Secure Multipliers Resilient to Strong Fault-Injection Attacks Using Multilinear Arithmetic Codes

Abstract

Public-key cryptographic devices are vulnerable to fault-injection attacks. As countermeasures, a number of secure architectures based on linear and nonlinear error detecting codes were proposed. Linear codes provide protection only against primitive adversaries with limited attack capabilities. On the other hand nonlinear codes provide protection against strong adversaries, but at the price of high area overhead (200%-400%). In this paper we propose a novel error detection technique based on the random selection of linear arithmetic codes and explore the use of this technique for the protection of the multiplier, which is a basic block in many public-key cryptographic devices. The error detection technique does not imply any limitations on the types of errors at the output of the device, e.g., the multiplicity of the error does not have to be small. Under mild assumptions the proposed construction achieves near nonlinear code error detection performance at a lower cost (at most 50% area overhead for the protection of multipliers) due to the fact that no nonlinear operations are needed for the encoder and decoder.

Secure Systolic Montgomery Modular Multiplier Over Prime Fields Resilient to Fault-Injection Attacks

“…Researchers make use of this property to protect basic adders and multipliers from faultinjection attacks [33]. Let C = A × B andC = ||A| p × Algorithm 1 Radix-2 l MMM Algorithm Over Prime Field |B| p | p be the predicted value of C mod p. One can compute C andC simultaneously, and tell whether the multiplier is compromised by comparing |C| p andC.…”

“…As a result, it is important to bring protection scheme to modular multipliers. Now a few works [33]- [41] focus on the security issue of modular multipliers. In [33], the multilinear arithmetic codes are used to protect integer multipliers.…”

“…Now a few works [33]- [41] focus on the security issue of modular multipliers. In [33], the multilinear arithmetic codes are used to protect integer multipliers. In [34]- [39], parity-based codes are used to protect bit-serial, digit-serial and bit-parallel Montgomery modular multiplication over binary fields (MMMobf).…”

“…The technique in [33] is applied to protect simple 16-bit and 32-bit integer multipliers. The method in [39] is used to protect MMMobf, and the average error-reporting delay is about 50% of whole MMM computing time.…”

“…In this paper, we extended the work in [33] and [39] to propose a class of secure systolic architectures for MMMopfs resilient to fault-injection attacks. Our secure architectures' resilience to fault-injection attacks is based on the detection and report of errors in arithmetic units caused by injected faults.…”