PPT-Cryptography Lecture 8 Pseudorandom functions

Keyed functions Let F 01 x 01 01 be an efficient deterministic algorithm Define F k x Fk x The first input is called the key A ssume F is length preserving. uoagr Abstract Pseudorandom sequences have many applications in cryp tography and spread spectrum communications In this dissertation on one hand we develop tools for assessing the randomness of a sequence and on the other hand we propose new constru 3b. . Pseudorandomness. .. B. ased on: Jonathan . Katz and Yehuda . Lindell. . Introduction . to . Modern Cryptography. 2. Pseudorandomness. An introduction. A distribution . D. is pseudorandom if no PPT . Vadim . Lyubashevsky. Cryptography. Allows for secure communication in the presence of malicious parties. 2. Cryptography. Allows for secure communication in the presence of malicious parties. 3. Cryptography. Vadim . Lyubashevsky. Cryptography. Allows for secure communication in the presence of malicious parties. 2. Cryptography. Allows for secure communication in the presence of malicious parties. 3. Cryptography. Ali. Neslisah Torosdagli . Josiah . Wong . Introduction. Cryptography. : . the field of study that is related to encoded information. The name comes from combining two Greek words that mean “hidden word”. . Based on: William . Stallings, Cryptography and Network Security . . Chapter 7. Pseudorandom Number Generators . and Stream Ciphers. Random Numbers. A number of cryptographic protocols make use of random binary numbers:. Hash functions. (Cryptographic) hash function: deterministic function mapping arbitrary length inputs to a short, fixed-length output (sometimes called a . digest. ). Hash functions can be . keyed. or . Cryptography Lecture 6 Pseudorandom generators (PRGs) Let G be an efficient, deterministic algorithm that expands a short seed into a longer output Specifically, let |G(x)| = p(|x|) G is a PRG if: when the distribution of x is uniform, the distribution of G(x) is “indistinguishable from uniform” Cryptography Lecture 8 Pseudorandom functions Keyed functions Let F: {0,1} * x {0,1} *  {0,1} * be an efficient, deterministic algorithm Define F k (x) = F(k, x) The first input is called the Cryptography Lecture 7 Pseudorandom functions Keyed functions Let F: {0,1} * x {0,1} *  {0,1} * be an efficient, deterministic algorithm Define F k (x) = F(k, x) The first input is called the Cryptography Lecture 6 Clicker quiz Let G(x) = x || parity(x). Which of the following proves that G is not a pseudorandom generator? G is not expanding Consider the following distinguisher D: D(y) outputs 1 k. c. m. c. . . . Enc. k. (m). k. m. 1. c. 1. . . . Enc. k. (m. 1. ). m. 2. c. 2. . . . Enc. k. (m. 2. ). c. 1. c. 2. Is the threat model too strong?. In practice, there are many ways an attacker can . Which of the following encryption schemes is CPA-secure (G is a PRG, F is a PRF)?. Enc. k. (m) chooses uniform r; outputs <r, G(r) .  . m>. Enc. k. (m) chooses uniform r; outputs <r, . F. . (PRGs). Let G be an efficient, deterministic algorithm . that expands a . short . seed. . into a . longer . output. Specifically, let |G(x)| = p(|x|). G is a PRG if: when the distribution of x is uniform, the distribution of G(x) is “indistinguishable from uniform”.