1 / 44

490 likes | 1.61k Views

Stream Cipher. Stream Cipher. A stream cipher breaks the message M into successive characters or bits m 1 , m 2 , ..., and enciphers each m i with the ith element k i of a key stream K=k 1 k 2 ...; that is, E K (M)=E k1 (m 1 )E k2 (m 2 ). Periodic.

Download Presentation
## Stream Cipher

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Stream Cipher**• A stream cipher breaks the message M into successive characters or bits m1, m2, ..., and enciphers each mi with the ith element ki of a key stream K=k1k2...; that is, • EK(M)=Ek1(m1)Ek2(m2)...**Periodic**• A stream cipher is periodic if the key stream repeats after d characters for some fixed d; otherwise, it is nonperiodic. • Periodic: • Rotor cipher, Hagelin cipher • Nonperiodic: • Vernam cipher (one-time pad), running-key cipher**Stream Cipher**• Two different approaches： • synchronous methods • self-synchronous methods**Synchronous Stream Cipher**• The key stream is generated independently of the message stream. • If a ciphertext character is lost during transmission, the sender and receiver must resynchronize their key generators before they can proceed further.**Synchronous Stream Cipher**• Must ensure no part of the key stream is repeated • Linear Feedback Shift Registers • Output-block Feedback Mode • Counter Method**Self-synchronous Methods**• Each key character is derived from a fixed number n of preceding ciphertext characters. • If a ciphertext character is lost or altered during transmission, the error propagates forward for n characters, but the cipher resynchronizes by itself after n correct ciphertext character have been received. • Autokey cipher and Cipher Feedback Mode (CFM) • Nonperiodic.**Error Handling**• If errors are propagated by the decryption algorithm, applying error detecting codes before encryption provides a mechanism for authenticity.**Synchronous Stream Cipher**• key stream is generated independently of the message stream • key stream must deterministic so the stream can be reproduced for decipherment. • How to generate a random key stream? • The starting stage of the key generator is initialized by a “seed” I0.**Stream Cipher**• Stream ciphers are often breakable if the key stream repeats or has redundancy. • To be un breakable, it must be a random sequence as long as the plaintext. • Each element in the key alphabet should be uniformly distributed over the key stream, and there should be no long repeated subsequences or other patterns. • No finite algorithm can generate truly random sequences.**LFSR**• LFSR (Linear Feedback Shift Register) • shift register R=(rn, rn-1, ..., r1) • “tap” sequence T=(tn, tn-1, ..., t1) • ti and ri are binary digit • bit r1 is appended to the key stream, • bits rn, ...,r2 are shifted right • a new bit derived from T and R is inserted into the left end of the register.**LFSR**• Letting R’=(rn’, rn-1’, ... r1’) denote the next state of R, we see that the computation of R’ is thus: • ri’=ri+1 i=1,...,n-1 • rn’=TR=∑ni=1tiri mod 2 • R’=HR mod 2, where H is the nxn matrix. • T(x)=tnxn + tn-1xn-1 + ... + t1x + 1 • 若T(x)為質多項式（primitive polynomial）則可以產生2n-1個sequence.**LFSR**• The feedback loop attempts to simulate a one-time pad by transforming a short key I0 into a long pseudo-random sequence K. • Unfortunately, the result is a poor approximation of the one-time pad.**Cryptanalysis of LFSR**• Known-plaintext attack • 2n pairs of plaintext-ciphertext pairs • M=m1...m2n, C=c1...c2n • mici=mi (mi ki)=ki, i=1,...,2n**Output-Block Feedback Mode**• weakness of LFSR is caused by the linearity of R’=HR mod 2 • Nonlinear block ciphers such as the DES seem to be good candidates for this.**Counter Method**• Successive input blocks are generated by a simple counter. • It is possible to generate the ith key character ki without generating the first i-1 key characters by setting the counter to I0 + i –1**Self-Synchronous Stream Cipher**• A Self-synchronous stream cipher derives each key character from a fixed number n of preceding ciphertext characters. • Autokey Cipher and Cipher Feedback**Autokey Cipher**• An autokey cipher is one in which the key is derived from the message it enciphers. • In Vigenere first cipher, the key is formed by appending the plaintext M= m1m2... to a “priming key” character k1; the ith key character (i>1) is thus given by ki=mi-1.**Autokey Cipher**• In Vigenere second cipher, the key is formed by appending each character of the ciphertext to the priming key k1; that is, ki=ci-1 (i > 1)**Aotukey Cipher**• 缺點：it exposes the key in the ciphertext stream • This problem is easily remedied by passing the ciphertext characters through a nonlinear block cipher to derive the key characters. • Cipher Feedback mode (CFM)**Cipher Feedback mode (CFM)**• The ciphertext characters participate in the feedback loop. • It is sometimes called “changing”, because each ciphertext character is functionally dependent on (chained to) preceding ciphertext characters.**亂數產生器**• LFSR • 線性同餘產生器 • 非線性亂數產生器 • 截切亂數產生器 • 數學計算產生器 • 分解因數法 • 離散對數法 • 二次剩餘法 • 質數法**線性同餘產生器**• xi=axi-1 + b (mod m) • x0為初值 • a, b, m 為KEY • 條件： • gcd(b,m)=1 • 對於每個能夠整除M之質數p而言，b=a-1必須為p 之整數倍 • IF 4|m then 4|b • 缺點：產生之亂數可預測**亂數產生器的安全性評估**• 好的亂數產生器具備之特性 • 週期長 • 不可預測性（Unpredictable） • 測試法： • Chi-Square 測試法 • Kolmogorov-Smirnov(KS)測試法

More Related