A Beautiful Mind

What did you learn from the movie – Beautiful Mind?

Reference:

Nash’s exposition developed von Neumann’s work, appearing Game Theory could clarify unpredictable just as straightforward aggressive conduct. It was not an exhaustive answer for every single amusement circumstance, yet it did establish the frameworks for the gigantic group of work on Game Theory which has been created since.

Nash is found in “A Beautiful Mind” Film as a capable manufacturer of the truth. He is attempting to lead an actual existence in an intricate situation that is brimming with conceptual images and implications that are inconspicuous to untrained eyes. Notwithstanding, the way that there is zero ability to see does not legitimize non-presence of the truth that Nash looked to appear. Nash’s battle and difficulties with schizophrenia gave halfway recuperation that constrained him to overlook prescriptions. In his words, the choice to overlook drugs lead to 25 years of in part cheated reasoning. Even though Nash accomplished a steady condition without medicine, schizophrenia side effects did not totally vanish, but instead diminished in force.

Question 2

How does Cryptography help with Privacy?

references

References

Bruce, S. (2015). Applied Cryptography: Protocols, Algorithms, and Source Code in C. New York: John Wiley & Sons.

Christof, P. J. (2009). Understanding Cryptography: A Textbook for Students and Practitioners. London: Springer Science & Business Media.

Jean, P. A. (2017). Serious Cryptography: A Practical Introduction to Modern Encryption. New York: No Starch Press.

Question 3

Father of Cryptography?

references

References:

“The Cryptographer”, Tobias Hill, Faber and Faber, 2003. Fiction. Insightful epic around the globe first Quadrillionaire who profited from code breaking.

Coe, Michael D. Breaking the Maya Code. London and New York: Thames and Hudson, 1992.

Szpiro, George G. The Secret Life of Numbers. Washington, DC: Joseph Henry Press, 2006

Question 4

Complexity of Ceasar Cipher?

Reference-

How difficult is it to break the Ceasar Cipher?

The Caesar cipher is one of the earliest known and simplest ciphers. It is a type of substitution cipher in which each letter in the plaintext is ‘shifted’ a certain number of places down the alphabet. For example, with a shift of 1, A would be replaced by B, B would become C, and so on. The Caesar cipher can be easily broken even in a cipher-text only scenario. Two situations can be considered:

an attacker knows (or guesses) that some sort of simple substitution cipher has been used, but not specifically that it is a Caesar scheme;

an attacker knows that a Caesar cipher is in use, but does not know the shift value

In the first case, the cipher can be broken using the same techniques as for a general simple substitution cipher, such as frequency analysis or pattern words.Frequency analysis is based on the fact that, in any given stretch of written language, certain letters and combinations of letters occur with varying frequencies.E, T, A and O are the most common, while Z, Q and X are the most rare occurring letters. Likewise, TH,ER, ON, and AN are the most common pairs of letters (termed bigrams or digraphs), and SS, EE, TT, and FF are the most common repeats.

In the second instance, breaking the scheme is even more straightforward. Since there are only a limited number of possible shifts (26 in English), they can each be tested in turn in a brute force attack. One way to do this is to write out a snippet of the cipher text in a table of all possible shifts – a technique sometimes known as “completing the plain component”.

references–

References

[1].          Wikipedia has a decent portrayal of the encryption/decoding procedure, history and cryptanalysis of this calculation

[2].          Simon Singh’s ‘The Code Book’ is a phenomenal prologue to figures and codes and incorporates an area on caesar figures.

[3].          Singh, Simon (2000). The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography. ISBN 0-385-49532-3.

Question 5

Birthday Attack?

reference

A Birthday attack is an example of a cryptographic attack which manipulates the mathematics in birthday problem embedded in the probability theory. It belongs to a group of brute force attacks. Its success mainly depends on the higher likelihood of the collisions found within random attempts of attack and a fixed degree of arrangements or permutations as is described in the birthday problem (Wagner, 2002). In probability theory, the paradox considers the probability that people in the same room are likely to share a birthday. For example, in a room consisting of 23 people or even more, the probability is greater than half that two will share a birthday. If you are in a room with 22 other people, the probability that you will share a birthday with others is 22/365. If you fail to match the birthdays, you will leave the room, and someone will have a 21/365 chance of sharing a birthday with the rest of the people in the room. If that person fails to match with others, he/she will also follow you out, and another one will have a chance of 20/365 of matching. This moves on and on, and the combination of all the probabilities gives a 50 percent chance of matching.

The birthday attack is used in creating hash collisions. Since matching birthdays is quite difficult, finding a particular input having a hash that collides with other inputs is also difficult. But also, like matching any birthday is simple, finding an input that creates a colliding hash with another input is simple due to the birthday attack (Bellare, & Kohno, 2004). A birthday attack is used to find collisions in hash functions when the output of the function is not conspicuously large. Therefore, the hash code length has to be substantial. However, the indicated birthday formula does not cater for having more people than items. For example, if you have 5 people picking 4 items (like colors), there is a guarantee of the items matching (Wagner, 2002).  For small numbers of people and items that are being matched, the calculation will still display a probability of less than 100 percent.

References

Bellare, M., & Kohno, T. (2004, May). Hash function balance and its impact on birthday attacks. In International Conference on the Theory and Applications of Cryptographic Techniques(pp. 401-418). Springer, Berlin, Heidelberg.

Wagner, D. (2002, August). A generalized birthday problem. In Annual International Cryptology Conference (pp. 288-304). Springer, Berlin, Heidelberg.