Digital signatures are basic cryptographic tools to provide authentication and integrity in the emerging ubiquitous systems in which resource-constrained devices are expected to operate securely and efficiently. However, existing digital signatures might not be fully practical for such resource-constrained devices (e.g., medical implants) that have energy limitations. Some other computationally efficient alternatives (e.g., one-time/multiple-time signatures) may introduce high memory and/or communication overhead due to large private key and signature sizes.
In this paper, our contributions are two-fold: First, we develop a new lightweight multiple-time digital signature scheme called Signer Efficient Multiple-time Elliptic Curve Signature (SEMECS), which is suitable for resource-constrained embedded devices. SEMECS achieves optimal signature and private key sizes for an EC-based signature without requiring any EC operation (e.g., EC scalar multiplication or addition) at the signer. We prove SEMECS is secure (in the random oracle model) with a tight security reduction. Second, we fully implemented SEMECS on an 8-bit AVR microprocessor with a comprehensive energy consumption analysis and comparison. Our experiments confirm up to 19× less battery-consumption for SEMECS as compared to its fastest (full-time) counterpart, SchnorrQ, while offering significant performance advantages over its multiple-time counterparts in various fronts. We open-source our implementation for public testing and adoption.
more »
« less
This content will become publicly available on July 12, 2024
Efficient and Side-Channel Resistant Design of High-Security Ed448 on ARM Cortex-M4
The demand for classical cryptography schemes continues
to increase due to the exhaustive studies on their security.
Thus, constant improvement of timing, power consumption, and
memory requirements are needed for the most widely used
classical Elliptic Curve Cryptography (ECC) primitives, suiting
high- as well as low-end devices. In this work, we present the
first implementation of the Edwards Curve Digital Signature
Algorithm (EdDSA) based on the Ed448 targeting the ARM
Cortex-M4-based STM32F407VG microcontroller, which forms a
large part of the Internet of Things (IoT) world. We report timing
and memory consumption results based on portable C and targetspecific
hand-crafted assembly code implementations of the lowlevel
finite filed arithmetics. We optimize the high-level group operations
by implementing the efficient scalar multiplication over
the Ed448 isogenous map to reduce the computation complexity.
Furthermore, we provide a side-channel analysis (SCA) and fault
attack protected design by developing point randomization, scalar
blinding techniques, and repeated signature, and evaluate the
performance. Our optimized architecture performs a signature
and verification in 39.88ms and 51.54ms, respectively, where SCA
protection can be achieved at less than 6.4% cost of performance
overhead.
more »
« less
- Award ID(s):
- 1801341
- NSF-PAR ID:
- 10486311
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- HOST: Hardware Oriented Security and Trust
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The elliptic curve family of schemes has the lowest computational latency, memory use, energy consumption, and bandwidth requirements, making it the most preferred public key method for adoption into network protocols. Being suitable for embedded devices and applicable for key exchange and authentication, ECC is assuming a prominent position in the field of IoT cryptography. The attractive properties of the relatively new curve Curve448 contribute to its inclusion in the TLS1.3 protocol and pique the interest of academics and engineers aiming at studying and optimizing the schemes. When addressing low-end IoT devices, however, the literature indicates little work on these curves. In this paper, we present an efficient design for both protocols based on Montgomery curve Curve448 and its birationally equivalent Edwards curve Ed448 used for key agreement and digital signature algorithm, specifically the X448 function and the Ed448 DSA, relying on efficient low-level arithmetic operations targeting the ARM-based Cortex-M4 platform. Our design performs point multiplication, the base of the Elliptic Curve Diffie-Hellman (ECDH), in 3,2KCCs, resulting in more than 48% improvement compared to the best previous work based on Curve448, and performs sign and verify, the main operations of the Edwards-curves Digital Signature Algorithm (EdDSA), in 6,038KCCs and 7,404KCCs, showing a speedup of around 11% compared to the counterparts. We present novel modular multiplication and squaring architectures reaching ∼25% and ∼35% faster runtime than the previous best-reported results, respectively, based on Curve448 key exchange counterparts, and ∼13% and ∼25% better latency results than the Ed448-based digital signature counterparts targeting Cortex-M4 platform.more » « less
-
The elliptic curve family of schemes has the lowest computational latency, memory use, energy consumption, and bandwidth requirements, making it the most preferred public key method for adoption into network protocols. Being suitable for embedded devices and applicable for key exchange and authentication, ECC is assuming a prominent position in the field of IoT cryptography. The attractive properties of the relatively new curve Curve448 contribute to its inclusion in the TLS1.3 protocol and pique the interest of academics and engineers aiming at studying and optimizing the schemes. When addressing low-end IoT devices, however, the literature indicates little work on these curves. In this paper, we present an efficient design for both protocols based on Montgomery curve Curve448 and its birationally equivalent Edwards curve Ed448 used for key agreement and digital signature algorithm, specifically the X448 function and the Ed448 DSA, relying on efficient lowlevel arithmetic operations targeting the ARM-based Cortex-M4 platform. Our design performs point multiplication, the base of the Elliptic Curve Diffie-Hellman (ECDH), in 3,2KCCs, resulting in more than 48% improvement compared to the best previous work based on Curve448, and performs sign and verify, the main operations of the Edwards-curves Digital Signature Algorithm (EdDSA), in 6,038KCCs and 7,404KCCs, showing a speedup of around 11% compared to the counterparts. We present novel modular multiplication and squaring architectures reaching 25% and s 35% faster runtime than the previous best-reported results, respectively, based on Curve448 key exchange counterparts, and s 13% and s 25% better latency results than the Ed448-based digital signature counterparts targeting Cortex-M4 platform.more » « less
-
Public Key Infrastructure (PKI) generates and distributes digital certificates to provide the root of trust for securing digital networking systems. To continue securing digital networking in the quantum era, PKI should transition to use quantum-resistant cryptographic algorithms. The cryptography community is developing quantum-resistant primitives/algorithms, studying, and analyzing them for cryptanalysis and improvements. National Institute of Standards and Technology (NIST) selected finalist algorithms for the post-quantum digital signature cipher standardization, which are Dilithium, Falcon, and Rainbow. We study and analyze the feasibility and the processing performance of these algorithms in memory/size and time/speed when used for PKI, including the key generation from the PKI end entities (e.g., a HTTPS/TLS server), the signing, and the certificate generation by the certificate authority within the PKI. The transition to post-quantum from the classical ciphers incur changes in the parameters in the PKI, for example, Rainbow I significantly increases the certificate size by 163 times when compared with RSA 3072. Nevertheless, we learn that the current X.509 supports the NIST post-quantum digital signature ciphers and that the ciphers can be modularly adapted for PKI. According to our empirical implementations-based study, the post-quantum ciphers can increase the certificate verification time cost compared to the current classical cipher and therefore the verification overheads require careful considerations when using the post-quantum-cipher-based certificates.more » « less
-
Internet of Things (IoT) is an integral part of application domains such as smart-home and digital healthcare. Various standard public key cryptography techniques (e.g., key exchange, public key encryption, signature) are available to provide fundamental security services for IoTs. However, despite their pervasiveness and well-proven security, they also have been shown to be highly energy costly for embedded devices. Hence, it is a critical task to improve the energy efficiency of standard cryptographic services, while preserving their desirable properties simultaneously. In this paper, we exploit synergies among various cryptographic primitives with algorithmic optimizations to substantially reduce the energy consumption of standard cryptographic techniques on embedded devices. Our contributions are: (i) We harness special pre-computation techniques, which have not been considered for some important cryptographic standards to boost the performance of key exchange, integrated encryption, and hybrid constructions. (ii) We provide self-certification for these techniques to push their performance to the edge. (iii) We implemented our techniques and their counterparts on 8-bit AVR ATmega 2560 and evaluated their performance. We used microECC library and made the implementations on NIST-recommended secp192 curve, due to its standardization. Our experiments conirmed signiicant improvements on the battery life (up to 7×) while preserving the desirable properties of standard techniques. Moreover, to the best of our knowledge, we provide the first open-source framework including such set of optimizations on low-end devices.more » « less
