ECDH Key-Extraction via Low-Bandwidth Electromagnetic Attacks on PCs

We present the first physical side-channel attack on elliptic curve cryptography running on a PC. The attack targets the ECDH public-key encryption algorithm, as implemented in the latest version of GnuPG\u27s Libgcrypt. By measuring the target\u27s electromagnetic emanations, the attack extracts the secret decryption key within seconds, from a target located in an adjacent room across a wall. The attack utilizes a single carefully chosen ciphertext, and tailored time-frequency signal analysis techniques, to achieve full key extraction

Key Randomization Countermeasures to Power Analysis Attacks on Elliptic Curve Cryptosystems

It is essential to secure the implementation of cryptosystems in embedded devices agains side-channel attacks. Namely, in order to resist differential (DPA) attacks, randomization techniques should be employed to decorrelate the data processed by the device from secret key parts resulting in the value of this data. Among the countermeasures that appeared in the literature were those that resulted in a random representation of the key known as the binary signed digit representation (BSD). We have discovered some interesting properties related to the number of possible BSD representations for an integer and we have proposed a different randomization algorithm. We have also carried our study to the $\tau$-adic representation of integers which is employed in elliptic curve cryptosystems (ECCs) using Koblitz curves. We have then dealt with another randomization countermeasure which is based on randomly splitting the key. We have investigated the secure employment of this countermeasure in the context of ECCs

Efficient Arithmetic for the Implementation of Elliptic Curve Cryptography

The technology of elliptic curve cryptography is now an important branch in public-key based crypto-system. Cryptographic mechanisms based on elliptic curves depend on the arithmetic of points on the curve. The most important arithmetic is multiplying a point on the curve by an integer. This operation is known as elliptic curve scalar (or point) multiplication operation. A cryptographic device is supposed to perform this operation efficiently and securely. The elliptic curve scalar multiplication operation is performed by combining the elliptic curve point routines that are defined in terms of the underlying finite field arithmetic operations. This thesis focuses on hardware architecture designs of elliptic curve operations. In the first part, we aim at finding new architectures to implement the finite field arithmetic multiplication operation more efficiently. In this regard, we propose novel schemes for the serial-out bit-level (SOBL) arithmetic multiplication operation in the polynomial basis over F_2^m. We show that the smallest SOBL scheme presented here can provide about 26-30\% reduction in area-complexity cost and about 22-24\% reduction in power consumptions for F_2^{163} compared to the current state-of-the-art bit-level multiplier schemes. Then, we employ the proposed SOBL schemes to present new hybrid-double multiplication architectures that perform two multiplications with latency comparable to the latency of a single multiplication. Then, in the second part of this thesis, we investigate the different algorithms for the implementation of elliptic curve scalar multiplication operation. We focus our interest in three aspects, namely, the finite field arithmetic cost, the critical path delay, and the protection strength from side-channel attacks (SCAs) based on simple power analysis. In this regard, we propose a novel scheme for the scalar multiplication operation that is based on processing three bits of the scalar in the exact same sequence of five point arithmetic operations. We analyse the security of our scheme and show that its security holds against both SCAs and safe-error fault attacks. In addition, we show how the properties of the proposed elliptic curve scalar multiplication scheme yields an efficient hardware design for the implementation of a single scalar multiplication on a prime extended twisted Edwards curve incorporating 8 parallel multiplication operations. Our comparison results show that the proposed hardware architecture for the twisted Edwards curve model implemented using the proposed scalar multiplication scheme is the fastest secure SCA protected scalar multiplication scheme over prime field reported in the literature