Elliptic Curve Cryptography Security Analysis and Applications

This assignment presents a discussion on the security of Elliptic Curve Cryptography (ECC), exploring its vulnerabilities, applications, and comparisons to RSA. The discussion covers the ongoing debate about backdoors in ECC's random number generators, its resilience against quantum attacks, and the impact of technology advancements on its security. It highlights the successful implementation of ECC in smart cards, blockchain, and IoT, emphasizing its resource efficiency and shorter key lengths. The discussions also address the potential risks of incorrect ECC implementations, the challenges of interoperability, and the algorithm's role in securing modern technologies. References to relevant research papers and articles provide supporting evidence for the arguments presented, offering a comprehensive overview of ECC's current status and future prospects.

Elliptic Curve Cryptography 1
Elliptic Curve Cryptography Security
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Elliptic Curve Cryptography 2
Elliptic Curve Cryptography Security
Week 5-1
Discussion 1
Thank you for your insightful post. It is in no doubt that there has been a prolonged
debate on whether elliptic curve cryptography algorithm has a backdoor to random number
generators. The algorithm, however, remains secure since the few vulnerabilities that have
appeared in the side-channel have been tactfully mitigated. Although quantum attacks loom over
ECC, they are yet to be available (Bauer, 2016). Additionally, it is a common vulnerability for all
cryptographic algorithms to have their keys broken. History has shown that ECC is both
theoretically secured and properly implemented. However, there are cases that require proper
security testing and implementation especially with the exponent growth of technology. The
major question is whether the algorithm will stand the test of time as hackers and technology get
more sophisticated. Will it stand out to secure IoT, blockchain, and other applications in the era
of quantum computing?
Discussion 2
Many applications, smart cards, blockchain and even smart cards have successfully
implemented ECC. The major influencing factors being minimal resource utilization, shorter
key-lengths, and its performance that rivals that of RSA and other cryptographic algorithms.
ECC is one of the algorithms that have highly complicated security solutions (Stolbikova, 2016).
While RSA is the first algorithm to use public ke generation, ECC has gained popularity over the
past few decades. To this end, it is the best known algorithm for solving ECDLP problem within
sub-exponential time. As an example, RSA algorithm needs 2048 bit-key size in order to achieve

Elliptic Curve Cryptography 3
a 112 bit security level while ECC only needs 224-255 bits (Mahto, et al., 2016). As NSA
ponders abandoning the ECC algorithm, we ponder whether it will be possible given the
popularity it is gaining, and what will happen of technologies already using it?
Discussion 3
The security of ECC algorithm is theoretically possible and practically impossible.
Incorrect implementations of the algorithm may lead to leakages of the private key when
incorrect results are calculated or when inputs do not end up on the selected curve. Failed
implementation of ECC can lead to serious vulnerabilities such as the ECDSA security disaster
and the Common Vulnerability and Exposure (The Central Scrutinizer, 2010). Such
vulnerabilities range from malformed signitures to server key exchange message problems and
can lead to unauthenticated SSL attack. This raises the concern whether organizations will still
risk by incorrectly implementing ECC?
Week 5-2
Discussion 1
ECC encryption algorithm has become a major alternative to common public key
cryptosystems since their inception in 1980s. Their utilization is very promising thanks to their
powerful resistance index-calculus attacks (Güneysu, et al., 2006). When compared to RSA,
ECC cryptosystems allow efficient implementation at the same security level by using smaller
operand bit sizes. Estimation of costs incurred to break security mechanisms in ECC revealed
that it can only be possible using dedicated hardware and would be fatally expensive or
otherwise infeasible (Güneysu, et al., 2006).

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Discussion 2
With the present day security challenges, comparisons between RSA and ECC
algorithms’ security frameworks has heightened, possibly due to their ability to adapt and
generate improved keys. Most arguably, RSA was designed before ECC and has traditionally
been used to secure web services. ECC was first proposed in 1980s and is overtaking RSA in
acceptability and usage thus creating need for a thorough comparison between the two. Many
researchers recommend ECC since it allows the creation of ‘extra security’, it is fast and
computationally feasible (Alam, et al., 2016). The question that stills remains unanswered is
given the complexity of this algorithm, is it still a calm contender for the open key framework?
Discussion 3
The present day technologies such as block chain and internet of things require intensive
security mechanisms. Such security frameworks must be matched against computational
requirements for each technology. I agree with you that ECC is theoretically advantageous over
RSA and one can easily believe that PKI based on ECC will become more reliable in the long
run, going by the fact that it is not resource intensive. My question, however, is what challenges
are related to interoperability and infrastructure requirements when switching from one
cryptosystem to another?

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References
Alam, M., Jahan, I., Rosario, L. J. & Israt, J., 2016. A Comparative Study of RSA and ECC and
Implementation of ECC on Embedded Systems. Algorithms, Volume 1, p. 2.
Bauer, C. P., 2016. Secret history: The story of cryptology. s.l.:Chapman and Hall/CRC.
Güneysu, T., Paar, C. & Jan, P., 2006. On the security of elliptic curve cryptosystems against
attacks with special-purpose hardware. Special-Purpose Hardware for Attacking Cryptographic
Systems–SHARCS, Volume 6, pp. 3-4.
Mahto, D., Danish, A. K. & Dilip, K. Y., 2016. Security analysis of elliptic curve cryptography
and RSA. s.l., s.n., pp. 419-422.
Stolbikova, V., 2016. Can Elliptic Curve Cryptography be Trusted? A Brief Analysis of the
Security of a Popular Cryptosystem. ICASA Journal, 3(1).
The Central Scrutinizer, 2010. Sony's PS3 Security is Epic Fail - Videos Within. [Online]
Available at: http://psx-scene.com/forums/content/sony-s-ps3-security-epic-fail-videos-within-
581/?s=68e141dc91333038e2223ee86e3c748f
[Accessed 2019].