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Cryptology Making & Breaking Codes & Ciphers

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AJ 1152 Cryptology Cryptography –Science of creating codes or ciphers Cryptanalysis –Science of breaking codes and ciphers

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AJ 1153 Codes vs. Ciphers Code –Substitution of words or phrases by others –Example: Navajo “code talkers” of WW II: turtle means tank sea turtle means landing craft Cipher –Algorithmic scrambling/unscrambling –Example: Caesar cipher Replace each letter with the letter 3 positions after it in the alphabet (a d, b e, etc.)

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AJ 1154 Terminology Plaintext –The unencrypted (readable) message Ciphertext –The encrypted version of the message Secure channel –A communications path safe from eavesdropping Insecure channel –A communications path that may be tapped

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AJ 1155 Stream & Block Ciphers Stream cipher acts on one character at a time –Replaces each character with a different symbol –Fixed: Each plaintext ‘a’ is always replace by the same ciphertext symbol Example: Caesar cipher (‘a’ always replaced by ‘d’) Example: rot13 (used to encode “obscene” text) –Variable: Different occurrences of ‘a’ in the plaintext are replaced with different symbols in the ciphertext Example: German Enigma cipher machine of WWII

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AJ 1156 Jefferson’s Cipher Machine A stack of code wheels threaded on a central axis –Could be any length, but typically ~30 –Each had all letters of the alphabet, but no two were identical To encrypt a message –Divide message into blocks = stack size –Turn wheels so plaintext shows on one row –Lock the wheels –Transmit any other row

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AJ 1157 Jefferson’s Cipher Machine To decrypt a message –Set wheels to match the ciphertext for each block –Lock the wheels –Look for the one row that contains readable plaintext Jefferson’s machine was used, successfully, for almost a century

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AJ 1158 Zimmermann Telegram

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AJ 1159 Enigma & Ultra Used by Germany during WW II –Considered it “unbreakable” Broken in 1940 by Britain (“Ultra”) –Team at Bletchley Park, headed by Alan M. Turing

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AJ 11510 How Enigma Worked Operator typed plaintext message 3 rotors scrambled each letter Ciphertext character lit up on upper panel Rotors turned after every letter

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AJ 11511 How Enigma was Solved Lots of similar messages –Germans sent weather information to U-boats every day, all in same format Human error –Lazy or tired operators re-used rotor settings instead of changing them –Repeated first 3 characters of message Weakness of algorithm –Would never translate a letter to itself

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AJ 11512 How Enigma was Solved The “Bombe” –Computer at Bletchley Park –Searched thousands of possible Enigma settings, looking for one that yielded readable plaintext Captured code books –Naval vessels carried books of Enigma settings –British captured U-559 in Sept. 1942 By 1943, Britain could read intercepted Enigma messages before the Germans could!

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AJ 11513 Exchanging Keys Prior to 1976, all ciphers were “symmetric” –Used the same key to encrypt and decrypt Problem with all old encryption schemes is the key exchange –Recipient must have the same key as the sender –How do you transmit a secret key over an insecure channel?

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AJ 11514 Public-Key Cryptography New Directions in Cryptography –Whitfield Diffie & Martin Hellman, 1976 Proposed using two keys –One to encrypt messages (the public key) –A different key to decrypt (the private key) –Also known as asymmetric cryptography Two keys are related, but one cannot be derived from the other –Public key can be published

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AJ 11515 The RSA System Select two prime numbers, p and q –Ex: choose p = 11, q = 3 Compute n = pq, f = (p-1)(q-1) –Ex: n = 11 3 = 33, f = 10 2 = 20 Choose e, the encryption key, less than n, so that e and f have no common factors –Ex: choose e = 3

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AJ 11516 The RSA System Find d (the decryption key) –Need ( e d / f ) to leave a remainder of 1 –Ex: 3 d / 20 leaves remainder 1 if d = 7 Key pair is (n,e) and (n,d) –Encryption (public) key is (33, 3) –Decryption (private) key is (33, 7)

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AJ 11517 The RSA System Encrypting a message –ciphertext = (plaintext) e mod n –Ex: plaintext = 13 ciphertext = 13 3 mod 33 = 2197 mod 33 = 19 Decrypting the message –plaintext = (ciphertext) d mod n plaintext = 19 7 mod 33 = 893871739 mod 33 = 13

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AJ 11518 Why is RSA Secure? Real versions use very large numbers –Modulus, n, is at least 1024 bits long About 340 decimal digits So p and q are each about 200 digits long Numbers are easy to multiply, but hard to factor –It’s easy to compute n if you know both p and q –It’s almost impossible to factor n into p & q

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AJ 11519 Just How Secure Is It? No cipher is 100% unbreakable –Except “one-time pads,” but they have other problems By making the modulus larger, RSA can be made arbitrarily hard to break –With a 2048-bit modulus, all the computing power in the world would take over 70 years to break one cipher

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AJ 11520 What are the Problems? Asymmetric encryption is S-L-O-W –Can take even powerful computers 1-2 seconds to encrypt or decrypt a message Can be fooled by someone posing as someone else –If Eve claims to be Bob and publishes “Bob’s” public key, any messages encrypted with it will be readable by Eve, not Bob

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AJ 11521 Speeding Things Up DES (Data Encryption Standard) –Proposed in 1974 by NSA, IBM –Symmetric cipher –Algorithm can be implemented in hardware Key very short –56 bits long (40-bit key and 16-bit header) –Could be broken “by force” with enough computing power (which NSA has)

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AJ 11522 DES and 3DES Shortness of key used by DES considered a weakness Newer version is “triple-DES” or 3DES –136 bits long (120-bit key + 16-bit header) AES (Advanced Encryption Standard) –Uses 128-bit key DES, 3DES, and AES are all symmetric

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AJ 11523 SSL Secure Sockets Layer (SSL) –Invented by Netscape in 1995 Uses RSA to exchange a “session key” –DES, 3DES, or AES key used for that browser session only Gets both speed and security –RSA only used to exchange session key –Session key expires when user logs out

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AJ 11524 Digital Certificates Overcome “spoofing” attack –Perform same function as notary public Purchase from Certificate Authorities (CAs) –VeriSign, Thawte, Comodo, GeoTrust, … Contain my public key “Signed” by the root certificate –Located in your browser

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AJ 11525 Digital Signatures Asymmetric cryptography can be used to digitally “sign” documents –Achieves all purposes of conventional signature (but better): Cannot be forged Cannot be stolen and re-used Cannot be repudiated Assume Alice wants to sign a document and send it to Bob. Here goes …

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AJ 11526 Digital Signatures 1.Alice computes the MD5 (or SHA-1) digest value for the document 2.She encrypts the (document+digest) combination using her own private key 3.She then encrypts the previous message using Bob’s public key and sends Bob the result.

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AJ 11527 Digital Signatures 1.Bob decrypts the message from Alice using his own private key. 2.He then decrypts the resulting message using Alice’s public key. 3.He isolates the digest value and compares it with the value he computes for the rest of the message. 4.If everything matches, he knows that Alice signed this document.

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AJ 11528 Digital Signatures Can Alice later repudiate her signature? –No, because only she has her private key Can Bob or Eve forge Alice’s signature? –No, for the same reason Can Eve steal Alice’s signature and use it to “sign” a different document? –No, because then the digest values wouldn’t match

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AJ 11529 State of the Art Public-key cryptography allows people to communicate securely even if they have never met –Necessary for electronic commerce Ciphers cannot be made 100% secure, but they can be made arbitrarily secure –Use longer keys Both good guys and bad guys can use this technology –Cryptanalysis is essentially obsolete

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