Atomicity and Regularity Principles Do Not Ensure Full Resistance of ECC Designs against Single-Trace Attacks

Abstract

Elliptic curve cryptography (ECC) is one of the commonly used standard methods for encrypting and signing messages which is especially applicable to resource-constrained devices such as sensor nodes that are networked in the Internet of Things. The same holds true for wearable sensors. In these fields of application, confidentiality and data integrity are of utmost importance as human lives depend on them. In this paper, we discuss the resistance of our fast dual-field ECDSA accelerator against side-channel analysis attacks. We present our implementation of a design supporting four different NIST elliptic curves to allow the reader to understand the discussion of the resistance aspects. For two different target platforms—ASIC and FPGA—we show that the application of atomic patterns, which is considered to ensure resistance against simple side-channel analysis attacks in the literature, is not sufficient to prevent either simple SCA or horizontal address-bit DPA attacks. We also evaluated an approach which is based on the activity of the field multiplier to increase the inherent resistance of the design against attacks performed.

Keywords

• elliptic curve cryptography (ECC)
• Montgomery <i>kP</i>
• atomic patterns
• B-curves
• P-curves
• side-channel analysis (SCA) attacks