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Random Numbers in Cryptography Presentation Transcript

Slide 1 - Random Numbers in Cryptography Part 1  Cryptography 1
Slide 2 - Random Numbers Random numbers used to generate keys Symmetric keys RSA: Prime numbers Diffie Hellman: secret values Random numbers used for nonces Sometimes a sequence is OK But sometimes nonces must be random Random numbers also used in simulations, statistics, etc., where numbers only need to be “statistically” random Part 1  Cryptography 2
Slide 3 - Random Numbers Cryptographic random numbers must be statistically random and unpredictable Suppose server generates symmetric keys Alice: KA Bob: KB Charlie: KC Dave: KD Spse Alice, Bob and Charlie don’t like Dave Alice, Bob and Charlie working together must not be able to determine KD Part 1  Cryptography 3
Slide 4 - Bad Random Number Example Random numbers used to shuffle the deck Program did not produce a random shuffle Could determine the shuffle in real time! Part 1  Cryptography 4 Online version of Texas Hold ‘em Poker ASF Software, Inc.
Slide 5 - Card Shuffle There are 52! > 2225 possible shuffles The poker program used “random” 32-bit integer to determine the shuffle Only 232 distinct shuffles could occur Used Pascal pseudo-random number generator (PRNG): Randomize() Seed value for PRNG was function of number of milliseconds since midnight Less than 227 milliseconds in a day Therefore, less than 227 possible shuffles Part 1  Cryptography 5
Slide 6 - Card Shuffle Seed based on milliseconds since midnight PRNG re-seeded with each shuffle By synchronizing clock with server, number of shuffles that need to be tested < 218 Could try all 218 in real time Test each possible shuffle against “up” cards Attacker knows every card after the first of five rounds of betting! Part 1  Cryptography 6
Slide 7 - Poker Example Poker program is an extreme example But common PRNGs are predictable Only a question of how many outputs must be observed before determining the sequence Crypto random sequence is not predictable For example, keystream from RC4 cipher But “seed” (or key) selection is still an issue! How to generate initial random values? Applies to both keys and seeds Part 1  Cryptography 7
Slide 8 - Randomness True randomness is hard to define Entropy is a measure of randomness Good sources of “true” randomness Radioactive decay --- though radioactive computers are not too popular Hardware devices --- many good ones on the market Lava lamp --- relies on chaotic behavior Part 1  Cryptography 8
Slide 9 - Randomness Sources of randomness via software Software is (hopefully) deterministic So must rely on external “random” events Mouse movements, keyboard dynamics, network activity, etc., etc. Can get quality random bits via software But quantity of such bits is very limited Bottom line: “The use of pseudo-random processes to generate secret quantities can result in pseudo-security” Part 1  Cryptography 9
Slide 10 - Information Hiding Part 1  Cryptography 10
Slide 11 - Information Hiding Digital Watermarks Example: Add “invisible” identifier to data Defense against music or software piracy Steganography Secret communication channel A kind of covert channel Example: Hide data in image or music file Part 1  Cryptography 11
Slide 12 - Watermark Add a “mark” to data Several types of watermarks Invisible --- Not obvious the mark exists Visible --- Such as TOP SECRET Robust --- Readable even if attacked Fragile --- Mark destroyed if attacked Part 1  Cryptography 12
Slide 13 - Watermark Add robust invisible mark to digital music If pirated music appears on Internet, can trace it back to original source Add fragile invisible mark to audio file If watermark is unreadable, recipient knows that audio has been tampered (integrity) Combinations of several types are sometimes used E.g., visible plus robust invisible watermarks Part 1  Cryptography 13
Slide 14 - Watermark Example (1) US currency includes watermark Part 1  Cryptography 14 Image embedded in paper on rhs Hold bill to light to see embedded info
Slide 15 - Watermark Example (2) Add invisible watermark to photo print It is claimed that 1 square inch can contain enough info to reconstruct entire photo If photo is damaged, watermark can be read from an undamaged section and entire photo can be reconstructed! Part 1  Cryptography 15
Slide 16 - Steganography According to Herodotus (Greece 440BC) Shaved slave’s head Wrote message on head Let hair grow back Send slave to deliver message Shave slave’s head to expose message (warning of Persian invasion) Historically, steganography has been used more than cryptography! Part 1  Cryptography 16
Slide 17 - Images and Steganography Images use 24 bits for color: RGB 8 bits for red, 8 for green, 8 for blue For example 0x7E 0x52 0x90 is this color 0xFE 0x52 0x90 is this color While 0xAB 0x33 0xF0 is this color 0xAB 0x33 0xF1 is this color Low-order bits are unimportant! Part 1  Cryptography 17
Slide 18 - Images and Stego Given an uncompressed image file For example, BMP format Then we can insert any information into low-order RGB bits Since low-order RGB bits don’t matter, result will be “invisible” to human eye But a computer program can “see” the bits Part 1  Cryptography 18
Slide 19 - Stego Example 1 Left side: plain Alice image Right side: Alice with entire Alice in Wonderland (pdf) “hidden” in image Part 1  Cryptography 19
Slide 20 - Non-Stego Example View source Part 1  Cryptography 20 Walrus.html in web browser
Slide 21 - Stego Example 2 View source Part 1  Cryptography 21 stegoWalrus.html in web browser “Hidden” message: 110 010 110 011 000 101
Slide 22 - Steganography Some formats (jpg, gif, wav, etc.) are more difficult (than html) for humans to read Easy to hide information in unimportant bits Easy to destroy or remove info stored in unimportant bits! To be robust, information must be stored in important bits But stored information must not damage data! Collusion attacks also a major concern Robust steganography is trickier than it seems Part 1  Cryptography 22
Slide 23 - Information Hiding The Bottom Line Surprisingly difficult to hide digital information: “obvious” approach not robust Stirmark makes most watermarks in jpg images unreadable --- without damaging the image Watermarking is very active research area If information hiding is suspected Attacker can probably make information/watermark unreadable Attacker may be able to read the information, given the original document (image, audio, etc.) Part 1  Cryptography 23