Biblio

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 non-linear 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.

Functionally safe control logic design without full duplication is difficult due to the complexity of random control logic. The Reorder buffer (ROB) is a control logic function commonly used in high performance computing systems. In this study, we focus on a safe ROB design used in an industry quality Network-on-Chip (NoC) Advanced eXtensible Interface (AXI) Network Interface (NI) block. We developed and applied area efficient safe design techniques including partial duplication, Error Detection Code (EDC) and invariance checking with formal proofs and showed that we can achieve a desired safe Diagnostic Coverage (DC) requirement with small area and power overheads and no performance degradation.

This paper introduces the notion of one-way communication schemes with partial noisy feedback. To support this communication, the schemes suppose that Alice and Bob wish to communicate: Alice sends a sequence of alphabets over a channel to Bob, while Alice receives feedback bits from Bob for δ fraction of the transmissions. An adversary is allowed to tamper up to a constant fraction of these transmissions for both forward rounds and feedback rounds separately. This paper intends to determine the Maximum Error Rate (MER), as a function of δ (0 ≤ δ ≤ 1), under the MER rate, so that Alice can successfully communicate the messages to Bob via some protocols with δ fraction of noisy feedback. To provide a reasonable solution for the above problem, we need to explore a new kind of coding scheme for the interactive communication. In this paper, we use the notion of “non-malleable codes” (NMC) which relaxes the notions of error-correction and error-detection to some extent in communication. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message or a completely unrelated value. This property largely enforces the way to detect the transmission errors. Based on the above knowledge, we provide an alphabet-based encoding scheme, including a pair of (Enc, Dec). Suppose the message needing to be transmitted is m; if m is corrupted unintentionally, then the encoding scheme Dec(Enc(m)) outputs a symbol `⊥' to denote that some potential corruptions happened during transmission. In this work, based on the previous results, we show that for any δ ∈ (0; 1), there exists a deterministic communication scheme with noiseless full feedback(δ = 1), such that the maximal tolerable error fraction γ (on Alice's transmissions) can be up to 1/2, theoretically. Moreover, we show that for any δ ∈ (0; 1), there exists a communication scheme with noisy feedback, denoting the forward and backward rounds noised with error fractions of γ0and γ1respectively, such that the maximal tolerable error fraction γ0(on forward rounds) can be up to 1/2, as well as the γ1(on feedback rounds) up to 1.