1,721,162 research outputs found
Constructions of cheating immune secret sharing
No full textThe paper addresses the cheating prevention in secret sharing. We consider secret sharing with binary shares. The secret also is binary. This model allows us to use results and constructions from the well developed theory of cryptographically strong boolean functions. In particular, we prove that for given secret sharing, the average cheating probability over all cheating vectors and all original vectors, i.e., 1 n · 2−n ∑ n c=1 ∑α∈Vn ρc,α, denoted by ρ, satisfies ρ ≥ 1 2, and the equality holds if and only if ρc,α satisfies ρc,α = 1 2 for every cheating vector δc and every original vector α. In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions. This enables us to construct cheating-immune secret sharing
Cheating immune secret sharing
No full textWe consider secret sharing with binary shares. This model allows us to use the well developed theory of cryptographically strong boolean functions. We prove that for given secret sharing, the average cheating probability over all cheating and original vectors, i.e., ρ ¯= 1 n ⋅ 2 −n ∑ n c=1 ∑ α∈Vn ρ c,α , satisfies ρ ¯⩾ 1 2 , and the equality holds ⇔ ρc,α satisfies ρc,α = 1/2 for every cheating vector δc and every original vector α. In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions. This enables us to construct cheating-immune secret sharing
Ideal threshold schemes from MDS codes
No full textWe observe that MDS codes have interesting properties that can be used to construct ideal threshold schemes. These schemes permit the combiner to detect cheating, identify cheaters and recover the correct secret. The construction is later generalised so the resulting secret sharing is resistant against the Tompa-Woll cheating
Cheating prevention in linear secret sharing
No full textCheating detection in linear secret sharing is considered. The model of cheating extends the Tompa-Woll attack and includes cheating during multiple (unsuccessful) recovery of the secret. It is shown that shares in most linear schemes can be split into subshares. Subshares can be used by participants to trade perfectness of the scheme with cheating prevention. Evaluation of cheating prevention is given in the context of different strategies applied by cheaters
Pitfalls in Designing Substitution Boxes (Extended Abstract)
No full text) Jennifer Seberry, Xian-Mo Zhang and Yuliang Zheng Department of Computer Science University of Wollongong, Wollongong, NSW 2522, Australia fjennie, xianmo, [email protected] Abstract. Two significant recent advances in cryptanalysis, namely the differential attack put forward by Biham and Shamir [3] and the linear attack by Matsui [7, 8], have had devastating impact on data encryption algorithms. An eminent problem that researchers are facing is to design S-boxes or substitution boxes so that an encryption algorithm that employs the S-boxes is immune to the attacks. In this paper we present evidence indicating that there are many pitfalls on the road to achieve the goal. In particular, we show that certain types of S-boxes which are seemly very appealing do not exist. We also show that, contrary to previous perception, techniques such as chopping or repeating permutations do not yield cryptographically strong S-boxes. In addition, we reveal an important combinatorial structure..
Structures of Cryptographic Functions with Strong Avalanche Characteristics (Extended Abstract)
No full text) Jennifer Seberry, Xian-Mo Zhang and Yuliang Zheng Department of Computer Science University of Wollongong, Wollongong, NSW 2522, Australia fjennie, xianmo, [email protected] Abstract. This paper studies the properties and constructions of nonlinear functions, which are a core component of cryptographic primitives including data encryption algorithms and one-way hash functions. A main contribution of this paper is to reveal the relationship between nonlinearity and propagation characteristic, two critical indicators of the cryptographic strength of a Boolean function. In particular, we prove that (i) if f , a Boolean function on Vn , satisfies the propagation criterion with respect to all but a subset ! of vectors in Vn , then the nonlinearity of f satisfies Nf 2 n\Gamma1 \Gamma 2 1 2 (n+t)\Gamma1 , where t is the rank of !, and (ii) When j!j ? 2, the nonzero vectors in ! are linearly dependent. Furthermore we show that (iii) if j!j = 2 then n must be odd, the nonlinearit..
On Constructions and Nonlinearity of Correlation Immune Functions (Extended Abstract)
No full text) Jennifer Seberry ? , Xian-Mo Zhang ?? and Yuliang Zheng ??? Department of Computer Science, The University of Wollongong Wollongong, NSW 2522, AUSTRALIA E-mail: fjennie,xianmo,[email protected] Abstract. A Boolean function is said to be correlation immune if its output leaks no information about its input values. Such functions have many applications in computer security practices including the construction of key stream generators from a set of shift registers. Finding methods for easy construction of correlation immune functions has been an active research area since the introduction of the notion by Siegenthaler. In this paper we study balanced correlation immune functions using the theory of Hadamard matrices. First we present a simple method for directly constructing balanced correlation immune functions of any order. Then we prove that our method generates exactly the same set of functions as that obtained using a method by Camion, Carlet, Charpin and Sendrier. Advant..
Relationships among Nonlinearity Criteria (Extended Abstract)
No full text) Jennifer Seberry, Xian-Mo Zhang and Yuliang Zheng Department of Computer Science, University of Wollongong Wollongong, NSW 2522, Australia fjennie, xianmo, [email protected] Abstract. An important question in designing cryptographic functions including substitution boxes (S-boxes) is the relationships among the various nonlinearity criteria each of which indicates the strength or weakness of a cryptographic function against a particular type of cryptanalytic attacks. In this paper we reveal, for the first time, interesting connections among the strict avalanche characteristics, differential characteristics, linear structures and nonlinearity of quadratic S-boxes. In addition, we show that our proof techniques allow us to treat in a unified fashion all quadratic permutations, regardless of the underlying construction methods. This greatly simplifies the proofs for a number of known results on nonlinearity characteristics of quadratic permutations. As a by-product, we obtain a n..
Nonlinear secret sharing immune against cheating
No full textThe paper investigates the design of secret sharing that is immune against cheating (as defined by the Tompa-Woll attack). We examine secret sharing with binary shares and secrets. Bounds on the probability of successful cheating are given for two cases. The first case relates to secret sharing based on bent functions and results in a non-perfect scheme. The second case considers perfect secret sharing built on highly nonlinear balanced Boolean functions
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