Making Existential-Unforgeable Signatures Strongly Unforgeable in the Quantum Random-Oracle Model

Strongly unforgeable signature schemes provide a more stringent security guarantee than the standard existential unforgeability. It requires that not only forging a signature on a new message is hard, it is infeasible as well to produce a new signature on a message for which the adversary has seen valid signatures before. Strongly unforgeable signatures are useful both in practice and as a building block in many cryptographic constructions. This work investigates a generic transformation that compiles any existential-unforgeable scheme into a strongly unforgeable one, which was proposed by Teranishi et al. and was proven in the classical random-oracle model. Our main contribution is showing that the transformation also works against quantum adversaries in the quantum random-oracle model. We develop proof techniques such as adaptively programming a quantum random-oracle in a new setting, which could be of independent interest. Applying the transformation to an existential-unforgeable signature scheme due to Cash et al., which can be shown to be quantum-secure assuming certain lattice problems are hard for quantum computers, we get an efficient quantum-secure strongly unforgeable signature scheme in the quantum random-oracle model.Comment: 15 pages, to appear in Proceedings TQC 201

Ring Signature from Bonsai Tree: How to Preserve the Long-Term Anonymity

Signer-anonymity is the central feature of ring signatures, which enable a user to sign messages on behalf of an arbitrary set of users, called the ring, without revealing exactly which member of the ring actually generated the signature. Strong and long-term signer-anonymity is a reassuring guarantee for users who are hesitant to leak a secret, especially if the consequences of identification are dire in certain scenarios such as whistleblowing. The notion of \textit{unconditional anonymity}, which protects signer-anonymity even against an infinitely powerful adversary, is considered for ring signatures that aim to achieve long-term signer-anonymity. However, the existing lattice-based works that consider the unconditional anonymity notion did not strictly capture the security requirements imposed in practice, this leads to a realistic attack on signer-anonymity. In this paper, we present a realistic attack on the unconditional anonymity of ring signatures, and formalize the unconditional anonymity model to strictly capture it. We then propose a lattice-based ring signature construction with unconditional anonymity by leveraging bonsai tree mechanism. Finally, we prove the security in the standard model and demonstrate the unconditional anonymity through both theoretical proof and practical experiments

URDP: General Framework for Direct CCA2 Security from any Lattice-Based PKE Scheme

Design efficient lattice-based cryptosystem secure against adaptive chosen ciphertext attack (IND-CCA2) is a challenge problem. To the date, full CCA2-security of all proposed lattice-based PKE schemes achieved by using a generic transformations such as either strongly unforgeable one-time signature schemes (SU-OT-SS), or a message authentication code (MAC) and weak form of commitment. The drawback of these schemes is that encryption requires "separate encryption". Therefore, the resulting encryption scheme is not sufficiently efficient to be used in practice and it is inappropriate for many applications such as small ubiquitous computing devices with limited resources such as smart cards, active RFID tags, wireless sensor networks and other embedded devices. In this work, for the first time, we introduce an efficient universal random data padding (URDP) scheme, and show how it can be used to construct a "direct" CCA2-secure encryption scheme from "any" worst-case hardness problems in (ideal) lattice in the standard model, resolving a problem that has remained open till date. This novel approach is a "black-box" construction and leads to the elimination of separate encryption, as it avoids using general transformation from CPA-secure scheme to a CCA2-secure one. IND-CCA2 security of this scheme can be tightly reduced in the standard model to the assumption that the underlying primitive is an one-way trapdoor function.Comment: arXiv admin note: text overlap with arXiv:1302.0347, arXiv:1211.6984; and with arXiv:1205.5224 by other author

Learning with Errors is easy with quantum samples

Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with Errors and show that there exists an efficient quantum learning algorithm (with polynomial sample and time complexity) for the Learning with Errors problem where the error distribution is the one used in cryptography. While our quantum learning algorithm does not break the LWE-based encryption schemes proposed in the cryptography literature, it does have some interesting implications for cryptography: first, when building an LWE-based scheme, one needs to be careful about the access to the public-key generation algorithm that is given to the adversary; second, our algorithm shows a possible way for attacking LWE-based encryption by using classical samples to approximate the quantum sample state, since then using our quantum learning algorithm would solve LWE

Revocable Hierarchical Attribute-based Signatures from Lattices

Attribute-based Signatures (ABS) allow users to obtain attributes from issuing authorities, and sign messages whilst simultaneously proving compliance of their attributes with a verification policy. ABS demands that both the signer and the set of attributes used to satisfy a policy remain hidden to the verifier. Hierarchical ABS (HABS) supporting roots of trust and delegation were recently proposed to alleviate scalability issues in centralised ABS schemes. An important yet challenging property for privacy-preserving ABS is revocation, which may be applied to signers or some of the attributes they possess. Existing ABS schemes lack efficient revocation of either signers or their attributes, relying on generic costly proofs.Moreover, in HABS there is a further need to support revocation of authorities on the delegation paths, which is not provided by existing HABS constructions. This paper proposes a direct HABS scheme with a Verifier-Local Revocation (VLR) property. We extend the original HABS security model to address revocation and develop a new attribute delegation technique with appropriate VLR mechanism for HABS, which also implies the first ABS scheme to support VLR. Moreover, our scheme supports inner-product signing policies, offering a wider class of attribute relations than previous HABS schemes, and is the first to be based on lattices, which are thought to offer post-quantum security

A Lattice-Based Identity-Based Proxy Blind Signature Scheme in the Standard Model

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

Lattice-based Group Signature Scheme with Verifier-local Revocation

International audienceSupport of membership revocation is a desirable functionality for any group signature scheme. Among the known revocation approaches, verifier-local revocation (VLR) seems to be the most flexible one, because it only requires the verifiers to possess some up-to-date revocation information, but not the signers. All of the contemporary VLR group signatures operate in the bilinear map setting, and all of them will be insecure once quantum computers become a reality. In this work, we introduce the first lattice-based VLR group signature, and thus, the first such scheme that is believed to be quantum-resistant. In comparison with existing lattice-based group signatures, our scheme has several noticeable advantages: support of membership revocation, logarithmic-size signatures, and weaker security assumption. In the random oracle model, our scheme is proved to be secure based on the hardness of the SIVP_{SoftO(n^{1.5})}$ problem in general lattices - an assumption that is as weak as those of state-of-the-art lattice-based standard signatures. Moreover, our construction works without relying on encryption schemes, which is an intriguing feature for group signatures