Cryptography Midterm 1
What cryptanalytic attacks do we have? Why do we care about them?
(pi is the plaintexts leaked and ci is the corresponding cipher texts) Known Plaintext - Eve does not have the choice over pi or ci (somebody else picks pi). Alice and Eve observe the same event but eve eavesdrops to get cipher text ci. Eve knows that Alice will reports the event to Bob and can thus for ci, can guess pi Chosen-plaintext attack - pi are chosen by Eve and she also has the corresponding ci. Example, Even can make an event (like leaking information on purpose) and then eavesdrop to get ci. When Alice reports this event to bob, Eve can guess pi and thus has the (pi, ci) pair. Unlike known-plaintext, eve picks pi Chosen-ciphertext attack - ci are chosen by Eve and somehow she gets pi. Eve chooses all ci before she sees any pi. Ex, Eve picks ci and then persuades Bob to decrypt ci for her Adaptive chosen-cipher text attack - Before eve chooses ci, she can see {(p1, c1,), ... (pi-1, ci-1)}. Because of this, eve can pick ci, in a smarter way
AES
- was developed because of triple-DES was slow for modern information systems - secure against all known attacks - fast, even in software implementation -byte-oriented and thus is also suitable for implementations on smart cards that have small register size -small code size ( in C the AES implementation is about 350 lines of code_ -Simple by design and very elegant in implementation -Iterated block cipher with many rounds. Consists of 3 parts - ( key scheduling algorithm to generate multiple round keys from a cipher key, encryption alogorithm, and a decryption algorithm) -each AES encryption operation processes 128 plaintext bits (that is, 16 bytes) AES-128 key scheduling algorithm generates 11 128 bit sound keys from 128-bit cipher key. 16 byte round key RKi is arranged, in a column-wise way, into a 4x4 table similar to the AES state. Each column is also called a word and a round key has four words. AES 256 is stronger than AES 128 since it uses more rounds but it slower and widley seen as not needed in many situations
What difficulties does symmetric encryption such as AES-256 have?
-Not scalable have to meet in person to a share a key -takes longer
What is general use crypto system (I think this is just asking what a crypto system is)?
-crypto system has 5 parts Plaintext space - M CipherText space - C Key Space - K Encryption Algorithm - D
How does OTP (One Time Pad) work? How Secure is it? Is it useful for commercial applications?
-unbreakable encryption PlainText: binary stream Key: Random Same length as plaintext Requires use of a single-use pre-shared key that is no smaller than the message being sent Practical in situations where two parties in a secure environment must be able to depart from one another and communicate from two separate secure environments with perfect secrecy It is not useful for commercial applications because it requires meeting with the other side directly or using a trusted courier ( key transfer difficulty ) Leaks since you know the length of the plaintext and the length of the key based on the bit-wise exclusive-or operation plaintext xor with cipher text for encryption
How to use AES-256 to encrypt many blocks of plaintext?
Can Use CBC plaintext block is xored with an IV or the cipher text from the previous round. This value is then encrypted with the key
How does AES-128 work?
High Level view of AES-128 Round Key Generation AES is block encryption -Each transformation receives an AES state and transforms it to a new AES state, which is then fed to the next transformation. Bytes in the AES state after the last transformation are the 128-bit cipher text. -Clustered into 10 rounds, which are numbered as 1 to 10. Each round except for the last one has four transformations and the 10th round has 3 transformations only -Four transformations common to all except the last are SubBytes, ShiftRows, MixColums, and AddRoundKey SubBytes converts each byte of the AES state into a new byte value from a look up 16 x 16 S-box table. ShiftRows - first row - no shift Second row - is circularly left shifted one bye Third row - is circularly left shifted 2 bytes fourth row - is circularly left shifted 3 bytes MixColums - shuffles bits within a column of the AES state (this also changes the value within a column) d0 = (a0 * b0 xor a3 *b1 xor a2 * b2 xor a1 * b3) d1 = (a1 * b0 xor a0 * b1 xor a3 * b2 xor a2 * b3) d2 = (a2 *b0 xor a1 * b1 xor a0 * b2 xor a3 * b3) d3 = (a3 * b0 xor a2 * b1 xor a1 * b2 xor a0 * b3) AddRoundKey 16 byte round key is arranged into a 4x4 table and is then bit-wise exclusive-red with the AES state. ( AES-128 key scheduling algorithm generates 11 128bit round keys from a 128 bit cipher key) Decryption is just the opposite and in reverse order Steps for Encryption 128 bits of data are broken into 4 byte words and then put into a 4x4 grid called an AES state for rounds 1 - 10 Subytes Shift rows mixcolums addRound Key for last round SubBytes Shift Rows AddRoundkey
What difficulties does NTRU encryption have? How to improve?
N-th degree Truncated Polynomial Ring - resistant to quantum computing -uses asymmetric cyrtophrapihc primitives based on lattices -
How to improve?
RSA
What is restricted use crypto system?
Security rests upon the secrecy of the nature of the algorithms and the encryption method (approach is called security through obscurity) -not good since can be reverse engineered -to have robust data confidentiality we should not depend on the secrecy of the algorithm,
How does Playfair work?
The key square is a 5×5 grid of alphabets that acts as the key for encrypting the plaintext. Each of the 25 alphabets must be unique and one letter of the alphabet (usually J) is omitted from the table (as the table can hold only 25 alphabets). If the plaintext contains J, then it is replaced by I. (If Letter is repeated in the keyword then next occurrence is omitted) Keyword: PALMERSTON Grid: P A L M E R S T O N B C D F G H I K Q U V W X Y Z Encrypt Letters in Pairs, if two letters are the same insert x; Single letter at the end then Append z Same Row - replace with succeeding right letter in same row Same Column - replace with with succeeding down letter in the column Else- replace letters with opposite letters of a formed rectangle Plaintext: Hello John HELXLO JOHN Ciphertext: UPTLMT QSUR Keys = 25!
How does substitution cipher work?
a method of encrypting in which units of plaintext are replaced with the ciphertext, in a defined manner, with the help of a key; the "units" may be single letters (the most common), pairs of letters, triplets of letters, mixtures of the above, and so forth -ex vigenere cipher Suspect-able to frequency attacks (cipher text-only attack)
What is a cryptographic key?
a string of bits used by a cryptographic algorithm to transform plain text into cipher text or vice versa
How to achieve practical confidentiality with block ciphers? What are confusion and diffusion
confusion - refers to making the relationship between the key and the ciphertext as complex and involved as possible diffusion - the plaintext should be redistributed into the non-uniformity in the distribution of much larger structures of the ciphertext, which is much harder to detect.
How does a stream cipher (key stream) work?
encrypts a digital data stream one bit or one byte at a time and the encryption transformation varies over time -ex One time pad
polynomial mod q
f(x) = 6x^5 + 4x^3 + x^2 + 1 g(x) = 5x^4 + 5x^3 + 6x^2 + 6 (f(x) + g(x)) mod 7 add coefficients 6x^5 + 5x^4 + 9x^3 + 7x^2 + 7 then mod by q
How does Vigenere work?
is a method of encrypting alphabetic text by using a series of interwoven Caesar ciphers, based on the letters of a keyword. It employs a form of polyalphabetic substitution. Key Word "ELVIS" ABCDEFGHIJKLMNOPQRSTUVWXYZ EFGHIJKLMNOPQRSTUVWXYZABCD LMNOPQRSTUVWXYZABCDEFGHIJK VWXYZABCDEFGHIJKLMNOPQRSTU IJKLMNOPQRSTUVWXYZABCDEFGH STUVWXYZABCDEFGHIJKLMNOPQR Plain Text -THANK YOU, THANK YOU VERY MUCH -ELVIS ELV ISELV ISE LVIS ELVI Char T go to E row and find corresponding Char in the T Column Cipher Text -XSVVC CZP, BZEYF GGY GZZQ QFXP
How does transposition cipher work?
is a method of encryption by which the positions held by units of plaintext (which are commonly characters or groups of characters) are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext
How does a block cipher work?
plaintext is first partitioned into fixed-size blocks; a block of plaintext is treated as a whole and is encrypted into a cipher text block of equal length -does not vary over time
What does the Kerckhoffs principle say? Why is it important?
the security of a cryptosystem must lie in the choice of its keys only; everything else (including the algorithm itself) should be considered public knowledge - everything except for the keys should be publicly known (ex private keys aren't known but the encryption algorithm is)
How does symmetric key encryption work?
type of encryption that uses the same key to encrypt and decrypt data. Both the sender and the recipient have identical copies of the key, which they keep secret and don't share with anyone - Alice and Bob both share a cryptographic key called a "symmetric key" that must be securely distributed and should be unknown to eve