Understanding Cryptography - Stream Ciphers PDF

Cryptography (Course Code: CCY6322- 3) Dr. Mohammad Zunnun Khan Email: [email protected] 2024  Understanding Cryptography – A Textbook for Students and Practitioners by Christof Paar and Jan Pelzl www.crypto-t...

Cryptography (Course Code: CCY6322- 3) Dr. Mohammad Zunnun Khan Email: [email protected] 2024  Understanding Cryptography – A Textbook for Students and Practitioners by Christof Paar and Jan Pelzl www.crypto-textbook.com Chapter 2 – Stream Ciphers ver. October 29, 2009 These slides were prepared by Thomas Eisenbarth, Christof Paar and Jan Pelzl  Content of this Chapter Intro to stream ciphers Random number generators (RNGs) One-Time Pad (OTP) Linear feedback shift registers (LFSRs) 3/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl  Content of this Chapter Intro to stream ciphers Random number generators (RNGs) One-Time Pad (OTP) Linear feedback shift registers (LFSRs) Trivium: a modern stream cipher 4/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Stream Ciphers in the Field of Cryptology Cryptology Cryptography Cryptanalysis Symmetric Ciphers Asymmetric Ciphers Protocols Block Ciphers Stream Ciphers Stream Ciphers were invented in 1917 by Gilbert Vernam 5/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl  Stream Cipher vs. Block Cipher Stream Ciphers Encrypt bits individually Usually small and fast  common in embedded devices (e.g., A5/1 for GSM phones) Block Ciphers: Always encrypt a full block (several bits) Are common for Internet applications 6/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Encryption and Decryption with Stream Ciphers Plaintext xi, ciphertext yi and key stream si consist of individual bits Encryption and decryption are simple additions modulo 2 (aka XOR) Encryption and decryption are the same functions Encryption: yi = esi(xi ) = xi + si mod 2 xi , yi , si ∈ {0,1} Decryption: xi = esi(yi ) = yi + si mod 2 SID's 7/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl  Synchronous vs. Asynchronous Stream Cipher Security of stream cipher depends entirely on the key stream si : Should be random , i.e., Pr(si = 0) = Pr(si = 1) = 0.5 Must be reproducible by sender and receiver Synchronous Stream Cipher Key stream depend only on the key (and possibly an initialization vector IV) Asynchronous Stream Ciphers Key stream depends also on the ciphertext (dotted feedback enabled) 8/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Why is Modulo 2 Addition a Good Encryption Function? Modulo 2 addition is equivalent to XOR operation For perfectly random key stream si , each ciphertext output bit has a 50% chance to be 0 or 1  Good statistic property for ciphertext Inverting XOR is simple, since it is the same XOR operation xi si yi 0 0 0 0 1 1 1 0 1 1 1 0 9/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Stream Cipher: Throughput Performance comparison of symmetric ciphers (Pentium4): Cipher Key length Mbit/s DES 56 36.95 3DES 112 13.32 AES 128 51.19 RC4 (stream cipher) (choosable) 211.34 Source: Zhao et al., Anatomy and Performance of SSL Processing, ISPASS 2005 10/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl  Content of this Chapter Intro to stream ciphers Random number generators (RNGs) One-Time Pad (OTP) Linear feedback shift registers (LFSRs) Trivium: a modern stream cipher 11/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Random number generators (RNGs) RNG True RNG Cryptographically Pseudorandom NG Secure RNG 12/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   True Random Number Generators (TRNGs) coin Based on physical random processes: coin flipping, dice rolling, semiconductor noise, radioactive decay, mouse movement, clock jitter of digital circuits Output stream si should have good statistical properties: Pr(si = 0) = Pr(si = 1) = 50% (often achieved by post-processing) Output can neither be predicted nor be reproduced Typically used for generation of keys, nonces (used only-once values) and for many other purposes 13/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Pseudorandom Number Generator (PRNG) Generate sequences from initial seed value psi Typically, output stream has good statistical properties Output can be reproduced and can be predicted Often computed in a recursive way: s0  seed si 1  f ( si , si 1 ,..., si t ) Example: rand() function in ANSI C: s0  12345 si 1  1103515245si  12345mod 231 Most PRNGs have bad cryptographic properties! 14/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Cryptanalyzing a Simple PRNG Simple PRNG: Linear Congruential Generator S 0  seed Si 1  AS i  B mod m Assume unknown A, B and S0 as key Size of A, B and Si to be 100 bit 300 bit of output are known, i.e. S1, S2 and S3 Solving S 2  AS1  B mod m S 3  AS 2  B mod m …directly reveals A and B. All Si can be computed easily! Bad cryptographic properties due to the linearity of most PRNGs 15/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Cryptographically Secure Pseudorandom Number Generator (CSPRNG) Special PRNG with additional property: Output must be unpredictable More precisely: Given n consecutive bits of output si , the following output bits sn+1 cannot be predicted (in polynomial time). Needed in cryptography, in particular for stream ciphers Remark: There are almost no other applications that need unpredictability, whereas many, many (technical) systems need PRNGs. 16/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl  Content of this Chapter Intro to stream ciphers Random number generators (RNGs) One-Time Pad (OTP) Linear feedback shift registers (LFSRs) Trivium: a modern stream cipher 17/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   One-Time Pad (OTP) Unconditionally secure cryptosystem: A cryptosystem is unconditionally secure if it cannot be broken even with infinite computational resources One-Time Pad A cryptosystem developed by Mauborgne that is based on Vernam’s stream cipher: Properties: Let the plaintext, ciphertext and key consist of individual bits xi, yi, ki  {0,1}. Encryption: eki(xi) = xi  ki. Decryption: dki(yi) = yi  ki OTP is unconditionally secure if and only if the key ki. is used once! 18/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   One-Time Pad (OTP) Unconditionally secure cryptosystem: y0 = x 0  k0 y1 = x 1  k1 : Every equation is a linear equation with two unknowns  for every yi are xi = 0 and xi = 1 equiprobable! This is true iff k0, k1,... are independent, i.e., all ki have to be generated truly random  It can be shown that this systems can provably not be solved. Disadvantage: For almost all applications the OTP is impractical since the key must be as long as the message! (Imagine you 1 have to encrypt a 1GByte email attachment.) 19/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl  Content of this Chapter Intro to stream ciphers Random number generators (RNGs) One-Time Pad (OTP) Linear feedback shift registers (LFSRs) Trivium: a modern stream cipher 20/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Linear Feedback Shift Registers (LFSRs) Concatenated flip-flops (FF), i.e., a shift register together with a feedback path Feedback computes fresh input by XOR of certain state bits Degree m given by number of storage elements If pi = 1, the feedback connection is present (“closed switch), otherwise there is not feedback from this flip-flop (“open switch”) Output sequence repeats periodically Maximum output length: 2m-1 21/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Linear Feedback Shift Registers (LFSRs): Example with m=3 clk FF2 FF1 FF0=si 0 1 0 0 LFSR output described by recursive equation: 1 0 1 0 si 3  si 1  si mod 2 2 1 0 1 3 1 1 0 4 1 1 1 Maximum output length (of 23-1=7) achieved only for certain 5 0 1 1 feedback configurations,.e.g., the one shown here. 6 0 0 1 7 1 0 0 8 0 1 0 22/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Security of LFSRs LFSRs typically described by polynomials: P( x)  x m  pl 1 x m1 ...  p1 x  p0 Single LFSRs generate highly predictable output If 2m output bits of an LFSR of degree m are known, the feedback coefficients pi of the LFSR can be found by solving a system of linear equations* Because of this many stream ciphers use combinations of LFSRs *See Chapter 2 of Understanding Cryptography for further details. 23/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl  Content of this Chapter Intro to stream ciphers Random number generators (RNGs) One-Time Pad (OTP) Linear feedback shift registers (LFSRs) Trivium: a modern stream cipher 24/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   A Modern Stream Cipher - Trivium 1 Three nonlinear LFSRs (NLFSR) of length 93, 84, 111 XOR-Sum of all three NLFSR outputs generates key stream si Small in Hardware: Total register count: 288 782 Non-linearity: 3 AND-Gates 25/27 7 XOR-Gates (4 with three inputs) 155 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl   Lessons Learned Stream ciphers are less popular than block ciphers in most domains such as Internet security. There are exceptions, for instance, the popular stream cipher RC4. Stream ciphers sometimes require fewer resources, e.g., code size or chip area, for implementation than block ciphers, and they are attractive for use in constrained environments such as cell phones. The requirements for a cryptographically secure pseudorandom number generator are far more demanding than the requirements for pseudorandom number generators used in other applications such as testing or simulation The One-Time Pad is a provable secure symmetric cipher. However, it is highly impractical for most applications because the key length has to equal the message length. Single LFSRs make poor stream ciphers despite their good statistical properties. However, careful combinations of several LFSR can yield strong ciphers. 26/27 Chapter 2 of Understanding Cryptography by Christof Paar and Jan Pelzl