Definition Let K be the key space for a set of encryption transformations A

Definition let k be the key space for a set of

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Definition Let K be the key space for a set of encryption transformations A sequence of symbols e 1 e 2 e 3 . . . e i ϵ K , is called a keystream Definition Let A be an alphabet of q symbols and let E e be a simple substitution cipher with block length 1 where e ϵ K . Let m 1 m 2 m 3 be a plaintext string and let e 1 e 2 e 3 be a keystream from K . A stream cipher takes the plaintext string and produces a ciphertext string c 1 c 2 c 3 where c i = E ei (m i ). If d i denotes the inverse of e i , then D di (c i ) = m i decrypts the ciphertext string. 95
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Cont. A stream cipher applies simple encryption transformations according to the keystream being used. keystream generator . The keystream is generated by an algorithm which generates the keystream from an initial seed value 96
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The Vernam cipher Definition The Vernam Cipher is a stream cipher defined on the alphabet A = {0, 1}. A binary message m 1 m 2 . . . m t is operated on by a binary key string k 1 k 2 . . . k t of the same length to produce a ciphertext string c 1 c 2 . . . c t where c i = m i Xor k i 1 i t: one-time system or a one-time pad If the key string is randomly chosen and never used again 97
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The key space Size of the key space It is the number of encryption/decryption key pairs that are available in the cipher system. A key is a compact way to specify the encryption transformation (from the set of all encryption transformations) to be used For example, a transposition cipher of block length t has t! encryption functions from which to select. 98
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Cont. Fact: A necessary, but usually not sufficient, condition for an encryption scheme to be secure is that the key space be large enough to prevent exhaustive search. For instance, the simple substitution cipher in slide 61 has a key space of size 26! = 4 x 10 26 The polyalphabetic substitution cipher of has a key space of size (26!) 3 = 7 x 10 79 . Exhaustive search of either key space is completely infeasible, yet both ciphers are relatively weak and provide little security. 99
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Digital signatures A cryptographic primitive which is fundamental in authentication, authorization, and nonrepudiation Purpose to provide a means for an entity to bind its identity to a piece of information. Process of signing transforming the message and some secret information held by the entity into a tag called a signature . 100
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A signing and verification function for a digital signature scheme. Setup M is the set of messages which can be signed. S is a set of elements called signatures , possibly binary strings of a fixed length. S A is a signing transformation for entity A from the message set M to the signature set S .
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