid computing etc. Therefore, a more powerful non-DH type key exchange protocol is required which could resist the quantum and exponential attacks. In the year 2013, Lei and Liao, thus proposed a lattice-based key exchange protocol. Their protocol was related to the NTRU-ENCRYPT and NTRU-SIGN and so, was referred as NTRU-KE. In this paper, we identify that NTRU-KE lacks the authentication mechanism and suffers from the man-in-the-middle (MITM) attack. This attack may lead to the forging the authenticated users and exchanging the wrong key.