It is well known that conventional digital signature algorithms such as RSA and ECDSA are vulnerable to quantum computing attacks. Hash-based signature schemes are attractive as post-quantum signature schemes in that it is possible to calculate the quantitative security level and the security is proven. SPHINCS is a stateless hash-based signature scheme and introduces HORST few-time signature scheme which is an improvement of HORS. However, HORST as well as HORS suffers from pretty large signature sizes. HORSIC is proposed to reduce the signature size, yet does not provide in-depth security analysis. In this paper, we propose HORSIC+, which is an improvement of HORSIC. HORSIC+ differs from HORSIC in that HORSIC+ does not apply f as a plain function to the signature key, but uses a member of a function family. In addition, HORSIC+ uses the chaining function similar to W-OTS+. These enable the strict security proof without the need for the used function family to be a permutation or collision resistant. HORSIC+ is existentially unforgeable under chosen message attacks, assuming a second-preimage resistant family of undetectable one-way functions and cryptographic hash functions in the random oracle model. HORSIC+ reduces the signature size by as much as 37.5% or 18.75% compared to HORS and by as much as 61.5% or 45.8% compared to HORST for the same security level.

The distributed trigger counting (DTC) problem is defined as raising an alarm and notifying a user when the total number of received triggers reaches a predefined value w in a distributed system of n nodes. DTC algorithms can be used for environmental surveillance with sensor networks and global snapshots. In this paper, we propose a simple and efficient algorithm for the DTC problem. The proposed algorithm is based on a tree structure of degree n and height 2. The proposed algorithm operates in three phases depending on the remaining number of triggers. We prove the correctness of the proposed algorithm: the probability of not notifying a user even though the total number of received triggers reaches w is 0. Experimental results show that the proposed algorithm has lower message complexity than the best previous algorithms: CoinRand and TreeFill. MaxRcv (the maximum number of received messages per node) of the proposed algorithm is also smaller than CoinRand and TreeFill when the number of nodes is not very large.

No abstract

No abstract

No abstract