More than 98% of all microprocessors sold worldwide are used in embedded devices, and will continue to accelerate due to the emerging applications in Internet of Things (IoT). Cryptographic algorithms based on multivariate quadratic (MQ) equations are suitable for low-cost IoT-constrained devices since they require only modest computational resources. In this article, we describe the design and implementations of a new public-key signature scheme based on MQ equations highly optimized for practicability. The novel scheme is obtained as a result of the combination of solvable systems of quadratic equations and sparse polynomials. We provide a security analysis of our scheme against known algebraic attacks and derive a concrete parameter. Performance of our scheme on an 8-b AVR microprocessor is the fastest among known signature schemes: signing of our scheme is about 36.4× faster than that of ECDSA-256 (NIST P-256), the most widely deployed international standard signature scheme. The signing of our scheme is about 8.6× and 11.0× faster than those of Rainbow and BLISS-BI, respectively. The secret size of our scheme has reduced by a factor of 87% compared to Rainbow. Our scheme requires signatures of 80 B which is comparable to ECDSA-256 of 64 B. We also implement a protected version of our scheme on the 8-b microprocessor to prevent the current side-channel attacks presented in CHES 2018. Even our protected version is the fastest singing among the known signature schemes.

Energy cost of transmitting a single bit of information is approximately the same as that needed for processing a thousand operations in a typical sensor node. Thus, a practical way to prolong a wireless sensor network lifetime is to reduce the sensor energy consumption in data transmissions. Data aggregation is an efficient way to minimize energy consumption on sensors. In this paper, we propose a practical secure data aggregation scheme, Sen-SDA, based on an additive homomorphic encryption scheme, an identity-based signature scheme, and a batch verification technique with an algorithm for filtering injected false data. We then investigate the feasibility of our scheme using low-cost microcontrollers choosing two popular IEEE 802.15.4-compliant wireless sensor network hardware platforms, MICAz and Tmote Sky, used in real-life deployments.

ABSTRACT The vector decomposition problem has been considered as a hard problem, which is applicable to cryptography. Okamoto and Takashima proposed various types of public key cryptographic schemes based on the VDP. In this paper, we study the cryptographic implications of Okamoto‐Takashima schemes with respect to the properties of public keys. In the public key cryptography, one public key is associated to a unique private key, and an action using the public key implicitly assumes that the corresponding private action can be done only with the corresponding private key. We formalize this security issue by introducing the notion of equivalent public keys. We show that equivalent public keys exist in the Okamoto‐Takashima basic signature scheme and the homomorphic encryption scheme. We present a strong key substitution attack to their basic signature. We suggest how to prevent equivalent public keys and strong key substitution attack in their signature scheme. We point out that there are cases with no efficient methods to prevent equivalent public keys in their encryption scheme. Copyright © 2013 John Wiley & Sons, Ltd.

ABSTRACT Redactable signature schemes permit deletion of arbitrary substrings of a signed document while preserving the authenticity of the remaining document. Most of known redactable signatures based on pairing have large‐sized signatures and the sizes depend on the product of security parameter and the number of blocks of the redacted document. In this paper, we present a short redactable signature scheme based on pairing. We modify Waters signature scheme to obtain an underlying standard signature defined on composite‐order bilinear group. The modified scheme satisfies the unforgeability under the known message attack based on the Computational Diffie–Hellman assumption. Based on the modified Waters signature, we propose a short redactable signature that is existentially unforgeable under random message attack and weakly private. The size of the proposed scheme is 20% of known redactable signatures using aggregated pairing‐based signatures when half of the message blocks are deleted. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, we propose a new method for constructing a bilinear pairing over (hyper)elliptic curves, which we call the R-ate pairing. This pairing is a generalization of the Ate and Ateipairing, and can be computed more efficiently. Using the R-ate pairing, the loop length in Miller's algorithm can be as small as log (r1/phi(k)) some pairing-friendly elliptic curves which have not reached this lower bound. Therefore, we obtain savings of between 29% and 69% in overall costs compared to the Ateipairing. On supersingular hyperelliptic curves of genus 2, we show that this approach makes the loop length in Miller's algorithm shorter than that of the Ate pairing.