In 2007, Carlet and Ding introduced two parameters, denoted by NbF and NBF, quantifying respectively the balancedness of general functions F between finite Abelian groups and the (global) balancedness of their derivatives DaF(x) = F(x + a) - F(x), a ∈ G \ {0} (providing an indicator of the nonlinearity of the functions). These authors studied the properties and cryptographic significance of these two measures. They provided inequalities relating the nonlinearity NL(F) to NBF for S-box and specifically obtained an upper bound on the nonlinearity that unifies Sidelnikov-Chabaud-Vaudenay's bound and the covering radius bound. At the Workshop WCC 2009 and in its postproceedings in 2011, a further study of these parameters was made; in particular, the first parameter was applied to the functions F + L, where L is affine, providing more nonlinearity parameters. In 2010, motivated by the study of Costas arrays, two parameters called ambiguity and deficiency were introduced by Panario et al. for permutations over finite Abelian groups to measure the injectivity and surjectivity of the derivatives, respectively. These authors also studied some fundamental properties and cryptographic significance of these two measures. Further studies followed without comparing the second pair of parameters to the first one. In this paper, we observe that ambiguity is the same parameter as NBF up to additive and multiplicative constants (i.e., up to rescaling). We perform the necessary work of comparison and unification of the results on NBF and on ambiguity, which have been obtained in the five papers devoted to these parameters. We generalize some known results to any finite Abelian groups. More importantly, we derive many new results on these parameters.

Fault attack is one of the most efficient side channel attacks and has attracted much attention in recent public cryptographic literatures. In this work, we introduce a fault attack on the authenticated cipher ACORN v3. Our attack is done under the assumption that a fault is injected into an initial state of ACORN v3 randomly, and contains two main steps: fault locating and equation solving. At the first step, we introduce concepts of unique set and non-unique set, where differential strings belonging to unique sets can determine the fault location uniquely. For strings belonging to non-unique sets, we use some strategies to increase the probability of determining the fault location uniquely to almost 1. At the second step, we demonstrate several ways of retrieving equations, and then obtain the initial state by solving equations with the guess-and-determine method. With n fault experiments, we can recover the initial state with time complexity c⋅2146.5−3.52⋅n⁠, where c is the time complexity of solving linear equations and 26 <n< 43⁠. We also apply the attack to ACORN v2, which shows that the changes from ACORN v2 to ACORN v3 have reduced the security margin of this algorithm against the differential fault attack.

Fault attack is an efficient cryptanalysis method against cipher implementations and has attracted a lot of attention in recent public cryptographic literatures. In this work we introduce a fault attack on the CAESAR candidate ACORN v2. Our attack is done under the assumption of random fault injection into an initial state of ACORN v2 and contains two main steps: fault locating and equation solving. At the first step, we first present a fundamental fault locating method, which uses 99-bit output keystream to determine the fault injected location with probability 97.08% . And then several improvements are provided, which can further increase the probability of fault locating to almost 1. As for the system of equations retrieved at the first step, we give two solving methods at the second step, that is, linearization and guess-and-determine. The time complexity of our attack is not larger than c·2179.19-1.76N at worst, where N is the number of fault injections such that 31≤N≤88 and c is the time complexity of solving linear equations. Our attack provides some insights into the diffusion ability of such compact stream ciphers.

SPECK is a family of lightweight block cipherspublished by the U.S. National Security Agency in 2013. TheSPECK family consists of 10 versions, supporting a wide rangeof block and key sizes. Recently H. Tupsamudre et al. gave anapproach to recovering the last round key of SPECK familywith n/3 fault injections, where 2n is the block size. In thispaper, we present two improved differential fault attacks on theSPECK family under different fault models. The first attackassumes a more practical random fault model and recovers thelast round key with about 5 ~ 8 fault injections on all versionswith different block sizes, which is far less than that of H. Tupsamudre et al.'s attack. The second attack only requires 4specific faults to recover the last round key (except the mostsignificant bit) over an arbitrary block size under a chosen-valuefault model.

This paper presents the property of d-perfect m-dimensional multisequences based on the technique of m-continued fractions. The concept of perfect linear complexity profile (PLCP) to measure the unpredictability and randomness of pseudorandom sequences is presented. The properties of unpredictability and randomness are widely used in the fields of cryptography and communication.