|
Cyclometer
The cyclometer was a cryptologic device designed, "probably in 1934 or 1935," by Marian Rejewski of the Polish Cipher Bureau's German section (BS-4) to facilitate decryption of German Enigma ciphertext. The original machines are believed to have been destroyed shortly before the German invasion of Poland that launched the Second World War, to prevent the Germans learning that their cipher had been broken. Using drawings made by Rejewski, Hal Evans and Tim Flack at the Department of Engineering, University of Cambridge, in 2019 constructed a working version of the cyclometer. History Example message Frode Weierud provides the procedure, secret settings, and results that were used in a 1930 German technical manual. Daily key (shared secret): Wheel Order : II I III Ringstellung : 24 13 22 (XMV) Reflector : A Plugboard : A-M, F-I, N-V, P-S, T-U, W-Z Grundstellung: FOL Operator chosen message key : ABL Enciphered starting with FOL: PKPJXI Cleartext m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grill (cryptology)
The grill method ( pl, metoda rusztu), in cryptology, was a method used chiefly early on, before the advent of the cyclometer, by the mathematician-cryptologists of the Polish Cipher Bureau ('' Biuro Szyfrów'') in decrypting German Enigma machine ciphers. The Enigma rotor cipher machine changes plaintext characters into cipher text using a different permutation for each character, and so implements a polyalphabetic substitution cipher. Background The German navy started using Enigma machines in 1926; it was called ''Funkschlüssel C'' ("Radio cipher C"). By 15 July 1928, the German Army (''Reichswehr'') had introduced their own version of the Enigma—the ''Enigma G''; a revised ''Enigma I'' (with plugboard) appeared in June 1930. The Enigma I used by the German military in the 1930s was a 3-rotor machine. Initially, there were only three rotors labeled ''I'', ''II'', and ''III'', but they could be arranged in any order when placed in the machine. Rejewski identified the rot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marian Rejewski
Marian Adam Rejewski (; 16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who in late 1932 reconstructed the sight-unseen German military Enigma cipher machine, aided by limited documents obtained by French military intelligence. Over the next nearly seven years, Rejewski and fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski developed and used techniques and equipment to decrypt the German machine ciphers, even as the Germans introduced modifications to their equipment and encryption procedures. Five weeks before the outbreak of World War II the Poles, at a conference in Warsaw, shared their achievements with the French and British, thus enabling Britain to begin reading German Enigma-encrypted messages, seven years after Rejewski's original reconstruction of the machine. The intelligence that was gained by the British from Enigma decrypts formed part of what was code-named Ultra and contributed—perhaps decisively—to the d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perforated Sheets
The method of Zygalski sheets was a cryptologic technique used by the Polish Cipher Bureau before and during World War II, and during the war also by British cryptologists at Bletchley Park, to decrypt messages enciphered on German Enigma machines. The Zygalski-sheet apparatus takes its name from Polish Cipher Bureau mathematician–cryptologist Henryk Zygalski, who invented it about October 1938. Method Zygalski's device comprised a set of 26 perforated sheets for each of the, initially, six possible sequences for inserting the three rotors into the Enigma machine's scrambler. Each sheet related to the starting position of the left (slowest-moving) rotor. The 26 × 26 matrix represented the 676 possible starting positions of the middle and right rotors and was duplicated horizontally and vertically: ''a–z, a–y''. The sheets were punched with holes in the positions that would allow a "female" to occur. Polish mathematician–cryptologist Marian Rejewski writes about how ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Cipher Bureau
The Cipher Bureau, in Polish language, Polish: ''Biuro Szyfrów'' (), was the interwar Polish General Staff's Second Department of Polish General Staff, Second Department's unit charged with SIGINT and both cryptography (the ''use'' of ciphers and codes) and cryptanalysis (the ''study'' of ciphers and codes, for the purpose of "breaking" them). The precursor of the agency that would become the Cipher Bureau was created in May 1919, during the Polish-Soviet War (1919–21), and played a vital role in securing Poland's survival and victory in that war. In mid-1931, the Cipher Bureau was formed by the merger of pre-existing agencies. In December 1932, the Bureau began breaking Germany's Enigma machine, Enigma ciphers. Over the next seven years, Polish cryptologists overcame the growing structural and operating complexities of the plugboard-equipped Enigma. The Bureau also broke Soviet Union, Soviet cryptography. Five weeks before the outbreak of World War II, on 25 July 1939, in Wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Card Catalog (cryptology)
The card catalog, or "catalog of characteristics," in cryptography, was a system designed by Polish Cipher Bureau mathematician-cryptologist Marian Rejewski, and first completed about 1935 or 1936, to facilitate decrypting German Enigma ciphers. History The Polish Cipher Bureau used the theory of permutations to start breaking the Enigma cipher in late 1932. The Bureau recognized that the Enigma machine's doubled-key (see Grill (cryptology)) permutations formed cycles, and those cycles could be used to break the cipher. With German cipher keys provided by a French spy, the Bureau was able to reverse engineer the Enigma and start reading German messages. At the time, the Germans were using only 6 ''steckers'', and the Polish grill method was feasible. On 1 August 1936, the Germans started using 8 ''steckers'', and that change made the grill method less feasible. The Bureau needed an improved method to break the German cipher. Although the ''steckers'' would change which letter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squaring The Circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of lines and circles implied the existence of such a square. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi (\pi) is a transcendental number. That is, \pi is not the root of any polynomial with rational coefficients. It had been known for decades that the construction would be impossible if \pi were transcendental, but that fact was not proven until 1882. Approximate constructions with any given non-perfect accuracy exist, and many such constructions have been found. Despite the proof that it is impossible, attempts to square the circle have been common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans Thilo-Schmidt
Hans-Thilo Schmidt (13 May 1888 – 19 September 1943) codenamed Asché or Source D, was a spy who, during the 1930s, sold secrets about the Germans' Enigma machine to the French. The materials he provided facilitated Polish mathematician Marian Rejewski's reconstruction of the wiring in the Enigma's rotors and reflector; thereafter the Poles were able to read a large proportion of Enigma-enciphered traffic. Selling Enigma secrets A former officer, Schmidt had been forced to leave the army having suffered from gas during the First World War.May, Ernest ''Strange Victory'', New York: Hill & Wang, 2000 page 135. However, his brother, Rudolf Schmidt, secured him a civilian post at the German Armed Forces' cryptographic headquarters, the Cipher Office. Shortly after the military version of the Enigma machine was introduced, he contacted French intelligence and offered to supply information about the new machine. His offer was accepted by Captain Gustave Bertrand of French Intellig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bomba (cryptography)
The ''bomba'', or ''bomba kryptologiczna'' (Polish for "bomb" or "cryptologic bomb"), was a special-purpose machine designed around October 1938 by Polish Cipher Bureau cryptologist Marian Rejewski to break German Enigma-machine ciphers. Etymology How the machine came to be called a "bomb" has been an object of fascination and speculation. One theory, most likely apocryphal, originated with Polish engineer and army officer Tadeusz Lisicki (who knew Rejewski and his colleague Henryk Zygalski in wartime Britain but was never associated with the Cipher Bureau). He claimed that Jerzy Różycki (the youngest of the three Enigma cryptologists, and who had died in a Mediterranean passenger-ship sinking in January 1942) named the "bomb" after an ice-cream dessert of that name. This story seems implausible, since Lisicki had not known Różycki. Rejewski himself stated that the device had been dubbed a "bomb" "for lack of a better idea". Perhaps the most credible explanation is given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reflector (cipher Machine)
A reflector, in cryptology, is a component of some rotor cipher machines, such as the Enigma machine, that sends electrical impulses that have reached it from the machine's rotors, back in reverse order through those rotors. The reflector simplified using the same machine setup for encryption and decryption, but it creates a weakness in the encryption: with a reflector the encrypted version of a given letter can never be that letter itself. That limitation aided World War II code breakers in cracking Enigma encryption. The comparable WW II U.S. cipher machine, SIGABA In the history of cryptography, the ECM Mark II was a cipher machine used by the United States for message encryption from World War II until the 1950s. The machine was also known as the SIGABA or Converter M-134 by the Army, or CSP-888/889 by the ..., did not include a reflector. Other names The reflector is also known as the reversing drum or, from the German, the ''Umkehrwalze'' or ''UKW''. {{crypto-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cycle Graph (algebra)
In group theory, a subfield of abstract algebra, a group cycle graph illustrates the various cycles of a group and is particularly useful in visualizing the structure of small finite groups. A cycle is the set of powers of a given group element ''a'', where ''an'', the ''n''-th power of an element ''a'' is defined as the product of ''a'' multiplied by itself ''n'' times. The element ''a'' is said to ''generate'' the cycle. In a finite group, some non-zero power of ''a'' must be the group identity, ''e''; the lowest such power is the order of the cycle, the number of distinct elements in it. In a cycle graph, the cycle is represented as a polygon, with the vertices representing the group elements, and the connecting lines indicating that all elements in that polygon are members of the same cycle. Cycles Cycles can overlap, or they can have no element in common but the identity. The cycle graph displays each interesting cycle as a polygon. If ''a'' generates a cycle of order 6 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Table
In computing, a hash table, also known as hash map, is a data structure that implements an associative array or dictionary. It is an abstract data type that maps keys to values. A hash table uses a hash function to compute an ''index'', also called a ''hash code'', into an array of ''buckets'' or ''slots'', from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored. Ideally, the hash function will assign each key to a unique bucket, but most hash table designs employ an imperfect hash function, which might cause hash ''collisions'' where the hash function generates the same index for more than one key. Such collisions are typically accommodated in some way. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the table. Many hash table designs also allow arbitrary insertions and deletions of key–value pairs, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Function
A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or simply ''hashes''. The values are usually used to index a fixed-size table called a ''hash table''. Use of a hash function to index a hash table is called ''hashing'' or ''scatter storage addressing''. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally and storage space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees, and the often exponential storage requirements of direct access of state spaces of large or variable-length keys. Use of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.png "Click for more on -> Cycle Graph (algebra)")
