Lightweight EdDSA Signature Verification for the Ultra-Low-Power Internet of Things

in Deng, Robert; Bao, Feng; Wang, Guilin (Eds.) et al Information Security Practice and Experience, 16th International Conference, ISPEC 2021, Nanjing, China, December 17–19, 2021, Proceedings (2021, December)

EdDSA is a digital signature scheme based on elliptic curves in Edwards form that is supported in the latest incarnation of the TLS protocol (i.e. TLS version 1.3). The straightforward way of verifying an ... [more ▼]

EdDSA is a digital signature scheme based on elliptic curves in Edwards form that is supported in the latest incarnation of the TLS protocol (i.e. TLS version 1.3). The straightforward way of verifying an EdDSA signature involves a costly double-scalar multiplication of the form kP - lQ where P is a "fixed" point (namely the generator of the underlying elliptic-curve group) and Q is only known at run time. This computation makes a verification not only much slower than a signature generation, but also more memory demanding. In the present paper we compare two implementations of EdDSA verification using Ed25519 as case study; the first is speed-optimized, while the other aims to achieve low RAM footprint. The speed-optimized variant performs the double-scalar multiplication in a simultaneous fashion and uses a Joint-Sparse Form (JSF) representation for the two scalars. On the other hand, the memory-optimized variant splits the computation of kP - lQ into two separate parts, namely a fixed-base scalar multiplication that is carried out using a standard comb method with eight pre-computed points, and a variable-base scalar multiplication, which is executed by means of the conventional Montgomery ladder on the birationally-equivalent Montgomery curve. Our experiments with a 16-bit ultra-low-power MSP430 microcontroller show that the separated method is 24% slower than the simultaneous technique, but reduces the RAM footprint by 40%. This makes the separated method attractive for "lightweight" cryptographic libraries, in particular if both Ed25519 signature generation/verification and X25519 key exchange need to be supported. [less ▲]

Revisiting Test Cases to Boost Generate-and-Validate Program Repair

in IEEE International Conference on Software Maintenance and Evolution (ICSME) (2021, September)

Parallel Implementation of SM2 Elliptic Curve Cryptography on Intel Processors with AVX2

in Liu, Joseph K.; Cui, Hui (Eds.) Information Security and Privacy, 25th Australasian Conference, ACISP 2020, Perth, WA, Australia, November 30 - December 2, 2020, Proceedings (2020, November)

This paper presents an efficient and secure implementation of SM2, the Chinese elliptic curve cryptography standard that has been adopted by the International Organization of Standardization (ISO) as ISO ... [more ▼]

This paper presents an efficient and secure implementation of SM2, the Chinese elliptic curve cryptography standard that has been adopted by the International Organization of Standardization (ISO) as ISO/IEC 14888-3:2018. Our SM2 implementation uses Intel’s Advanced Vector Extensions version 2.0 (AVX2), a family of three-operand SIMD instructions operating on vectors of 8, 16, 32, or 64-bit data elements in 256-bit registers, and is resistant against timing attacks. To exploit the parallel processing capabilities of AVX2, we studied the execution flows of Co-Z Jacobian point arithmetic operations and introduce a parallel 2-way Co-Z addition, Co-Z conjugate addition, and Co-Z ladder algorithm, which allow for fast Co-Z scalar multiplication. Furthermore, we developed an efficient 2-way prime-field arithmetic library using AVX2 to support our Co-Z Jacobian point operations. Both the field and the point operations utilize branch-free (i.e. constant-time) implementation techniques, which increase their ability to resist Simple Power Analysis (SPA) and timing attacks. Our software for scalar multiplication on the SM2 curve is, to our knowledge, the first constant-time implementation of the Co-Z based ladder that leverages the parallelism of AVX2. [less ▲]