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A Provably Secure True Random Number Generator with Builtin Tolerance to Active Attacks
 IEEE Transactions on Computers
, 2007
"... This paper is a contribution to the theory of true random number generators based on sampling phase jitter in oscillator rings. After discussing several misconceptions and apparently insurmountable obstacles, we propose a general model which, under mild assumptions, will generate provably random bit ..."
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Cited by 32 (3 self)
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This paper is a contribution to the theory of true random number generators based on sampling phase jitter in oscillator rings. After discussing several misconceptions and apparently insurmountable obstacles, we propose a general model which, under mild assumptions, will generate provably random bits with some tolerance to adversarial manipulation and running in the megabitpersecond range. A key idea throughout the paper is the fill rate, which measures the fraction of the time domain in which the analog output signal is arguably random. Our study shows that an exponential increase in the number of oscillators is required to obtain a constant factor improvement in the fill rate. Yet, we overcome this problem by introducing a postprocessing step which consists of an application of an appropriate resilient function. These allow the designer to extract random samples only from a signal with only moderate fill rate and therefore many fewer oscillators than in other designs. Lastly, we develop faultattack models, and we employ the properties of resilient functions to withstand such attacks. All of our analysis is based on rigorous methods, enabling us to develop a framework in which we accurately quantify the performance and the degree of resilience of the design. Key Words: True (and pseudo) random number generators, resilient functions, cryptography. 1
Applications of Combinatorial Designs to Communications, Cryptography, and Networking
, 1999
"... ... In this paper, we focus on another collection of recent applications in the general area of communications, including cryptography and networking. Applications have been chosen to represent those in which design theory plays a useful, and sometimes central, role. Moreover, applications have been ..."
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Cited by 26 (2 self)
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... In this paper, we focus on another collection of recent applications in the general area of communications, including cryptography and networking. Applications have been chosen to represent those in which design theory plays a useful, and sometimes central, role. Moreover, applications have been chosen to reflect in addition the genesis of new and interesting problems in design theory in order to treat the practical concerns. Of many candidates, thirteen applications areas have been included. They are as follows:
Some New Results on Key Distribution Patterns and Broadcast Encryption
 Designs, Codes and Cryptography
, 1997
"... This paper concerns methods by which a trusted authority can distribute keys and/or broadcast a message over a network, so that each member of a privileged subset of users can compute a specified key or decrypt the broadcast message. Moreover, this is done in such a way that no coalition is able to ..."
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Cited by 25 (3 self)
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This paper concerns methods by which a trusted authority can distribute keys and/or broadcast a message over a network, so that each member of a privileged subset of users can compute a specified key or decrypt the broadcast message. Moreover, this is done in such a way that no coalition is able to recover any information on a key or broadcast message they are not supposed to know. The problems are studied using the tools of information theory, so the security provided is unconditional (i.e., not based on any computational assumption). In a recent paper [14], Stinson described a method of constructing key predistribution schemes by combining MitchellPiper key distribution patterns with resilient functions; and also presented a construction method for broadcast encryption schemes that combines FiatNaor key predistribution schemes with ideal secret sharing schemes. In this paper, we further pursue these two themes, providing several nice applications of these techniques by using combin...
On the Dealer's Randomness Required in Secret Sharing Schemes
 Proc. of EuroCrypt94, SpringerVerlag, Lecture Notes in Computer Science
, 1995
"... . In this paper we provide upper and lower bounds on the randomness required by the dealer to set up a secret sharing scheme for infinite classes of access structures. Lower bounds are obtained using entropy arguments. Upper bounds derive from a decomposition construction based on combinatorial desi ..."
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Cited by 9 (3 self)
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. In this paper we provide upper and lower bounds on the randomness required by the dealer to set up a secret sharing scheme for infinite classes of access structures. Lower bounds are obtained using entropy arguments. Upper bounds derive from a decomposition construction based on combinatorial designs (in particular, t(v; k; ) designs). We prove a general result on the randomness needed to construct a scheme for the cycle Cn ; when n is odd our bound is tight. We study the access structures on at most four participants and the connected graphs on five vertices, obtaining exact values for the randomness for all them. Also, we analyze the number of random bits required to construct anonymous threshold schemes, giving upper bounds. (Informally, anonymous threshold schemes are schemes in which the secret can be reconstructed without knowledge of which participants hold which shares.) Keywords: Secret Sharing Scheme, Randomness 1. Introduction Randomness plays an important role in severa...
On the Performance of Resilient Functions with Imperfect Inputs
 http://ece.wpi.edu/∼sunar/preprints/xresilient.pdf Inverter Rings Binary XOR Tree Sampler
"... Abstract – We analyze the performance of resilient functions for imperfect input bits. Specifically, we allow more input bits than the resiliency degree of the resilient function to be biased and analyze the output behavior under this new assumption. We develop bounds on the output distribution of r ..."
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Cited by 2 (2 self)
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Abstract – We analyze the performance of resilient functions for imperfect input bits. Specifically, we allow more input bits than the resiliency degree of the resilient function to be biased and analyze the output behavior under this new assumption. We develop bounds on the output distribution of resilient functions build from a number of families of linear codes. We develop an explicit formula for the probability of producing an imperfect output bit that works halfway beyond the resiliency degree. It turns out that this probability shrinks exponentially with increasing code length. We provide strong evidence that suggests that resilient functions build from linear codes performs close to perfect halfway beyond their designed resiliency degree. Index Words – Resilient functions, extractors, minentropy. 1
Search and Enumeration Techniques for Incidence Structures
, 1998
"... This thesis investigates a number of probabilistic and exhaustive computational search techniques for the construction of a wide variety of combinatorial designs, and in particular, incidence structures. The emphasis is primarily from a computer science perspective, and focuses on the algorithmic de ..."
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Cited by 2 (0 self)
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This thesis investigates a number of probabilistic and exhaustive computational search techniques for the construction of a wide variety of combinatorial designs, and in particular, incidence structures. The emphasis is primarily from a computer science perspective, and focuses on the algorithmic development of the techniques, taking into account running time considerations and storage requirements. The search and enumeration techniques developed in this thesis have led to the discovery of a number of new results in the field of combinatorial design theory. Page ii Page iii Acknowledgments I would like to extend my sincere thanks to a number of people who have given me a great deal of assistance and support throughout the preparation of this thesis. Firstly, my supervisor Peter Gibbons. I am very grateful for the encouragement and guidance he has given to me. His remarkable enthusiasm and friendliness have helped to make this thesis a most enjoyable experience. My family, for their...
Coding theory and algebraic combinatorics
, 2008
"... This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings, kissing numbers, lattices, and association schemes. In part ..."
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Cited by 1 (0 self)
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This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings, kissing numbers, lattices, and association schemes. In particular, special interest is devoted to the relationship between codes and combinatorial designs. We describe and recapitulate important results in the development of the state of the art. In addition, we give illustrative examples and constructions, and highlight recent advances. Finally, we provide a collection of significant open problems and challenges concerning future research.
On Zigzag Functions and Related Objects in New Metric An Braeken
"... this paper we will investigate the properties of zigzag functions. The zigzag functions, introduced in [?] and used for e#cient oblivious transfer in [?] were later generalized to szigzag functions for 2 n in [?]. Zigzag functions are related to selfintersecting codes and orthogonal arrays as ..."
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this paper we will investigate the properties of zigzag functions. The zigzag functions, introduced in [?] and used for e#cient oblivious transfer in [?] were later generalized to szigzag functions for 2 n in [?]. Zigzag functions are related to selfintersecting codes and orthogonal arrays as it is shown in [?] and [?]. We generalize the notion of zigzag functions and prove a connection with a subclass of #resilient functions, introduced in [?]. This new definition results in a better understanding of the properties of zigzag functions and provides a better insight in the space defined by the new metric. 2 Background Define the set n = {1, . . . , n} and denote the power set of n by P (P n ). Call the set which contains all subsets of weight k from n by k,n for 1 n. Recall that the Hamming distance between the binary vectors x and y is equal to d(x, y) = y) and the Hamming weight of x is wt(x) = sup(x). It was noted in [?] that #(x, y) has similar properties as a metric and sup(x) has similar properties as a norm. Notice that sup(x) and #(x, y) = sup(x y) are subsets of n and that n is partially ordered (i.e., x y if and only if sup(x) sup(y)). In order to work in the metric defined by #(x, y) and the corresponding norm sup(x), we will use the notion access structure (#, #), or shortly denoted by # . The set # (# P (P n )) is monotone increasing and the set # (# P (P n )) is monotone decreasing. A monotone increasing set # can be described e#ciently by the set #  consisting of the minimal elements (sets) in # , i.e., the elements in # for which no proper subset is also in # . Similarly, the set # consists of the maximal elements (sets) in #, i.e., the elements in # for which no proper superset is also in #. We set # = #...
Design and Implementation of a High Quality and High Throughput TRNG in FPGA
, 906
"... Abstract — This paper focuses on the design and implementation of a highquality and highthroughput truerandom number generator (TRNG) in FPGA. Various practical issues which we encountered are highlighted and the influence of the various parameters on the functioning of the TRNG are discussed. We ..."
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Abstract — This paper focuses on the design and implementation of a highquality and highthroughput truerandom number generator (TRNG) in FPGA. Various practical issues which we encountered are highlighted and the influence of the various parameters on the functioning of the TRNG are discussed. We also propose a few values for the parameters which use the minimum amount of the resources but still pass common random number generator test batteries such as DieHard and TestU01. I.