Quantum secret sharing schemes encrypting a quantum state into a multipartite entangled state are treated. The lower bound on the dimension of each share given by Gottesman [Phys. Rev. A 61, 042311 (2000)] is revisited based on a relation between the reversibility of quantum operations and the Holevo information. We also propose a threshold ramp quantum secret sharing scheme and evaluate its coding efficiency.
Abstract. Information theoretic cryptography is discussed based on conditional Rényi entropies. Our discussion focuses not only on cryptography but also on the definitions of conditional Rényi entropies and the related information theoretic inequalities. First, we revisit conditional Rényi entropies, and clarify what kind of properties are required and actually satisfied. Then, we propose security criteria based on Rényi entropies, which suggests us deep relations between (conditional) Rényi entropies and error probabilities by using several guessing strategies. Based on these results, unified proof of impossibility, namely, the lower bounds of key sizes is derived based on conditional Rényi entropies. Our model and lower bounds include the Shannon's perfect secrecy, and the min-entropy based encryption presented by Dodis, and Alimomeni and Safavi-Naini. Finally, a new optimal symmetric key encryption is proposed which achieve our lower bounds.
Abstract-Arbiter-basedPhysically Unclonable Function (PUF) is one kind of the delay-based PUFs that use the time difference of two delay-line signals. One of the previous work suggests that Arbiter PUFs implemented on Xilinx Virtex-5 FPGAs generate responses with almost no difference, i.e. with low uniqueness. In order to overcome this problem, Double Arbiter PUF was proposed, which is based on a novel technique for generating responses with high uniqueness from duplicated Arbiter PUFs on FPGAs. It needs the same costs as 2-XOR Arbiter PUF that XORs outputs of two Arbiter PUFs. Double Arbiter PUF is different from 2-XOR Arbiter PUF in terms of mode of operation for Arbiter PUF: the wire assignment between an arbiter and output signals from the final selectors located just before the arbiter. In this paper, we evaluate these PUFs as for uniqueness, randomness, and steadiness. We consider finding a new mode of operation for Arbiter PUF that can be realized on FPGA. In order to improve the uniqueness of responses, we propose 3-1 Double Arbiter PUF that has another duplicated Arbiter PUF, i.e. having 3 Arbiter PUFs and output 1-bit response. We compare 3-1 Double Arbiter PUF to 3-XOR Arbiter PUF according to the uniqueness, randomness, and steadiness, and show the difference between these PUFs by considering the mode of operation for Arbiter PUF. From our experimental results, the uniqueness of responses from 3-1 Double Arbiter PUF is approximately 50%, which is better than that from 3-XOR Arbiter PUF. We show that we can improve the uniqueness by using a new mode of operation for Arbiter PUF.
Ramp secret sharing (SS) schemes can be classified into strong ramp SS schemes and weak ramp SS schemes. The strong ramp SS schemes do not leak out any part of a secret explicitly even in the case where some information about the secret leaks from a non-qualified set of shares, and hence, they are more desirable than weak ramp SS schemes. However, it is not known how to construct the strong ramp SS schemes in the case of general access structures. In this paper, it is shown that a strong ramp SS scheme can always be constructed from a SS scheme with plural secrets for any feasible general access structure. As a byproduct, it is pointed out that threshold ramp SS schemes based on Shamir's polynomial interpolation method are not always strong.
In general, conventional Arbiter-based Physically Unclonable Functions (PUFs) generate responses with low unpredictability. The N-XOR Arbiter PUF, proposed in 2007, is a well-known technique for improving this unpredictability. In this paper, we propose a novel design for Arbiter PUF, called Double Arbiter PUF, to enhance the unpredictability on field programmable gate arrays (FPGAs), and we compare our design to conventional N-XOR Arbiter PUFs. One metric for judging the unpredictability of responses is to measure their tolerance to machine-learning attacks. Although our previous work showed the superiority of Double Arbiter PUFs regarding unpredictability, its details were not clarified. We evaluate the dependency on the number of training samples for machine learning, and we discuss the reason why Double Arbiter PUFs are more tolerant than the N-XOR Arbiter PUFs by evaluating intrachip variation. Further, the conventional Arbiter PUFs and proposed Double Arbiter PUFs are evaluated according to other metrics, namely, their uniqueness, randomness, and steadiness. We demonstrate that 3-1 Double Arbiter PUF archives the best performance overall.
Visual secret sharing schemes w i t h q plural secret images, for short VSS-q-PI schemes, are studied for general access structures and gray-scale a n d / o r color secret images.Let N = { 1 , 2 , . . . , n } and 2N be the set of n shares and the family of all the subsets of N, respectively. We suppose that all secret images are encrypted at once into n shares. Each secret image is denoted by SZ('), i = 1 , 2 , . . . , q, which has the same size. Let l?g:al, i = 1 , 2 , . . . , q, be the family of qualzfied sets for the i-th secret zmage, and let Forb be the family of forbidden sets. Then, any set in r:ial can decrypt the i-th secret image SI(^) while any set in r F o r b cannot gain any information of any secret image. w e call r = ({r$;a,);=l, r F o r b ) an access structure for q secret amages. Note that each satisfy the following monotonaczty.Therefore, for each I'gial, the mammal qualified sets of the i-th secret image can be defined as follows.It is worth noting that the VSS-1-PI scheme with the access structure (rd:)al, r F o r b ) coincides with the usual VSS scheme for one secret image. For a given set X & Af, the set of indices of the secret images that can be decr pted from X , say Z ( X ) , is represented as Z ( X ) = { i : X E r:;,,, 1 5 i 5 q } . For instance, Z ( N ) = { 1 , 2 , . . . , q } , and Z ( F ) = 0 for any 3 E r F o r b . Furthermore, we consider two categories A1 and A2 for the access structures of the VSS-q-PI schemes. Definition 1 Define that N(2) = UP(i))-Er(L)-Q(+, QWl (i) A n access structure r is in A 1 i f it satisfies Q(a)-n Ncz', # 0 for any i and i' such that Q(a)-E r$;al and (ii) A n access structure r is in A 2 i f it satisfies that Q ( 2 ) -n 0Let E be the set of colors used in all shares. In this paper, colors in E are expressed by lowercase san-serif fonts and the subtractive mixture of colors which corresponds to overlapping the colors printed on transparencies is represented by U. For example, the fact that the subtractive mixture of yellow and cyan generates green is represented as y U c = g. Furthermore, in the framework of the VSS-q-PI scheme, the colors of decrypted images are represented by the set of m subpixels which expresses the gray-scales or colors. For mdimensional row vectors of colors ?! = [ x1 x2". xm 1, y = [ y1 y p ... y m ] where x,,yi E E , we define an operation U as z U g = [ X I U y1 x2 U y2 ... xm U ym 1, which i' E T(Q(+)\{i} l . N(2') # 0 for any i and i'(# i). -m m 'For a set S C N , s means the complement of S. represents the subtractive mixtures of two pixels with m subpixels. For a matrix T = ' [ z 1 z 2 ... zn] E E"", where t means the transpose of the matrix, and an arbitrary set X = { U I , U Z , . .. ,U,-} C N , an 1x1 x m matrix TUX] is defined as TBX] = t[z,,z,, . . . z U T ] E E l X t m . Then, the colors obtained by stacking the %-th shares, i = 1,2,. . . , r , are represented by the mapping ,O : EIXlm + E" defined by Now we define a color matrix. Let V(') be the set of grayscales or colors on the secret image SI(') represented by m s...
Low uniqueness and vulnerability to machine-learning attacks are known as two major problems of Arbiter-Based Physically Unclonable Function (APUF) implemented on FPGAs. In this paper, we implement Double APUF (DAPUF) that duplicates the original APUF in order to overcome the problems. From the experimental results on Xilinx Virtex-5, we show that the uniqueness of DAPUF becomes almost ideal, and the prediction rate of the machine-learning attack decreases from 86% to 57%.
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