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Hill's cipher machine, from figure 4 of the patent. In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra.Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once.
In cryptography, unicity distance is the length of an original ciphertext needed to break the cipher by reducing the number of possible spurious keys to zero in a brute force attack. That is, after trying every possible key , there should be just one decipherment that makes sense, i.e. expected amount of ciphertext needed to determine the key ...
Lester S. Hill (1891–1961) was an American mathematician and educator who was interested in applications of mathematics to communications.He received a bachelor's degree (1911) and a master's degree (1913) from Columbia College and a Ph.D. from Yale University (1926).
Lattice-based cryptography began in 1996 from a seminal work by Ajtai [1] who presented a family of one-way functions based on the SIS problem. He showed that it is secure in an average case if S V P γ {\displaystyle \mathrm {SVP} _{\gamma }} (where γ = n c {\displaystyle \gamma =n^{c}} for some constant c > 0 {\displaystyle c>0} ) is hard in ...
In the first category are those functions whose designs are based on mathematical problems, and whose security thus follows from rigorous mathematical proofs, complexity theory and formal reduction. These functions are called provably secure cryptographic hash functions. To construct these is very difficult, and few examples have been introduced.
The difficulty or impossibility of solving certain geometric problems like trisection of an angle using ruler and compass only is the basis for the various protocols in geometric cryptography. This field of study was suggested by Mike Burmester, Ronald L. Rivest and Adi Shamir in 1996. [1]
For a repeating-key polyalphabetic cipher arranged into a matrix, the coincidence rate within each column will usually be highest when the width of the matrix is a multiple of the key length, and this fact can be used to determine the key length, which is the first step in cracking the system.
The parameters of the puzzle game can be chosen to make it considerably harder to for an eavesdropper to break the code than for the parties to communicate, but Merkle puzzles do not provide the enormous qualitative differences in difficulty that are required for (and define) security in modern cryptography.