Efficient forward secure identity-based shorter signature from lattice

Recently, Tsai et al. constructed an efficient identity-based signature (IBS) scheme and claimed that it was strongly unforgeable in the standard model. Unfortunately, we find that their scheme is insecure. By giving concrete attack, we show that their scheme does not meet the requirement of strong unforgeability. Meanwhile, we demonstrate that there are serious flaws in their security proof. The simulator cannot correctly answer the signing query in the security model. Furthermore, we propose an improved strongly unforgeable IBS scheme without random oracles. Compared with other strongly unforgeable IBS schemes in the standard model, our scheme is more efficient in terms of computation cost and signature size.

Cryptographic Primitives that Resist Backdooring and Subversion

Comment on “An efficient identity-based signature scheme with provable security”

Recently, the notion of the key-insulated public- key system has been suggested to protect the security of users' private keys. A general idea of this system is changing the user's private key along with the time, but the user's public key remains unchanged. In this paper, we propose a new identity (ID)-based key-insulated signature scheme from bilinear pairings. As compared with the recently proposed ID-based key-insulated signature schemes, our proposed scheme has better performance in the batch verifying phase. For security analysis, our scheme is a provably secure key-insulated signature scheme in the random oracle model and under the computational Diffie-Hellman assumption. Meanwhile, to demonstrate the additional advantage of a key-insulated signature, we present a novel application based on the proposed scheme, called full delegation ID-based proxy signature scheme with time restriction. To our best knowledge, no such a proxy signature scheme is proposed until now.

A revocable and comparable attribute-based signature scheme from lattices for IoMT

Identity-based signature (IBS) which is a paradigm built on public key cryptography has played a significant role in light-weight authentication. With the advent of the post quantum era, the lattice has become a main mathematical tool to construct quantum-immune cryptographic schemes. By utilizing an admissible hash function with compatible algorithms and lattice trapdoors as basic building blocks, we propose a new IBS scheme over lattices. The scheme is proved existentially unforgeable against adaptive identity attacks and chosen message attacks in the standard model under inhomogeneous short integer solution assumption via the generalized partitioning proof technique. Moreover, the scheme needs only logarithmic basic matrices as master public key while keeping the same private key size and signature size as those of other standard model lattice-based IBS schemes. This construction is the first adaptive-ID secure standard model IBS scheme over lattice with such space efficiency.

We present a quantumly secure identity-based signature scheme based on the standard short integer solution problem, featuring tight security reductions in the quantum and classic random oracle models. The scheme has short signatures. Each signature contains a single lattice vector plus a single bit. Compared to the existing tightly secure, short lattice identity-based signature schemes by Pan and Wagner (PQCrypto’21), our scheme has a shorter signature size (around 30% shorter), stronger unforgeability, relies on a weaker assumption, and has detailed proof in the quantum random oracle model.

A novel ID-based proxy-protected signature scheme based on identity information is presented in this paper. We review the concept ID-Based signature introduced by Shamir, define the security notion of an ID-Based signature. We also improve the Shamir’s ID-Based signature and prove its security under the proposed security notion. From the improved Shamir’s ID-Based signature scheme we construct an ID-Based proxy signature scheme, the security is based on the underlying ID-based signature scheme. Our scheme is efficient and easy to implement. The scheme simplifies the public key as the user’s id and can be easily applied to all the RSA-type cryptosystems.

One important property of group signatures is forward-security, which prevents an attacker in possession of a group signing key to forge signatures produced in the past. In case of exposure of one group member’s signing key, group signatures lacking forward-security need to invalidate all group public and secret keys (by re-initializing the whole system) but also invalidate all previously issued group signatures. Most of the existing forward-secure group signatures (FS-GS) are built from number-theoretic security assumptions which are vulnerable to quantum computers. The only post-quantum secure FS-GS scheme is built from lattices by Ling et al. (PQCrypto 19) in the random oracle model, following the classical framework of encrypt-then-prove, thus using non-interactive zero-knowledge (NIZK) proofs. In this work, we achieve the first FS-GS from lattices in the standard model. Our starting point is the group signature of Katsumada and Yamada (Eurocrypt 19) which replaces NIZK by attribute-based signatures (ABS), thus removing the need for random oracles. We first modify the underlying ABS of Tsabary (TCC 17) to equip it with forward-security property. We then prove that by plugging it back in the group signature framework of Katsumada and Yamada (Eurocrypt 19), we can design a FS-GS scheme secure in the standard model with public key and signature size constant in the number of users. Our constant size is achieved by relying on complexity leveraging, which further implies relying on the subexponential hardness of the Short Integers Solution (SIS) assumption.

在传统的公钥加密方案中,一旦解密密钥泄漏,系统的安全性将完全丧失.特别是随着越来越多的加密系统被应用到移动的、安全性低的设备中,密钥泄漏显得难以避免.入侵容忍公钥加密的提出就是为了减小密钥泄漏对加密系统的危害,具有比前向安全加密、密钥隔离加密更强的安全性.在这种体制下,整个生命周期被分割成离散的时间阶段,公钥固定不变,密钥信息分享在解密者和基地中,前者独立完成解密操作,而后者则在每个时间周期中提供一个更新信息来帮助演化解密密钥.此外,每个时间段内有多次密钥刷新的操作,可以刷新解密者的密钥和基密钥.当解密者和基地被入侵时,只要不是同时被入侵,安全性就可以得到保证.即使入侵者同时入侵解密者和基地,也不会影响以前时间段密文的安全性.提出了一个入侵容忍公钥加密方案,所有费用参数关于总共时间段数的复杂性均不超过对数的平方.证明了该方案是标准模型下安全的.这是一个不需要随机预言的可证明安全的入侵容忍公钥加密方案.;In traditional public-key encryption schemes, security guarantees will be fully lost once decryption secret keys are exposed. With the ever-increase in encryption systems used in mobile and low secuirity devices, key exposure seems unavoidable. An intrusionresilient public-key encryption is proposed to mitigate the damage for the encryption systems brought by key exposure, which provides more security than the forward-secure encryption and key-insulated encryption. In its primitive, the whole lifetime is divided into discrete periods where the public key is fixed. Secret keys are shared in a decrypter and a base. The former performs the decrypting operations on his own while the latter provides an updated message to help evolve secret keys in each period. Furthermore, multiple operations of refresh secret keys are performed to refresh decrypter and base secrets periodically. The security can be preserved when both the user and base are compromised, as long as they are not compromised simultaneously. In addition, the simultaneous compromise doesn't affect the security of the ciphertext generated in previous periods. This paper proposes an intrusion-resilient public-key encryption scheme. All the parameters in this scheme have at most a log-squared complexity in terms of the total number of time periods. The proposed scheme is proven to be secure in the standard model and is a provably secure intrusion-resilient public-key encryption scheme without random oracles.

PurposeThe practical purpose of this research is to propose a candidate for post-quantum signature standard that is free of significant drawback of the finalists of the NIST world competition, which consists in the large size of the signature and the public key. The practical purpose is to propose a fundamentally new method for development of algebraic digital signature algorithms.Design/methodology/approachThe proposed method is distinguished by the use of two different finite commutative associative algebras as a single algebraic support of the digital signature scheme and setting two different verification equation for a single signature. A single public key is computed as the first and the second public keys, elements of which are computed exponentiating two different generators of cyclic groups in each of the algebras.FindingsAdditionally, a scalar multiplication by a private integer is performed as final step of calculation of every element of the public key. The same powers and the same scalar values are used to compute the first and the second public keys by the same mathematic formulas. Due to such design, the said generators are kept in secret, providing resistance to quantum attacks. Two new finite commutative associative algebras, multiplicative group of which possesses four-dimensional cyclicity, have been proposed as a suitable algebraic support.Originality/valueThe introduced method is novel and includes new techniques for designing algebraic signature schemes that resist quantum attacks. On its base, a new practical post-quantum signature scheme with relatively small size of signature and public key is developed.

In this paper, we propose a new hard problem, called bilateral inhomogeneous small integer solution (Bi-ISIS), which can be seen as an extension of the small integer solution problem on lattices. The main idea is that, instead of choosing a rectangle matrix, we choose a square matrix with small rank to generate Bi-ISIS problem without affecting the hardness of the underlying SIS problem. Based on this new problem, we present two new hardness problems: computational Bi-ISIS and decisional problems. As a direct application of these problems, we construct a new lattice-based key exchange (KE) protocol, which is analogous to the classic Diffie- Hellman KE protocol. We prove the security of this protocol and show that it provides better security in case of worst-case hardness of lattice problems, relatively efficient implementations, and great simplicity.

In the problem of gradual key exposure, the secret key is assumed to be slowly compromised over time, so that more and more information about a secret key is eventually leaked. This models the general situation in the real world where memory, storage systems and devices cannot perfectly hide all information for long time. In this setting, in order to protect against exposure threats, the secret key is represented in an "exposure- resilient" form, which is periodically refreshed with the following guarantee: as long as the adversary does not learn "too much" information about the current representation of the secret between successive refreshes, the system should remain secure. To measure the efficiency of a given solution, one considers the "natural" secret key representation A, the "exposure- resilient" representation B, and examines the following three measures: (1) space loss which is the extra space required by B over A; (2) time loss which is the operation slowdown when B is used in place of A: and (3) exposure-resilience which is the fraction of B which can be "safely leaked". All the current solutions to the problem - including proactive secret sharing, all-or-nothing transforms and exposure-resilient functions - always suffered from non-trivial losses in both space and time in order to achieve varying levels of exposure-resilience. It was, therefore, informally believed that these losses are inevitable in even, reasonable application, since a "natural" representation A is unlikely to offer any exposure-resilience. We show this belief is false for the elegant "hierarchical identity-based encryption" (HIBE) of Gentry and Silverberg (2002), which is the only known fully junctional HIBE up to date. Specifically, we show that the natural secret key representation for the HIBE admits a simple and efficient refresh operation, which offers very high level of exposure-resilience, while incurring absolutely no space or time losses for decryption. We argue that this simple fact is quite powerful from a key storage security perspective, is highly applicable for such tasks as threshold decryption, and that it further makes HIBE a much more attractive alternative in various real life scenarios. On a philosophical level, while previous techniques protected against gradual key exposure in a generic way, oblivious to the application, we show that in certain situations one might achieve much better parameters by concentrating on the application at hand.

Attribute-based signature is a versatile class of digital signatures. In attribute-based signature, a signer obtains his private key corresponding to the set of his attributes from a trusted authority, and then he can sign a message with any predicate that is satisfied by his attributes set. Unfortunately, there does not exist an attributebased signature which is resistance to the quantum attacks. This means we do not have secure attribute-based signature schemes in a post-quantum world. Based on this consideration, an attribute-based signature on lattices, which could resist quantum attacks, is proposed. This scheme employs “bonsai tree” techniques, and could be proved secure under the hardness assumption of small integer solution problem.

In this paper, we first propose an efficient provably secure identity-based signature (IBS) scheme based on bilinear pairings, then propose an efficient identity-based blind signature (IBBS) scheme based on our IBS scheme. Assuming the intractability of the Computational Diffie-Hellman Problem, our IBS scheme is unforgeable under adaptive chosen-message and ID attack. Efficiency analyses show that our schemes can offer advantages in runtime over the schemes available. Furthermore, we show that, contrary to the authors claimed, Zhang and Kim’s scheme in ACISP 2003 is one-more forgeable, if the ROS-problem is solvable.