The document discusses cryptography concepts including symmetric and asymmetric encryption algorithms like DES, AES, RSA. It explains the basic working principles of RSA including key generation using large prime numbers, modular arithmetic and the concept of one-way functions that make private key derivation difficult. It also covers cryptographic modes of operation like ECB, CBC that are used to encrypt data blocks of arbitrary length.
6. The use of a one-time pad for encryption and the possibility of getting any possible plaintext from the ciphertext by the use of some other pad.
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14. The function consists of four steps, carried out in sequence. Step-1 Expansion - a 48-bit number, E, is constructed by expanding the 32-bit according to a fixed transposition and duplication rule. Step-2 Key mixing - E and K i are XORed together. Sixteen 48-bit subkeys — one for each round — are derived from the main key using the key schedule. Step-3 Substitution This output is then partitioned into eight groups of 6 bits each (8x6), each of which is fed into a different S-box. Each of the 32 possible inputs to an S-box is mapped onto a 4-bit output. Step-4 Permutation these 32 (8 x 4) bits are passed through a P-box
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16. Triple DES uses a "key bundle" which comprises three DES keys, K1, K2 and K3, each of 56 bits (excluding parity bits). The encryption algorithm is: ciphertext = EK3(DK2(EK1(plaintext))) I.e., DES encrypt with K1, DES decrypt with K2, then DES encrypt with K3. Decryption is the reverse: plaintext = DK1(EK2(DK3(ciphertext))) I.e., decrypt with K3, encrypt with K2, then decrypt with K1. Each triple encryption encrypts one block of 64 bits of data. In each case the middle operation is the reverse of the first and last. This improves the strength of the algorithm when using keying option 2, and provides backward compatibility with DES with keying option 3. [edit] Keying options The standards define three keying options: Keying option 1: All three keys are independent. Keying option 2: K1 and K2 are independent, and K3 = K1. Keying option 3: All three keys are identical, i.e. K1 = K2 = K3. Keying option 1 is the strongest, with 3 × 56 = 168 independent key bits. Keying option 2 provides less security, with 2 × 56 = 112 key bits. This option is stronger than simply DES encrypting twice, e.g. with K1 and K2, because it protects against meet-in-the-middle attacks. Keying option 3 is equivalent to DES, with only 56 key bits. This option provides backward compatibility with DES, because the first and second DES operations cancel out
124. ABCD=f F (ABCD,m i ,T[1..16]) ABCD=f G (ABCD,m i ,T[17..32]) ABCD=f H (ABCD,m i ,T[33..48]) ABCD=f I (ABCD,m i ,T[49..64]) m i + + + + A B C D MD i MD i+1
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178. An example RRSet for bob.com . The KEY record is Bob's public key. The SIG record is the top-level com server's signed has of the A and KEY records to verify their authenticity.
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190. Etymology Originally, radio or radiotelegraphy was called "wireless telegraphy", which was shortened to "wireless" by the British. The prefix radio- in the sense of wireless transmission, was first recorded in the word radioconductor, coined by the French physicist Édouard Branly in 1897 and based on the verb to radiate (in Latin "radius" means "spoke of a wheel, beam of light, ray"). "Radio" as a noun is said to have been coined by the advertising expert Waldo Warren (White 1944). This word also appears in a 1907 article by Lee De Forest, was adopted by the United States Navy in 1912 and became common by the time of the first commercial broadcasts in the United States in the 1920s. (The noun "broadcasting" itself came from an agricultural term, meaning "scattering seeds widely".) The term was then adopted by other languages in Europe and Asia. British Commonwealth countries continued to mainly use the term "wireless" until the mid 20th century, though the magazine of the BBC in the UK has been called Radio Times ever since it was first published in the early 1920s. In recent years the term "wireless" has gained renewed popularity through the rapid growth of short-range computer networking, e.g., Wireless Local Area Network (WLAN), WiFi, and Bluetooth, as well as mobile telephony, e.g., GSM and UMTS. Today, the term "radio" often refers to the actual transceiver device or chip, whereas "wireless" refers to the system and/or method used for radio communication, hence one talks about radio transceivers and Radio Frequency Identification (RFID), but about wireless devices and wireless sensor networks.
191. Processes Radio systems used for communications will have the following elements. With more than 100 years of development, each process is implemented by a wide range of methods, specialized for different communications purposes. Each system contains a transmitter. This consists of a source of electrical energy, producing alternating current of a desired frequency of oscillation. The transmitter contains a system to modulate (change) some property of the energy produced to impress a signal on it. This modulation might be as simple as turning the energy on and off, or altering more subtle properties such as amplitude, frequency, phase, or combinations of these properties. The transmitter sends the modulated electrical energy to a tuned resonant antenna; this structure converts the rapidly-changing alternating current into an electromagnetic wave that can move through free space (sometimes with a particular polarization (waves)). Electromagnetic waves travel through space either directly, or have their path altered by reflection, refraction or diffraction. The intensity of the waves diminishes due to geometric dispersion (the inverse-square law); some energy may also be absorbed by the intervening medium in some cases. Noise will generally alter the desired signal; this electromagnetic interference comes from natural sources, as well as from artificial sources such as other transmitters and accidental radiators. Noise is also produced at every step due to the inherent properties of the devices used. If the magnitude of the noise is large enough, the desired signal will no longer be discernible; this is the fundamental limit to the range of radio communications. The electromagnetic wave is intercepted by a tuned receiving antenna; this structure captures some of the energy of the wave and returns it to the form of oscillating electrical currents. At the receiver, these currents are demodulated, which is conversion to a usable signal form by a detector sub-system. The receiver is "tuned" to respond preferentially to the desired signals, and reject undesired signals. Early radio systems relied entirely on the energy collected by an antenna to produce signals for the operator. Radio became more useful after the invention of electronic devices such as the vacuum tube and later the transistor, which made it possible to amplify weak signals. Today radio systems are used for applications from walkie-talkie children's toys to the control of space vehicles, as well as for broadcasting, and many other applications. Electromagnetic spectrum Main article: Electromagnetic spectrum Radio frequencies occupy the range from a few tens of hertz to three hundred gigahertz, although commercially important uses of radio use only a small part of this spectrum.[2] Other types of electromagnetic radiation, with frequencies above the RF range, are microwave, infrared, visible light, ultraviolet, X-rays and gamma rays. Since the energy of an individual photon of radio frequency is too low to remove an electron from an atom, radio waves are classified as non-ionizing radiation.
Hinweis der Redaktion
Here walk through example using “trivial” sized numbers. Selecting primes requires the use of primality tests. Finding d as inverse of e mod ø( n ) requires use of Inverse algorithm (see Ch4)
Rather than having to laborious repeatedly multiply, can use the "square and multiply" algorithm with modulo reductions to implement all exponentiations quickly and efficiently (see next).
Stallings Fig 12.1
The padded message is broken into 512-bit blocks, processed along with the buffer value using 4 rounds, and the result added to the input buffer to make the new buffer value. Repeat till run out of message, and use final buffer value as hash. nb. due to padding always have a full final block (with length in it).
Each round mixes the buffer input with the next "word" of the message in a complex, non-linear manner. A different non-linear function is used in each of the 4 rounds (but the same function for all 16 steps in a round). The 4 buffer words (a,b,c,d) are rotated from step to step so all are used and updated. g is one of the primitive functions F,G,H,I for the 4 rounds respectively. X[k] is the kth 32-bit word in the current message block. T[i] is the ith entry in the matrix of constants T. The addition of varying constants T and the use of different shifts helps ensure it is extremely difficult to compute collisions.
Compare using the design goals listed earlier. SHA-1 is probbaly the preferred hash function for new applications. Currently no problems are known with it.