Robust codes C(n, k)qare nonlinear q-ary codes of dimension k and length n ≤ 2k. Robust codes can detect any error with nonzero probability; hence, they can effectively detect fault injection attacks. Most high rate robust codes are either restricted to certain ratios between n and k, or have relatively high hardware complexity. This paper presents new constructions for optimum or close to optimum low complexity high rate robust codes. These codes exist for any k and n. The hardware complexity of each construction is discussed, and a method to choose the one with the smallest implementation cost is presented.

Security oriented codes are considered as one of the most efficient countermeasures against fault injection attacks. Their efficiency is usually measured in terms of their error masking probability. This criterion is applicable in cases where it is possible to distinguish between random errors and malicious attacks. In practice, if the induced errors are not fixed for several clock cycles, it is difficult to distinguish between the two. Moreover, a decoder that tries to correct the tampered word can conceal the fact that the device is under attack. This paper defines a new criterion, named t-robustness, for evaluating the efficiency of robust codes that provide both reliability and security. An error correcting code is called t-robust, if it can correct up to t errors and at the same time detect any attack that changes the data. The paper presents a general structure for concatenated codes that have this property.

Security-oriented codes are used in cryptographic devices to maximize the probability of detecting fault injection attacks. This paper introduces a new class of binary security-oriented codes of rate >1/2. The codes are derived from the cubic code by applying a linear transformation on the codewords before puncturing. The codes are systematic and robust in that any nonzero error can be detected with a probability >0. The error masking probability of the codes is upper bounded by 2-r+1where r is the number of redundancy bits. It is shown that in some cases, by choosing the proper transformation and puncturing matrices, it is possible to increase the minimum distance of the code, or to reduce the maximal error masking probability to meet its lower bound.

Robust and partially robust codes are codes used in cryptographic devices for maximizing the probability of detecting errors injected by malicious attackers. The set of errors that are masked (undetected) by all codewords form the detection-kernel of the code. Codes whose kernel contains only the zero vector, i.e. codes that can detect any nonzero error (of any multiplicity) with probability greater than zero, are called robust. Codes whose kernel is of size greater than one are considered as partially-robust codes. Partially-robust codes of rate greater than one-half can be derived from the the cubic Karpovsky-Taubin code [6]. This paper introduces a construction of robust codes of rate >; 1/2. The codes are derived from the Karpovsky-Taubin code by puncturing the redundancy bits. It is shown that if the number of remaining redundancy bits (r) is greater than one then the code is robust and any error vector is detected with probability 1, 1-2-ror 1 - 2-r+1. The number of the error vectors associated with each probability is given for robust codes having odd number of information bits.