We present a constant-size signature scheme under the CDH assumption. It has a tighter security reduction than any other constant-size signature scheme with a security reduction to solving some intractable search problems. Hofheinz, Jager, and Knapp (PKC 2012) presented a constant-size signature scheme under the CDH assumption with a reduction loss of O(q), where q is the number of signing queries. They also proved that the reduction loss of O(q) is optimal in a black-box security proof. To the best of our knowledge, no constant-size signature scheme has been proposed with a tighter reduction (to the hardness of a search problem) than that proposed by Hofheinz et al., even if it is not re-randomizable. We remark that our scheme is not re-randomizable. We achieve the reduction loss of O(q/d), where d is the number of group elements in a public key.

No abstract

No abstract

A secure messaging protocol, such as the Signal protocol, provides end-to-end encrypted asynchronous communication. This paper focuses on a secure group messaging (SGM) protocol, and proposes a method capable of hiding membership information from the viewpoint of non group members, which we call “membership privacy”. In this work, we add membership privacy to the Asynchronous Ratcheting Trees (ART) protocol (proposed by Cohn-Gordon et al., (ACM CCS 2018)). For hiding membership-related values in the setup phase, we employ a key-private and robust publickey encryption (Abdalla et al., TCC2010/JoC2018). Moreover, we introduce a group common key to encrypt membership information in the key update phase. Our modification achieves asymptotically the same efficiency of the ART protocol in the setup phase. Any additional cost for key update does not depend on the number of group members. Therefore, the proposed protocol can add membership privacy to the ART protocol with a quite small overhead. Specifically, one encryption and decryption of a symmetric-key encryption scheme and one execution of a key-derivation function for each key update are employed. Finally, we discuss how to extend our protocol to provide sender-specific authentication, dynamic groups, group-size hiding, and how to adopt our technique to the Messaging Layer Security (MLS) protocol. We note that, although Chase et al. (ACM CCS 2020) have considered the same notion, their proposal is an extension of Signal so called “Pairwise Signal” where a group message is repeatedly sent over individual Signal channels. Thus their protocol is not scalable.

We propose a short signature scheme under the ring-SIS assumption in the standard model. Specifically, by revisiting an existing construction [Ducas and Micciancio, CRYPTO 2014], we demonstrate lattice-based signatures with improved reduction loss. As far as we know, there are no ways to use multiple tags in the signature simulation of security proof in the lattice tag-based signatures. We address the tag-collision possibility in the lattice setting, which improves reduction loss. Our scheme generates tags from messages by constructing a scheme under a mild security condition that is existentially unforgeable against random message attack with auxiliary information. Thus our scheme can reduce the signature size since it does not need to send tags with the signatures. Our scheme has short signature sizes of 𝑂 (1) and achieves tighter reduction loss than that of Ducas et al.'s scheme. Our proposed scheme has two variants. Our scheme with one property has tighter reduction and the same verification key size of 𝑂 (log 𝑛) as that of Ducas et al.'s scheme, where 𝑛 is the security parameter. Our scheme with the other property achieves much tighter reduction loss of 𝑂 (𝑄/𝑛) and verification key size of 𝑂 (𝑛), where 𝑄 is the number of signing queries.

No abstract

No abstract

No abstract