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This paper is devoted to the study of hyperbent functions in n variables, i.e., bent functions which are bent up to a change of primitive roots in the finite field GF(2<sup>n</sup>). Our main purpose is to obtain an explicit trace representation for some classes of hyperbent functions. We first exhibit an infinite class of monomial functions which is not(More)
—Outsourcing data to cloud servers, while increasing service availability and reducing users' burden of managing data, inevitably brings in new concerns such as data privacy, since the server may be honest-but-curious. To mediate the conflicts between data usability and data privacy in such a scenario, research of searchable encryption is of increasing(More)
Bent functions have maximal minimum distance to the set of affine functions. In other words, they achieve the maximal minimum distance to all the coordinate functions of affine monomials. In this paper we introduce a new class of bent functions which we call hyper-bent functions. Functions within this class achieve the maximal minimum distance to all the(More)
2601 where s(k) is any function such that 1 s(k) k. Encoding and decoding require T = O(ks(k) + k log k) bit operations and the area is A = O(s 3 (k) + k) memory bits. If, for example, we let s(k) = log 2 k, then the proposed scheme has the same complexity as the codes given in [10] and a redundancy of N (k) 0 k = 3 log 2 k + 2:5 log 2 log 2 k + O(log log(More)
DES can be regarded as a nonlinear feedback shift register (NLFSR) with input. From this point of view, the tools for pseudo-random sequence analysis are applied to the S-boxes in DES. The properties of the S-boxes of DES under Fourier transform, Hadamard transform, extended Hadamard transform and Avalanche transform are investigated. Two important results(More)
In order to reduce key sizes and bandwidth, cryptographic systems have been proposed using minimal polynomials to represent finite field elements. These systems are essentially equivalent to systems based on characteristic sequences generated by a linear feedback shift register (LFSR). We propose a general class of LFSR-based key agreement and signature(More)
—New designs for families of sequences over GF () with low cross correlation, balance property, and large linear span are presented. The key idea of the new designs is to use short-ary sequences of period with the two-level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties. The(More)
—We find new families of nonbinary sequences of period 1 with symbols from a finite field for any prime 3. The sequences have two-level ideal autocorrelation and are generalizations of recently found ternary sequences with ideal autocorrelation. Difference sets with parameters 1 1 1 1 1 2 1 1 can also be derived from these sequences in a natural way.
Two lightweight block cipher families, Simon and Speck, have been proposed by researchers from the NSA recently. In this paper, we introduce Simeck, a new family of lightweight block ciphers that combines the good design components from both Simon and Speck, in order to devise even more compact and efficient block ciphers. For Simeck32/64, we can achieve(More)
Hummingbird is a new ultra-lightweight cryptographic algorithm targeted for resource-constrained devices like RFID tags, smart cards, and wireless sensor nodes. In this paper, we describe efficient hardware implementations of a stand-alone Hummingbird component in field-programmable gate array (FPGA) devices. We implement an encryption only core and an(More)