Introduction to Cryptography

Introduction to Cryptography(with focus on Stream Ciphers)

Made By –Akshay Gautam

14315002711Cse 1 VII Sem

Definition

• Cryptography is the study of mathematical techniques related to aspects of information security such as confidentiality, data integrity, entity authentication, and data origin authentication.

• Cryptography is not the only means of providing information security, but rather one set of techniques.

Cryptographic GoalsThe following four cryptographic goals form a framework upon which the others will be derived –

1. Confidentiality is a service used to keep the content of information from all but those authorized to have it.

2. Data integrity is a service which addresses the unauthorized alteration of data. To assure data integrity, one must have the ability to detect data manipulation by unauthorized parties.

3. Authentication is a service related to identification. This function applies to both entities and information itself.

4. Non-repudiation is a service which prevents an entity from denying previous commitments or actions.

Conventional Cyrptosystem

Cryptology, the study of cryptosystems, can be subdivided into two disciplines. Cryptography concerns itself with the design of cryptosystems, while cryptanalysis studies the breaking of cryptosystems. These two aspects are closely related; when setting up a cryptosystem the analysis of its security plays an important role.

The formal definition of a conventional cryptosystem as well as the mathematical foundation of the underlying theory is due to C.E. Shannon. The figure is attached in the next slide.

Basic Terminology• An entity or party is someone or something which sends, receives, or

manipulates information. Alice and Bob are entities. An entity may be a person, a computer terminal, etc.

• A sender is an entity in a two-party communication which is the legitimate transmitter of information. In Figure 1.1, the sender is Alice.

• A receiver is an entity in a two-party communication which is the intended recipient of information. In Figure 1.1, the receiver is Bob.

• An adversary is an entity in a two-party communication which is neither the sender nor receiver, and which tries to defeat the information security service being provided between the sender and receiver. Various other names are synonymous with adversary such as enemy, attacker, opponent, tapper, eavesdropper, intruder, and interloper.

Cryptographic Techniques

• Cryptographic techniques are typically divided into two generic types:

• Symmetric-key Encryption• Public-key Encryption

Symmetric Key Cryptography• Symmetric-key algorithms are a class of algorithms for

cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext. The keys may be identical or there may be a simple transformation to go between the two keys. The keys, in practice, represent a shared secret between two or more parties that can be used to maintain a private information link.

• One of the major issues with symmetric-key systems is to find an efficient method to agree upon and exchange keys securely. This problem is referred to as the key distribution problem. It is assumed that all parties know the set of encryption/decryption transformations (i.e they all know the encryption scheme).

Types of Symmetric Key Cryptography

There are two classes of symmetric-key encryption schemes which are commonly distinguished: Block ciphers and Stream ciphers.

Block CipherA block cipher is an encryption scheme which breaks up the plaintext messages to be transmitted into strings (called blocks) of fixed length ß over an alphabet A, and encrypts one block at a time. Stream Cipher Stream ciphers form an important class of symmetric-key encryption schemes. They are, in one sense, very simple block ciphers having block length equal to one. What makes them useful is the fact that the encryption transformation can change for each symbol of plaintext being encrypted.

Public Key Cryptography• Public-key cryptography, also known as asymmetric

cryptography, is a class of cryptographic algorithms which requires two separate keys, one of which is secret (or private) and one of which is public. Although different, the two parts of this key pair are mathematically linked.

• The public key is used to encrypt plaintext or to verify a digital signature; whereas the private key is used to decrypt ciphertext or to create a digital signature.

• The term "asymmetric" stems from the use of different keys to perform these opposite functions, each the inverse of the other – as contrasted with conventional ("symmetric") cryptography which relies on the same key to perform both.

Symmetric-key vs. Public-key cryptography

Advantages of symmetric-key cryptography

1. Symmetric-key ciphers can be designed to have high rates of data throughput. Some hardware implementations achieve encrypt rates of hundreds of megabytes per second, while software implementations may attain throughput rates in the megabytes per second range. 2. Keys for symmetric-key ciphers are relatively short. 3. Symmetric-key ciphers can be employed as primitives to construct various cryptographic mechanisms including pseudorandom number generators hash functions and computationally efficient digital signature schemes to name just a few. 4. Symmetric-key ciphers can be composed to produce stronger ciphers. Simple transformations which are easy to analyze, but on their own weak, can be used to construct strong product ciphers.

Advantages of public-key cryptography

1. Only the private key must be kept secret (authenticity of public keys must, however, be guaranteed). 2. The administration of keys on a network requires the presence of only a functionally trusted TTP as opposed to an unconditionally trusted TTP. Depending on the mode of usage, the TTP might only be required in an “off-line” manner, as opposed to in real time. 3. Depending on the mode of usage, a private key/public key pair may remain unchanged for considerable periods of time, e.g., many sessions (even several years).4. Many public-key schemes yield relatively efficient digital signature mechanisms. The key used to describe the public verification function is typically much smaller than for the symmetric-key counterpart.

Stream Cipher

We consider 3 real stream ciphers• ORYX — weak cipher, uses shift registers,

generates 1 byte/step• RC4 — strong cipher, widely used but used

poorly in WEP, generates 1 byte/step• PKZIP — intermediate strength, unusual

mathematical design, generates 1 byte/step

Pseudo Random Generators• A pseudorandom generator (PRG) for a class of statistical tests is a

deterministic procedure that maps a random seed to a longer pseudorandom string such that no statistical test in the class can distinguish between the output of the generator and the uniform distribution. The random seed is typically a short binary string drawn from the uniform distribution.

• Pseudorandom generators have numerous applications in cryptography. For instance, pseudorandom generators provide an efficient analog of one-time pads. It is well known that in order to encrypt a message m in a way that the cipher text provides no information on the plaintext, the key k used must be random over strings of length |m|. Perfectly secure encryption is very costly in terms of key length. Key length can be significantly reduced using a pseudorandom generator if perfect security is replaced by semantic security. Common constructions of stream ciphers are based on pseudorandom generators.

Linear Feedback Shift Register• In computing, a linear-feedback shift register (LFSR) is a shift register

whose input bit is a linear function of its previous state. The most commonly used linear function of single bits is exclusive-or (XOR). Thus, an LFSR is most often a shift register whose input bit is driven by the XOR of some bits of the overall shift register value.

• Applications of LFSRs include generating pseudo-random numbers, pseudo-noise sequences, fast digital counters, and whitening sequences.

• LFSRs have long been used as pseudo-random number generators for use in stream ciphers (especially in military cryptography), due to the ease of construction from simple electromechanical or electronic circuits, long periods, and very uniformly distributed output streams. However, an LFSR is a linear system, leading to fairly easy cryptanalysis.

A 4-bit Fibonacci LFSR with its state diagram. The XOR gate provides feedback to the register that shifts bits from left to right. The maximal sequence consists of every possible state except the "0000" state.

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