On sharing secrets and Reed-Solomon codes
TL;DR: Decoding algorithms for Reed-Solomon codes provide extensions and generalizations of Shamir's method, which is closely related to Reed- Solomon coding schemes.
Abstract: Shamir's scheme for sharing secrets is closely related to Reed-Solomon coding schemes. Decoding algorithms for Reed-Solomon codes provide extensions and generalizations of Shamir's method.
Citations
More filters
01 Jan 1988
TL;DR: It is shown that any reasonable multiparty protocol can be achieved if at least 2n/3 of the participants are honest and the secrecy achieved is unconditional.
Abstract: Under the assumption that each pair of participants can communicate secretly, we show that any reasonable multiparty protocol can be achieved if at least 2n/3 of the participants are honest. The secrecy achieved is unconditional. It does not rely on any assumption about computational intractability.
1,663 citations
Patent•
15 May 1991TL;DR: In this article, the authors propose a method for distributed data storage, data communication, and parallel computing applications, where information to be transmitted in a data signal or stored is represented as N elements of a field or computational structure, and dispersed among a set of n pieces that are to either be transmitted or stored in a manner yielding no fewer than m pieces used in subsequent reconstruction.
Abstract: Method and apparatus applicable to a variety of data storage, data communication, and parallel computing applications, efficiently improving information availability and load balancing. Information to be transmitted in a data signal or stored is represented as N elements of a field or computational structure, and dispersed among a set of n pieces that are to be transmitted or stored in a manner yielding no fewer than m pieces used in subsequent reconstruction. For dispersal, n vectors a i each having m elements are used and the n pieces are assembled from elements obtained as products of these vectors with m element groups taken from the N elements representing the information. For reconstruction from m available pieces, m m-element vectors α i are derived from the vectors a i , and the N elements representing the information are obtained as products of these vectors with m-element groups taken from the pieces. The vector products may be implemented using an appropriate processor, including a vector processor, systolic array, or parallel processor. For fault-tolerant storage in a partitioned or distributed system, information is dispersed into n pieces so that any m suffice for reconstruction, and the pieces are stored in different parts of the medium. For fault-tolerant and congestion-free transmission of packets in a network or a parallel computer, each packet is dispersed into n pieces so that any m pieces suffice for reconstruction and the pieces are routed to the packet's destination along independent paths or at different times.
998 citations
Patent•
17 Jan 1997
TL;DR: In this paper, a method and system for transferring data from a host computer to one or more subscriber computers, the data consisting of k original packets, is described, which includes the steps of encoding the k original packet to form n encoded packets, where n>k, transmitting the encoded packets from the host computer, receiving some of the transmitted packets, and decoding any combination of k correctly-received encoded packets to reconstruct the original packets.
Abstract: A method and system are provided for transferring data from a host computer to one or more subscriber computers, the data consisting of k original packets. The method includes the steps of encoding the k original packets to form n encoded packets, where n>k, transmitting the encoded packets from the host computer to the subscriber computers, receiving some of the transmitted packets, and decoding any combination of k correctly-received encoded packets to reconstruct the k original packets.
995 citations
Patent•
06 Apr 2000
TL;DR: In this paper, a method for encoding a stream of source packets, in which a plurality of k source packets are packet-level forward error correction encoded to form an n-k error-correcting wildcard packets, is presented.
Abstract: A method is provided for encoding a stream of source packets, in which a plurality of k source packets are packet-level forward error correction encoded to form a plurality of n-k error-correcting wildcard packets, wherein the k source packets and n-k wildcard packets are to be transmitted to a receiver. After the arrival of each source packet, for each byte of the source packet, the respective error correction contributions to the corresponding bytes of the plurality of wildcard packets are computed. The source packet is transmitted to the receiver without waiting for the arrival of another source packet of the plurality of source packets. For each wildcard packet byte, the error correction contribution of the source packet is summed in an accumulator. After the error correction contributions have been computed using all k source packets and summed for all n-k wildcard packets, the wildcard packets are transmitted to the receiver.
979 citations
Patent•
19 Apr 2002
TL;DR: In this paper, a system for protecting the transmission of packet streams between a host computer and one or more client computers, and upon reception, reconstructing any outage damage caused during the transmission to the packet streams, and digitally recording the reconstructed packet streams to a file.
Abstract: The present invention relates to a system for (1) protecting the transmission of packet streams between a host computer and one or more client computers, and (2) upon reception, (a) reconstructing any outage damage caused during the transmission to the packet streams, and (b) digitally recording the reconstructed packet streams to a file. The present invention also relates to a method for dynamically generating a file index table as the packet stream is being digitally recorded.
968 citations
References
More filters
Book•
01 Jan 1968
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Abstract: A fuel pin hold-down and spacing apparatus for use in nuclear reactors is disclosed. Fuel pins forming a hexagonal array are spaced apart from each other and held-down at their lower end, securely attached at two places along their length to one of a plurality of vertically disposed parallel plates arranged in horizontally spaced rows. These plates are in turn spaced apart from each other and held together by a combination of spacing and fastening means. The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid. This apparatus is particularly useful in connection with liquid cooled reactors such as liquid metal cooled fast breeder reactors.
17,939 citations
TL;DR: This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.
Abstract: In this paper we show how to divide data D into n pieces in such a way that D is easily reconstructable from any k pieces, but even complete knowledge of k - 1 pieces reveals absolutely no information about D. This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.
14,340 citations
"On sharing secrets and Reed-Solomon..." refers background or methods in this paper
...We wish to remark that Shamir's scheme [ 5 ] for sharing a secret among many persons is very closely related to Reed-Solomon coding schemes [ 1-3], and that there are several advantages to discussing the former in the context of the latter....
[...]
...From the practical point of view the two load factors approximately satisfy the equation a = et'/~, where a and a' are, respectively, the load factors in open addressing and in external chaining [ 5 ]....
[...]
...Dk = bk; indeed, D can be found by Lagrange interpolation as suggested by Shamir [ 5 ] or by standard Reed-Solomon encoding algorithms [1, 2]. Only the r - 1 - k pieces Dk+l ........
[...]
TL;DR: A mapping of m symbols into 2 symbols will be shown to be (2 m)/2 or ( 2 m 1)/2 symbol correcting, depending on whether m is even or odd.
Abstract: a._) into the 2-tuple (P(0), P(a), P(a:), P(1 ); this m-tuple might be some encoded message and the corresponding 2n-tuple is to be transmitted. This mapping of m symbols into 2 symbols will be shown to be (2 m)/2 or (2 m 1)/2 symbol correcting, depending on whether m is even or odd. A natural correspondence is established between the field elements of K and certain binary sequences of length n. Under this correspondence, code E may be regarded as a mapping of binary sequences of mn bits into binary sequences of n2 bits. Thus code E can be interpreted to be a systematic multiple-error-correcting code of binary sequences.
2,931 citations
Book•
01 Jan 2015
TL;DR: This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.
Abstract: This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose–Chaudhuri–Hocquenghem codes that subsequently became known as the Berlekamp–Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.
2,912 citations
"On sharing secrets and Reed-Solomon..." refers methods in this paper
...Dk = bk; indeed, D can be found by Lagrange interpolation as suggested by Shamir [5] or by standard Reed-Solomon encoding algorithms [ 1 , 2]. Only the r - 1 - k pieces Dk+l ........
[...]
Book•
01 Jan 1977TL;DR: In this paper, the authors present a survey of advanced topics for part I and a survey for part II of a survey on the Gaussian channel and the source coding theorem, including linear codes, BCH Goppa codes, and variable-length source coding.
Abstract: 1. Entropy and mutual information 2. Discrete memoryless channels and their capacity-cost functions 3. Discrete memoryless sources and their rate-distortion functions 4. The Gaussian channel and source 5. The source-channel coding theorem 6. Survey of advanced topics for part I 7. Linear codes 8. BCH Goppa, and related codes 9. Convolutional codes 10. Variable-length source coding 11. Survey of advanced topics for part II.
673 citations