Cryptography has raised many human rights issues, ethical issues and also legal issues due to the fact that it can be used for good purposes but also for bad ones. You can read more about this on this post: Cryptography is Everywhere.

Note that there a lot of research being undertaken out there about post-quantum computing and its use for code-breaking. By using
post-quantum computing will be highly likely possible to break any modern
cypher, but there is no proof of that yet; In fact, I think this does not mean the end of security, on the contrary, the best is yet to come!

With respect to classical algorithms, some can be done by hand allowing to get a a better understanding of what is involved, such as shift cipher, substitution cipher, Vigenère cipher and permutation cipher. Most of them are outdated, however, many ideas are still used as components of modern ciphers and also many of methods of breaking these ciphers are valid for modern ciphers as well, for instance, exhaustive key search, letter frequency and other statistical properties of the text, and known/guessed plaintext.

It is widely agreed that cryptographic
algorithms are basically classified into two big categories depending on the number
of keys that are used for encryption and decryption, that is, symmetric cryptography
and public-key (asymmetric) cryptography. The first one uses only one secret
key for encryption and decryption, whereas the latter uses two keys, a public
key for encryption and a private key for decryption. This aspect is
particularly important when it comes to working on breaking cryptographic
algorithms because it is assumed some things in terms of what is available to
the attacker such as the algorithm in use and whether the key is the same or
not.

Similarly, symmetric cryptography
can be classified into two parts: block ciphers and stream ciphers. They mostly
recommend using the block cipher AES, and explains the uses of stream cipher in
different applications. For example, RC4 for WEP, WAP, SSL, TLS1.2, A5 for GSM
mobile phones SNOW and ZUC for 4G LTE, ChaCha20 for TLS1.3. Some big names in
cryptography such as Golbreich and Stallings clearly mention in their books the
importance of having a good understanding of the different operation modes of
symmetric cryptography such as ECB, CBC, OFB, CFB, CTR, and GCM.

Block ciphers and stream ciphers
have to face multiple types of attacks such as differential attacks and
algebraic attacks, respectively. Also, several works have been done to prevent
differential, the cube and the AIDA attacks, many other types of attacks, the vast majority of which are painstakingly detailed in Antoine Joux’s book “Algorithm
Cryptanalysis”.

Stream ciphers have strongly
relationship with certain concepts such as one-time pad, perfect secrecy,
pseudo-random numbers generators, linear feedback, theory about shift registers
(LFSR), NLFSR, shrinking generator, T-function, and IV. There is a special book
that presents these aspects in a very detailed manner such as Stallings’ book in
which he goes much deeper

Besides, hash functions and message
authentication codes (MAC) are also crucial in cryptography. They are used in
tandem with symmetric and public-key cryptography to achieve confidentiality,
authentication, integrity, non-repudiation. In fact, Douglas Stinson in his
book “*Cryptography: Theory and
Practice*” explains
clearly and concisely about hash functions and MAC, giving theorems and
algorithms along with other related-mathematical applications.

Talking of public-key cryptography, algorithms
in this area are classified depending on the number theory they use. For
instance, RSA uses integer factorization whereas Diffie Hellman (DH) uses
discrete logarithm and Elliptic Curve (ECC) is based on elliptic curves over
finite fields. Actually, Antoine Joux explains RSA, DH and ECC from the
mathematical and algorithmic cryptanalysis perspective

With regard to cryptanalysis, it is all about understanding cryptographic algorithms and finding solutions to break them. In this area, the most famous techniques to attack all the types of ciphers go from the very classical approach to the most sophisticated and modern techniques which make use of algebraic cryptanalysis and mostly based on Polynomial Systems (especially Multivariate Quadratic), Algebraic coding and optimisation.

Essentially, algebraic attack is
based on the main idea of finding and solving a system of multivariate
polynomial equations over a finite field, for example, some algebraic attacks
have been successfully carried out against various stream ciphers based on
LFSRs. In addition, Gregory V. Bard in his book “*Algebraic Cryptanalysis*”, details all the mathematical aspects behind
it, particularly topics such as Gröbner bases algorithms, linearization, the XL
algorithm, complexity calculation, converting ANF to CNF, NP-Complete problem,
MQ Problem, linear algebra over GF(2), Boolean matrices, and GF(2)-Matrix
Operations.

It's all for now. I do hope to have cleared some things up. If you have any questions please do let me know in the comment section below. Have a good day!

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