Crypto_1(M1卡破解).pdf

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Cryptography Part 1, Basics

Introduction • Cryptography is the art of designing mathematical methods for protecting information • A means of transmitting confidential information securely over open networks: encryption • Classical cryptographical algorithms have been known for hundreds of years • Innovations in the last two decades have created a whole new branch of cryptography: asymmetric (public key) cryptography – Digital signatures – Secure on-line key exchange 2

Symmetric Cryptography • Based on using a shared secret, a secret piece of information – Used to transform information to an encrypted form – Only those who know the secret are able to recover the content of encrypted data • Two facts determine the procedure: – Transformation method: the encryption (enciphering) algorithm – Shared piece of information: the secret key plaintext secret key Encryption ciphertext secret key Decryption original plaintext 3

Example: Caesar Cipher • Alice and Bob agree that they use Caesar Cipher to encrypt their communication, with the number 4 as their secret key – Alice encrypts the message M = YES ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZ – Alice sends Bob the encrypted message C = E(M) = UAO – Now that Bob knows the secret key 4, he can calculate the inverse transformation E-1 ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZ – Bob decrypts C (applies the inverse transformation) to recover the original message: E-1(C) = M = YES 4

Example: Analysis of Caesar Cipher Is it possible for an attacker to find out the content of the encrypted message? • • Kerkhoff’s Principle: we assume that the attacker knows the encryption algorithm used – The set of good encryption algorithms is small, the potential attacker can try all of them relatively easily • Assume that an attacker, Eve, gets to know C=UAP – Since Eve knows that the algorithm is Caesar Cipher, she may start ciphering C with different keys – Using the English alphabet, there are only 26 possible keys – In at most 26 trials, Eve breaks the cipher • The method of trying all possible keys is called brute force 5

One-Time Pad • Instead of using Caesar Cipher, with the constant shift of 4 for every letter, Alice and Bob may alternatively agree: – Left-shift the first letter by 11 positions, the second letter by 1 position and the third letter by 3 positions – This algorithm would produce, when applied to the word M = YES, C = E(M) = ODP – Here the secret key constitutes of the triplet (11,1,3) • Now the number of all possible keys is 26*26*26=17576 – This is still very small a key space to be exhaustively searched with today’s computing resources – However, trying every possible key would yield all English three letter words! 6

One-Time Pad (cont.) • This algorithm, called One-Time Pad, is perfectly secure against brute force attacks (and all other imaginable cryptographic attack methods) In computer-based cryptography, the set of letters is 0 and 1 • • For example, the bit-string K = 001101 could be used as a secret key for One-Time Pad to encrypt a 6-bit string M = 011001, C = E(M) = M xor K: M 011001 K 001101 C 010100 • One-Time Pad has two major limitations – The same key may be used only once (otherwise there is a statistical attack for breaking the cipher) – The length of the key is equal to the length of the message 7

Cryptanalysis • Cryptanalysis is the art of finding techniques for breaking cryptographical algorithms • Usually based on statistical methods – Counting frequencies of different patterns in ciphertext may reveal some redundancies in the original plaintext • Cryptographical attacks may be categorized as follows: – Ciphertext only attack means determining the secret key from the knowledge of a set of encrypted messages – Known plaintext attack means determining the secret key using the knowledge of a set of plaintext/ciphertext -pairs – In a chosen plaintext attack the attacker has gained knowledge of plaintext/ciphertext -pairs for chosen plaintexts 8

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