Blar i Bergen Open Research Archive på forfatter "Helleseth, Tor"

Binary Linear Codes With Few Weights From TwotoOne Functions
Li, Kangquan; Li, Chunlei; Helleseth, Tor; Qu, Longjiang (Journal article; Peer reviewed, 2021)In this paper, we apply twotoone functions over b F 2n in two generic constructions of binary linear codes. We consider twotoone functions in two forms: (1) generalized quadratic functions; and (2) (x 2t +x) e with ... 
Cryptographically strong permutations from the butterfly structure
Li, Kangquan; Li, Chunlei; Helleseth, Tor; Qu, Longjiang (Journal article; Peer reviewed, 2021)Boomerang connectivity table is a new tool to characterize the vulnerability of cryptographic functions against boomerang attacks. Consequently, a cryptographic function is desired to have boomerang uniformity as low as ... 
The differential spectrum of a ternary power mapping
Xia, Yongbo; Zhang, Xianglai; Li, Chunlei; Helleseth, Tor (Journal article; Peer reviewed, 2020)A function f(x)from the finite field GF(pn)to itself is said to be differentially δuniform when the maximum number of solutions x ∈GF(pn)of f(x +a) −f(x) =bfor any a ∈GF(pn)∗and b ∈GF(pn)is equal to δ. Let p =3and d =3n−3. ... 
A New Family of APN Quadrinomials
Budaghyan, Lilya; Helleseth, Tor; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2020)The binomial B(x) = x 3 +βx 36 (where β is primitive in F 2 2) over F 2 10 is the first known example of an Almost Perfect Nonlinear (APN) function that is not CCZequivalent to a power function, and has remained unclassified ... 
On the Distance Between APN Functions
Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2020)We investigate the differential properties of a vectorial Boolean function G obtained by modifying an APN function F . This generalizes previous constructions where a function is modified at a few points. We characterize ... 
Optimal ternary cyclic codes with minimum distance four and five
Li, Nian; Li, Chunlei; Helleseth, Tor; Ding, Cunsheng; Tang, Xiaohu (Journal article, 201411)Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are ... 
Relation between oequivalence and EAequivalence for Niho bent functions
Davidova, Diana; Budaghyan, Lilya; Carlet, Claude Michael; Helleseth, Tor; Ihringer, Ferdinand; Penttila, Tim (Journal article; Peer reviewed, 2021)Boolean functions, and bent functions in particular, are considered up to socalled EAequivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent ... 
The Weight Distributions of Several Classes of Cyclic Codes From APN Monomials
Li, Chunlei; Li, Nian; Helleseth, Tor; Ding, Cunsheng (Peer reviewed; Journal article, 201408)Let m ≥ 3 be an odd integer and p be an odd prime. In this paper, a number of classes of threeweight cyclic codes C(1,e) over Fp, which have paritycheck polynomial m1(x)me (x), are presented by examining general conditions ...