Fault tolerant nonlinear techniques for scalar multiplication in ECC Elliptic curve cryptography (ECC) has shorter key length than other asymmetric cryptography algorithms such as RSA with the same security level. Existing faults in cryptographic computations can cause faulty results. If a fault occurs during encryption, false information will be sent to the destination, in which case channel error detection codes are unable to detect the fault. In this paper, we consider the error detection in elliptic curve scalar multiplication point, which is the most important operation in ECC. Our technique is based on nonlinear error detection codes. We consider an algorithm for scalar multiplication point proposed by Microsoft research group. The proposed technique in our methods has less overhead for additions (36.36%) and multiplications (34.84%) in total, compared to previous works. Also, the proposed method can detect almost 100% of injected faults.

Loop abort Faults on LatticeBased FiatShamir & Hashn Sign signatures As the advent of generalpurpose quantum computers appears to be drawing closer, agencies and advisory bodies have started recommending that we prepare the transition away from factoring and discrete logarithmbased cryptography, and towards postquantum secure constructions, such as latticebased schemes. Almost all primitives of classical cryptography (and more!) can be realized with lattices, and the efficiency of primitives like encryption and signatures has gradually improved to the point that key sizes are competitive with RSA at similar security levels, and fast performance can be achieved both in software and hardware. However, little research has been conducted on physical attacks targeting concrete implementations of postquantum cryptography in general and latticebased schemes in particular , and such research is essential if lattices are going to replace RSA and elliptic curves in our devices and smart cards. In this paper, we look in particular at fault attacks against some instances of the FiatShamir family of signature scheme on lattices (BLISS, GLP, TESLA and PASSSign) and on the GPV scheme, member of the Hashu0027n Sign family. Some of these schemes have achieved recordsetting efficiency in software and hardware. We present several possible fault attacks, one of which allows a full key recovery with as little as a single faulty signature, and discuss possible countermeasures to mitigate these attacks.