Title: Secrets for Sharing

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Instead, (1) can be performed using the binary operation in any group. For example, take the cyclic group of integers with addition modulo 2 32, which corresponds to 32-bit integers with addition defined with the binary overflow being discarded. The secret s can be partitioned into a vector of M 32-bit integers, which we call v secret. Then ( n − 1) of the players are each given a vector of M 32-bit integers that is drawn independently from a uniform probability distribution, with player i receiving v i. The remaining player is given v n = v secret − v 1 − v 2 − ... − v n−1. The secret vector can then be recovered by summing across all the players' vectors.

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Encode the secret as a binary number s of any length. Give to each player i aside from the last a random binary number p i of the same length as s. Give to the last player the share calculated as p n = s ⊕ p 1 ⊕ p 2 ⊕ ... ⊕ p n−1, where ⊕ denotes bitwise exclusive or. The secret is the bitwise exclusive-or of all the players' numbers ( p i, for 1 ≤ i ≤ n).Each share of the secret must be at least as large as the secret itself. This result is based in information theory, but can be understood intuitively. Given t − 1 shares, no information whatsoever can be determined about the secret. Thus, the final share must contain as much information as the secret itself. There is sometimes a workaround for this limitation by first compressing the secret before sharing it, but this is often not possible because many secrets (keys for example) look like high-quality random data and thus are hard to compress. All secret-sharing schemes use random bits for constructing the shares. [ citation needed] To distribute a one-bit secret shares with a threshold of t shares, t − 1 random bits are needed. [ citation needed] To distribute a secret of b bits, entropy of ( t − 1) × b bits is necessary. [ citation needed] To test for the best ways to share files securely we first set up an account with the relevant software platform. We then tested the service to see how the software could be used with different files and folders, from different devices, in different situations. The aim was to push each platform to see how useful its basic tools were and also how easy it was to get to grips with any more advanced tools. SyncThing is a free and open source P2P file-syncing program, similar to Resilio (formerly known as BitTorrent Sync). Like Resilio, it uses the Bittorrent protocol to efficiently copy files between devices on the same network or over the Internet.

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When deciding which secure file sharing platform to use, first consider what your actual needs are, as sometimes free and budget software may only provide basic tools and saving options, so if you need to use advanced features you may find a paid platform is much more worthwhile. Additionally, higher-end software can really cater for every need, so do ensure you have a good idea of which features you think you may require from your secure file sharing platform. How we tested the best ways to share files securely A secure secret sharing scheme distributes shares so that anyone with fewer than t shares has no more information about the secret than someone with 0 shares. The Chinese remainder theorem can also be used in secret sharing, for it provides us with a method to uniquely determine a number S modulo k many pairwise coprime integers m 1 , m 2 , . . . , m k {\displaystyle m_{1},m_{2},...,m_{k}} , given that S < ∏ i = 1 k m i {\displaystyle S<\prod _{i=1} SyncThing uses TLS to protect data in transit, which combined with the open BitTorrent protocol makes for ultra-secure communications. Another advantage of using TLS is that SyncThing can make use of digital certificates to authenticate devices, so only those you authorize can access your data.Blakley's scheme is less space-efficient than Shamir's; while Shamir's shares are each only as large as the original secret, Blakley's shares are t times larger, where t is the threshold number of players. Blakley's scheme can be tightened by adding restrictions on which planes are usable as shares. The resulting scheme is equivalent to Shamir's polynomial system. The "Direct Message" feature supports sending file attachments. There's a file size limit of 2GB but no restriction on the type of files that you can send. There's also no limit on the overall number of files sent.