In the present scenario where thousands and millions of digital documents are transferred every day, the security of data has become a topic of global concern. Along with other cryptographic primitives, the proxy signature scheme is also widely used in various applications. The main part of our paper is a lattice-based proxy signature scheme. A Proxy Signature scheme is an arrangement that allows the transfer of singing rights from one entity or person to another on behalf of the original signer. Our scheme is based on the Ring-Learning with Error(R-LWE) problem which provides strong security with the worst-case to average-case reduction problem. Key construction and operations in our scheme are based on a ring of polynomials due to which both public and private keys are reduced and the size of the proxy signature also shrunk, while the security of our proposed scheme is based on the Short Integer Solution (SIS) problem.
In the present scenario where thousands and millions of digital documents are transferred every day, the security of data has become a topic of global concern. Along with other cryptographic primitives, the proxy signature scheme is also widely used in various applications. The main part of our paper is a lattice-based proxy signature scheme. A Proxy Signature scheme is an arrangement that allows the transfer of singing rights from one entity or person to another on behalf of the original signer. Our scheme is based on the Ring-Learning with Error(R-LWE) problem which provides strong security with the worst-case to average-case reduction problem. Key construction and operations in our scheme are based on a ring of polynomials due to which both public and private keys are reduced and the size of the proxy signature also shrunk, while the security of our proposed scheme is based on the Short Integer Solution (SIS) problem.
A proxy signature scheme permits an entity to delegate its signing rights to another. Proxy signature scheme has been widely used in numerous applications. This paper proposed a proxy signature scheme based on lattice cryptography which is different from traditional proxy signature schemes. This scheme combines the idea of the traditional proxy signature and the lattice-based signature together. The security of the proposed scheme is based on the Short Integer Solution (SIS) problem, the proposed proxy signature scheme has smaller key size and lower computation cost. We use the Bimodal Gaussian Distribution, Reject Sampling, Hash matrix and other technologies to extend the original digital signature scheme to the proxy signature scheme. In this paper we will give the security proof of the proxy signature scheme. Moreover, since the key construction of the scheme is based on the operation of the ring, so the public and private key size can be greatly shrunk.
We propose a variant version of ring learning with errors (R-LWE) assumption. Under the modified slightly assumption which is reducible to the worst-case problems on ideal lattice, we present a construction of digital signatures. So the scheme is provably secure based on the hardness of lattice problems (such as approximating the length of the shortest vector within a fixed poly(n) factor). Compared with some existing typical lattice-based signature schemes, the construction enjoys many advantages, including simple and efficient key generation algorithm, signing algorithm and verification algorithm to improve the efficiency of the scheme as well as to reduce the overhead. The sizes of the secret and public keys and the signature are almost linear O(n log n) (up to poly-logarithmic factors) in the dimension n of the lattice.
A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message. It combines the advantages of proxy signature and blind signature. Up to date, most proxy blind signature schemes rely on hard number theory problems, discrete logarithm, and bilinear pairings. Unfortunately, the above underlying number theory problems will be solvable in the postquantum era. Lattice‐based cryptography is enjoying great interest these days, due to implementation simplicity and provable security reductions. Moreover, lattice‐based cryptography is believed to be hard even for quantum computers. In this paper, we present a new identity‐based proxy blind signature scheme from lattices without random oracles. The new scheme is proven to be strongly unforgeable under the standard hardness assumption of the short integer solution problem (SIS) and the inhomogeneous small integer solution problem (ISIS). Furthermore, the secret key size and the signature length of our scheme are invariant and much shorter than those of the previous lattice‐based proxy blind signature schemes. To the best of our knowledge, our construction is the first short lattice‐based identity‐based proxy blind signature scheme in the standard model.
Proxy signature is one of the important primitives of public-key cryptography and plays an essential role in delivering security services in modern communications. However, existing post quantum proxy signature schemes with larger signature sizes might not be fully practical for some resource-constrained devices (e.g., Internet of Things devices). A signature scheme with message recovery has the characteristic that part or all of the message is embedded in the signature, which can reduce the size of the signature. In this paper, we present a new identity-based proxy signature scheme over an NTRU lattice with message recovery (IB-PSSMR), which is more efficient than the other existing identity-based proxy signature schemes in terms of the size of the signature and the cost of energy. We prove that our scheme is secure under a Short Integer Solution (SIS) assumption that is as hard as approximating several worst-case lattice problems in the random oracle model. We also discussed some application scenarios of IB-PSSMR in blockchain and Internet of Things (IOT). This paper provides a new idea for the design of lattice signature schemes in low resource constrained environments.
Proxy signature schemes safely ensure that an original signer transfers the signing right to a proxy signer, and a variety of these schemes have been developed for secure applications. Constructions of proxy signature schemes vary; recently developed schemes utilize lattices to safeguard against quantum attacks. However, existing lattice-based proxy schemes proved secure in the standard model have many public system parameters, reducing the efficiency of these schemes. To solve this problem, we utilize an admissible hash function with compatible algorithms (AHFwCA) and lattice trapdoors as an initial framework to propose a new lattice-based proxy signature scheme. While maintaining a similar key and signature size as prior schemes, this new proxy signature scheme requires fewer public system parameters. Compared with requiring linear basic matrices as public system parameters found in other standard model schemes, the proposed new scheme depends upon logarithmic basic matrices. Under the standard inhomogeneous short integer solution (ISIS) assumption, we prove that the scheme is existentially unforgeable against chosen message attacks and chosen warrant attacks (EUF-CMA-CWA) in the standard model by using the generalized partitioning proof technique. Thus, this paper partially solves the many parameters problem existed in the standard model lattice-based signature schemes.
Lattice-based cryptography is a branch of cryptography exploiting the presumed hardness of some well-known problems on lattices. Its main advantages are its simplicity, efficiency, and apparent security against quantum computers. The principle of the security proofs in lattice-based cryptography is to show that attacking a given scheme is at least as hard as solving a particular problem, as the Learning with Errors problem (LWE) or the Small Integer Solution problem (SIS). Then, by showing that those two problems are at least as hard to solve than a hard problem on lattices, presumed polynomial time intractable, we conclude that the constructed scheme is secure.In this thesis, we improve the foundation of the security proofs and build new cryptographic schemes. We study the hardness of the SIS and LWE problems, and of some of their variants on integer rings of cyclotomic fields and on modules on those rings. We show that there is a classical hardness proof for the LWE problem (Regev's prior reduction was quantum), and that the module variants of SIS and LWE are also hard to solve. We also give two new lattice-based group signature schemes, with security based on SIS and LWE. One is the first lattice-based group signature with logarithmic signature size in the number of users. And the other construction allows another functionality, verifier-local revocation. Finally, we improve the size of some parameters in the work on cryptographic multilinear maps of Garg, Gentry and Halevi in 2013.