Nasdaq and Citi Announce Pioneering Blockchain and Global Banking Integration

Sharing information on the Blockchain project where I was the Technology Lead from Citi side.
It was a ground breaking project and first production implementation of Blockchain technology by a major global bank and exchange.

For Immediate Release
Citigroup Inc. (NYSE: C)
May 22, 2017

Nasdaq and Citi Announce Pioneering Blockchain and Global Banking Integration

HIGHLIGHTS

Solution leverages Chain’s blockchain technology

New York – Nasdaq, Inc. (Nasdaq:NDAQ) and Citi (NYSE: C) Treasury and Trade Solutions announced today a new integrated payment solution that enables straight through payment processing and automates reconciliation by using a distributed ledger to record and transmit payment instructions. A number of payment transactions have been concluded, including Citi’s automated processing of cross-border payments via a link between the CitiConnect® for Blockchain connectivity platform and the Linq Platform powered by the Nasdaq Financial Framework. This collaboration has created a pioneering institutional banking solution that tightly integrates blockchain technology with Citi’s global financial network leveraging API technology.

The partnership between Citi and Nasdaq leverages Chain’s blockchain infrastructure platform and draws on core competencies from industry leaders who are at the forefront of innovation in the global financial sector. Emerging technologies like Distributed Ledger Technology (“DLT”) are driving digitization and enabling new platforms and blockchain ecosystems that can provide real-time digital solutions. For example, this integration can allow businesses such as Nasdaq Private Market to address the challenges of liquidity in private securities by streamlining payment transactions between multiple parties.

Key benefits that this integration can offer:

  • A seamless end-to-end transactional process for private company securities
  • Direct access to global payments from Nasdaq’s Linq platform using CitiConnect® for Blockchain and WorldLink® Payment Services, Citi’s cross border, multicurrency payments service.
  • Increased operational efficiency and ease of reconciliation with real-time visibility of payment transactional activity on the blockchain ledger.

“This new payment capability marks a milestone in the global financial sector and represents an important moment in the commercial application of blockchain technology,” said Adena Friedman, CEO, Nasdaq. “Through this effective integration of blockchain technology and global financial systems, we can realize greater operational transparency and ease of reconciliation, which can have profound implications for outdated administrative functions in the capital markets. We are excited about this accomplishment in collaboration with our partners, Citi and Chain, and are looking forward to continuing our work together to scale this offering.”

Naveed Sultan, Citi’s Global Head of Treasury and Trade Solutions Group said, “CitiConnect® for Blockchain provides a crucial bridge between blockchain platforms and Citi’s global financial network. Our partnership with Nasdaq showcases Citi’s client-centric approach to innovation and is an example of how we actively engage with our clients to co-create innovative, leading and differentiated solutions for the global market.”

“Chain is delighted that our technology is supporting this industry leading network. Through this effort, we have seen firsthand that Citi and Nasdaq are pioneers, successfully leveraging breakthrough technology in order to enable world-class solutions for their clients,” said Adam Ludwin, Chain’s CEO.

This solution leverages Nasdaq and Citi’s founding membership of the IDEO CoLab in June 2015 to explore emerging technologies such as blockchain. In September of that year, both Nasdaq and Citi Ventures invested in Chain’s series B funding round with other leading financial institutions.

Media contacts:
NASDAQ: Stephanie Lowenthal, 646 441 5073 Stephanie.lowenthal@nasdaq.com
Citi: Nina Das, 212 816 9267 Nina.das@citi.com
Chain: Elizabeth Alinikoff, 415 598 0346 Elizabeth@chain.com

Nasdaq
Nasdaq (Nasdaq: NDAQ) is a leading global provider of trading, clearing, exchange technology, listing, information and public company services. Through its diverse portfolio of solutions, Nasdaq enables customers to plan, optimize and execute their business vision with confidence, using proven technologies that provide transparency and insight for navigating today’s global capital markets. As the creator of the world’s first electronic stock market, its technology powers more than 89 marketplaces in 50 countries, and 1 in 10 of the world’s securities transactions. Nasdaq is home to 3,800 total listings with a market value of $11 trillion. To learn more, visit: http://business.nasdaq.com http://business.nasdaq.com/

Cautionary Note Regarding Forward-Looking Statements
The matters described herein contain forward-looking statements that are made under the Safe Harbor provisions of the Private Securities Litigation Reform Act of 1995. These statements include, but are not limited to, statements about Nasdaq and its products and offerings. We caution that these statements are not guarantees of future performance. Actual results may differ materially from those expressed or implied in the forward-looking statements. Forward-looking statements involve a number of risks, uncertainties or other factors beyond Nasdaq’s control. These factors include, but are not limited to factors detailed in Nasdaq’s annual report on Form 10-K, and periodic reports filed with the U.S. Securities and Exchange Commission. We undertake no obligation to release revisions to any forward-looking statements

Citi
Citi, the leading global bank, has approximately 200 million customer accounts and does business in more than 160 countries and jurisdictions. Citi provides consumers, corporations, governments and institutions with a broad range of financial products and services, including consumer banking and credit, corporate and investment banking, securities brokerage, transaction services, and wealth management.

Additional information may be found at www.citigroup.com | Twitter: @Citi | YouTube: www.youtube.com/citi | Blog: http://blog.citigroup.com | Facebook: www.facebook.com/citi | LinkedIn: www.linkedin.com/company/citi.

Citi Treasury and Trade Solutions (TTS) enables our clients’ success by providing an integrated suite of innovative and tailored cash management and trade finance services to multinational corporations, financial institutions and public sector organizations across the globe. Based on the foundation of the industry’s largest proprietary network with banking licenses in over 90 countries and globally integrated technology platforms, TTS continues to lead the way in offering the industry’s most comprehensive range of digitally enabled treasury, trade and liquidity management solutions.

Chain
Chain, Inc. (www.chain.com) is a technology company that partners with leading organizations to build, deploy and operate blockchain networks that enable breakthrough financial products and services. Chain is the author of the Chain Protocol, which powers the award-winning Chain Core blockchain platform. Chain was founded in 2014 and has raised over $40MM in venture funding.

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Vande Matram

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Mere Rashk-e-Qamar – Sufi Ghazal

This Urdu ghazal was penned by the Pakistani poet Fana Buland Shehri. Fana’s Real name was Muhammad Hanif, he was shagird (student) of well known Urdu Poet Qamar Jalalvi

میرے رشکِ قمر تو نے پہلی نظر، جب نظر سے ملائی مزہ آ گیا
mere rashk-e-qamar tu ne pehli nazar, jab nazar se milaaii maza aa gaya
O my envy of the moon, when your eyes first met mine, I was overjoyed

برق سی گر گئی، کام ہی کر گئی، آگ ایسی لگائی مزہ آ گیا
barq si gir gaii kaam hi kar gaii, aag aisi lagaaii maza aa gaya
Lightning struck and destroyed me; you ignited such a fire that it made me ecstatic

جام میں گھول کر حسن کی مستیاں، چاندنی مسکرائی مزہ آ گیا
jaam mein ghol kar husn ki mastiyaan, chaandni muskuraaii maza aa gaya
Mixing beauty’s mischief into my drink, the moonlight smiled – how enjoyable!

چاند کے سائے میں اے میرے ساقیا، تو نے ایسی پلائی مزہ آ گیا
chaand ke saaey mein ae mere saaqiya, tu ne aisi pilaaii maza aa gaya
In the moon’s shadow, O my cup-bearer, you made me drink such a wine that I was ecstatic

نشہ شیشے میں انگڑائی لینے لگا، بزمِ رنداں میں ساغر کھنکنے لگے
nasha sheeshe mein angraaii lene laga, bazm-e-rindaan mein saaghar khanakne lage
Intoxication spread through the bottle, and goblets clinked in the party of debauchees

میکدے پہ برسنے لگیں مستیاں، جب گھٹا گھر کے چھائی مزہ آ گیا
maikade pe barasne lagiin mastiyaan, jab ghata ghir ke chaaii maza aa gaya
Mischief descended upon the tavern, and when storm clouds poured down, I was overjoyed

بےحجبانہ وہ سامنے آ گئے، اور جوانی جوانی سے ٹکرا گئی
behijaabana woh saamne aa gae, aur jawaani jawaani se takra gaii
Unveiled, she came before me, and her youthful splendor collided with mine

آنکھ اُن کی لڑی یوں میری آنکھ سے، دیکھ کر یہ لڑائی مزہ آ گیا
aankh un ki lari yuun meri aankh se, dekh kar yeh laraaii maza aa gaya
Her eyes clashed with mine in such a way that seeing this fight made me joyful

آنکھ میں تھی حیاہ ہر ملاقات پر، سرخ عارض ہوئے وصل کی بات پر
aankh mein thi hayaa har mulaaqaat par, surkh aariz hue wasl ki baat par
Modesty was in her eyes every time we met; her cheeks blushed red when I spoke of our union

اُس نے شرما کے میرے سوالات پہ، ایسے گردن جھکائی مزہ آ گیا
us ne sharma ke mere sawaalaat pe, aise gardan jhukaaii maza aa gaya
Embarrassed by my questions, she lowered her head in such a way that I was delighted

شیخ صاحب کا ایمان مٹ ہی گیا، دیکھ کر حسنِ ساقی پگھل ہی گیا
shaikh saahib ka eemaan mit hi gaya, dekh kar husn-e-saaqi pighal hi gaya
The shaikh’s faith was obliterated; upon seeing the cup-bearer’s beauty, it melted away

آج سے پہلے یہ کتنے مغرور تھے، لٹ گئی پارسائی مزہ آ گیا
aaj se pehle ye kitne maghroor the, lut gaii paarsaaii maza aa gaya
Before today, how proud he was; now his piety has been lost – how enjoyable!

اے فناؔ شکر ہے آج بعدِ فنا، اُس نے رکھلی میرے پیار کی آبرو
ae Fana shukar hai aaj baad-e-fana, us ne rakhli mere pyaar ki aabroo
O Fana, today I am grateful that after my demise, she has maintained the honor of my love

اپنے ہاتھوں سے اُس نے میری قبر پر، چادرِ گل چڑھائی مزہ آ گیا
apne haathon se us ne meri qabar par, chaadar-e-gul charhaaii maza aa gaya
With her own hands, she spread a sheet of flowers on my grave – how delightful!

Fana Buland Shehri included his takhallus in this qawwali when he says, “ae Fana shukar hai aaj baad-e-fana, us ne rakhli mere pyaar ki aabroo”. Fana is the author’s name, but it also means “death”. This adds another meaning to that line: “O death, today I am grateful that after my demise, she has maintained the honor of my love”.

Credits: http://www.hamzashad.com/mere-rashk-e-qamar/

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Airfield Reader’s Day: Mountains To Sea DLR Book Festival

Today, I attended along with my wife the Reader’s day event at Airfield estate held as part of Mountains To Sea DLR Book Festival mountainstosea.ie. It was a great event and an opportunity to meet with a number of talented Irish writers.

The first event of the day was titled ‘From Stage to Page’ where Tara Flynn discussed with Claudia Carroll and Kate Beaufoy their transition from being stage actors to becoming successful authors. Tara Flynn   herself is an actress and an author and she moderated the event very well. Claudia Carroll is a Dubliner and has been a successful stage actress. She now writes full-time and her 2013 novel ‘Me and You‘ was shortlisted for the Bord Gais Popular Choice Irish Book Award. She has knocked out a book a year for the last 12 years and did a short reading from her latest novel ‘Our Little Secret’. Kate Beaufoy also began her career as a professional actor before becoming a full time writer. She also has a dozen novels published including the number one bestseller ‘The Blue Hour’. She read an excerpt from her latest novel ‘The Gingerbread House’. Both gave insights on what prompted them to become authors and the challenges they faced on their journey. One of the questions was on how much input they provide on the design of their book covers and why it is that covers on the books written by female writers are so different from those of male writers? I found it amazing that both said that they’d almost no say in deciding the book covers and were guided by their publishers. They said that they are primarily writers and have no experience in marketing so they would leave it on publishers to take care of that aspect of book publishing. Both seemed pretty happy with the book covers chosen by their publishers. On the question about the discipline of writing, Kate summed it up very nicely that discipline is nothing but pure hardwork. The last question that Tara had for them was that if they’ve to chose between acting and writing, what would they chose? Both answered that they would chose writing over acting. Kate told the audience that she almost had a fright on every stage opening night. For her, the best part of the acting profession was rehearsal as it was a creative process, the opening stage night was really scary and after that it was plain delivery and did not involve much creativity. Whereas writing is a creative process end to end. Carroll did mention that she still has a big fright when she sends her new book draft to her editor, she said that she is not a mother or a parent but she can imagine that it would feel similar to the moment when a new mother wraps up her baby and hand it over to someone visiting and wait for the feeback if her baby is beautiful or ugly.

After the wonderful talk, there was a tea break and we’re able to chat with both Kate and Carroll and got their latest books signed.

The second event was titled ‘The Writing Life’ and audience were treated to Carmel Harrington, Hazel Gaynor and Fionnuala Kearney discussing the ideas behind their latest book and writing life with RTE’s Evelyn O’Rourke. Carmel Harrington lives with her family in County Wexford. She has won several international awards including Kindle Book of the Year and Romantic ebook of Year. Her latest novel ‘The Things I Should Have Told You’ was nominated for an Irish Book Award. Originally from Yorkshire, Hazel Gaynor now lives in Ireland with her family. Her novels ‘The Girl Who Came Home’ and ‘A Memory of Violets’ achieved New York Times and USA Today bestseller status and her latest novel ‘The Girl from the Savoy’ was nominated for an Irish Book Award. Finnuala Kearney writes about the nuances and subtle layers of humanity relationships, peeling them away to see what’s really going on beneath. ‘The Day I Lost You’ is her second novel; her first was the Top Ten Irish Times bestselling ‘You, Me and Other People’. All the authors read from their latest novels and enlightened the audience with anecdotes from their journey to become successful writers. Carmel and Hazel actually got self published before Harper Collins embraced them and gave them book contracts. Both of them encouraged aspiring writers not to shy away from self publishing on Amazon but to be passionate to explore any avenues to take their stories to the readers. All of them mentioned that writing the book is the easy part but getting it published is more of a combination of right allignment of stars and right agent. The right agent can do wonders but it is hard to secure one and needs a lot of knocking on the doors. It was a treat to listen to their challenges in keeping themselves disciplined while rearing young children. On the question if writing can provide a living, they said it took years before they started to earn a living from writing, for Carmel it took 7 years and 5 novels before she started earning enough to make a living and same struggle was faced by Hazel and Finnuala.

After this really educative discourse, there was a break for lunch and thankfully the kitchen could serve vegetarian sandwiches and soup. We’d our lunch with a group of old ladies from Wexford and had a good chat with them over lunch. Then tea was served with delicious sweet oaties and we could also get hold of Finnuala to get her latest novel signed.

The last event of the day was titled ‘Partners in Crime’ in which crime writers Alex Marwood, Jane Casey and Sam Blake talked about their latest novels and the reasons why women so excel in the crime genre? Declan Burke who himself is a crime writer, journalist and critic moderated the event. Alex Marwood began her career as Fleet Street journalist before turning her hard to the wirting of crime fiction. Her novels ‘The Wicked Girl’ and ‘The Killer Next Door’ have won many awards. Alex herself is a figment of the imagination of the novelist and sometime journalist Serena Mackesy. Sam Blake is a pseudonym for Vanessa Fox O’Loughlin who runs writing.ie, the national writing resources website, as well as a publishing consultancy. In 2016 her first crime novel ‘Little Bones‘ became a Number 1 bestseller and was nominated for an Irish Book Award. Married to a criminal barrister, Dubliner Jane Casey infuses her novels with an unerring authencity. They have been nominated for several awards and in 2015, Jane won both the Mary Higgins Clark Award and Irish Crime Novel of the Year. The first question Declan posed to the crime writers was on their insight on why women excel in crime genre? Jane had a theory that women have a far developed sense of threat and could easily sense threat in every situation and location. Another generalisation she made was that women crime writers develop characters who are close of their real life personas whereas with male crime writers the protagonists are people they aspire to be… who could punch better than the next guy… and that is perhaps the reason why writers like Ian Fleming could come up with heroes like James Bond but the characters from women crime writers are more grounded. All the writers read from their latest books and told the audience anecdotes from their lives and works. Sam Blake told the audience how she came up with the idea of child bones inside the helm of a wedding dress for his latest crime thriller and Alex told the audience how her both grandmothers were successful crime writers in 1930s.

Overall it was a great event and both I and my wife thoroughly enojoyed it.

Tarun Rattan

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Brexit Blues: Why Dublin is Turning Into a Haven for Blockchain

http://www.coindesk.com/brexit-blues-why-dublin-is-turning-into-a-haven-for-blockchain/

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How to be a leader in the digital age

The coming years will be a time of “Digital Leaders”. Around the world, leaders in different fields have already started to embrace the digital revolution and recognize the power of game-changing technology. “Every country needs a Minister of the Future,” said Saleforce’s founder and CEO Marc Benioff, at the World Economic Forum in Davos this year. And he was right.

1. But what does leadership actually mean?

There is a plethora of literature on leadership, but only some of it addresses an issue of how disruptive technologies can define the new wave of leaders in today’s world. Before we move on to digital leadership, we should take a step back and look at what leadership means in general and whether universal characteristics of leadership apply to the fast-changing world of disruptive technologies.
Different ages require different kinds of leadership, but many leading theorists claim that there are certain universal characteristics that are timeless.

First, personal charisma. A charismatic person possesses a rare gift that allows them to influence followers while inspiring loyalty and obedience.
However, Max Weber predicted a decline in charismatic leadership in what he described as “routinization” Arguably he was right, especially in the Western World where charismatic leadership over the years has been, to some extent, “succeeded by a bureaucracy controlled by a rationally established authority or by a combination of traditional and bureaucratic authority”. This process is evident in the European Union’s bureaucratic system, where politicians are often accused of being unable to take brave and visionary decisions. A huge system of checks and balances and the competing national interests of 28 member states makes it harder for high-ranked officials to act decisively.
Even those who possess natural charisma are not able to pursue their right course of action because they are forced to balance various interests, maintain order and seek consensus. Margaret Thatcher once described European leaders as being “weak” and “feeble”; the same, unfortunately, could be said about a number of leaders in Europe today. It is because their personal charisma, if they ever had it, has been silenced by bureaucracy.

Second, aside from ‘inner’ or personal levels of leadership, there is also an ‘outer’ or behavioral level which relates to how leaders deliver results, according to more integrated psychological theory. There are several universal skills that are worth mentioning, such as: (1) motivational skills; (2) team building; (3) emotional intelligence.
Obviously, this list of skills is not exhausted but indicates the core abilities required to deliver successful results. And although these ‘outer’ characteristics have largely remained the same, there are also a few which have changed substantially due to the unprecedented impact of technology.

2. The human impact of technology

We live in a world of rapidly advancing technology which is influencing lives like never before. Digital technology is transforming politics, businesses, economies and society, as well as our day-to-day lives.
Digital technology has not only broken down the old, familiar models of organizations, but has also created a broad set of new challenges.
The best example of transformative change is probably within the space industry. In 2015, we could observe how SpaceX’s Falcon 9 rocket landed safely at Cape Canaveral, which was hailed almost immediately as another giant leap for mankind. Reusable rockets are a fantastic business opportunity, a source of entertainment and, more importantly, another step forward in the commercialization of space travel and ultimately toward a possible colonization of other planets.
Back here on earth, we can’t deny that our world is changing as never before. Technological revolution is evident and examples of our new reality abound. The most popular social media creates no content (Facebook), the fastest growing banks have no actual money (SocietyOne), the world’s largest taxi company owns no taxis (Uber), and the largest accommodation provider owns no real estate (Airbnb). Today’s game changers drive with completely different fuel and sometimes – as the above examples clearly indicate – they revolutionize even the most basic characteristics of particular industries.
On a conceptual level, the Digital Age – called sometimes the knowledge society or networked society – is marked by several key structural changes that are reshaping leadership: (1) rapid and far-reaching technological changes, (2) globalization leading to the dynamic spread of information; (3) a shift from physical attributes toward knowledge and (4) more dispersed, less hierarchical organizational forms of organization.

3. The impact of the Digital Age on leadership

Traditional skills have not been supplanted but they now co-exist with a mix of new factors.

First of all, digital leadership can be defined by a leader’s contribution to the transition toward a knowledge society and their knowledge of technology. Digital leaders have an obligation to keep up with the ongoing global revolution. They must understand technology, not merely as an enabler but also for its revolutionary force.
Leadership must be driven by an attitude of openness and a genuine hunger for knowledge. Of course, no rule dictates that leaders must be literate in coding or that they graduated from machine-learning but yes, there is an imperative to understand the impact of breakthrough technologies.
Today’s leaders must have the ability to identify technological trends across different sectors, such as big data, cloud computing, automation, and robotics. However, first and foremost they must possess sufficient knowledge and the vision to use these resources most effectively.

Secondly, in a knowledge society, what we do not know is as important as what we do know. Leaders should know their limits and know how to acquire missing knowledge. A leader of the future is more like a community manager rather than an authoritarian.
These days, we are observing the decline of traditional hierarchical models of organization. Take a look at how the organization of governments has changed across Western societies in recent years. A number of governments have introduced or reinforced public consultation processes as well as opened up public data for the benefit of their citizens.

These processes, by and large, will continue to grow. As a result, the hierarchical model tends to be suppressed and replaced by horizontal structures among executives, leaders from different sectors, researchers and representatives from civic society. Hierarchy fails in the digital age because it’s slow and bureaucratic, whereas the new world is constantly changing and requires immediate responses.

Information is key. In today’s world, power is not gained by expanding new territories or areas of influence but by deepening and widening networks and connections. But what is the role of the individual or leader, or of qualities that distinguish one grain of sand from another?

4. Why leaders should turn their attention to tech for good

We have to shift our focus from the threat of new technologies to the opportunities they bring.
Of course, we cannot ignore the threat of new technologies. In India, for example, around 850 government websites have been hacked since 2012. Meanwhile, hackers recently breached US Government networks and stole more than 5.6 million fingerprint records from the Office of Personnel Management (OPM). And the government is not always a victim, they can also be the predator. Not long ago, Twitter warned a number of users that they may have been the target of a state-sponsored attack.
The debate concerning the threat of technologies, especially the internet, will never end. Policymakers have proposed different ways of regulating the web, but they always are one or two steps behind. This is because law and regulations are stable and designed to be long-lasting, whereas the digital environment is changing rapidly. As Hugh Fiennes, CEO of Electric Imp, puts it: “The reality seems to be that when it comes to the internet-connected device there is no such thing as absolute security. Your device can start by being secure today and then not be secure tomorrow.”
We do not claim that regulation is purely ineffective, and thus we should abandon any legal solutions for creating a more secure environment. But we do suggest that we look at technologies through different lenses. We can transform the one thing that is good and bad in breakthrough technologies – the human factor.
Having acknowledged that digital technology will play a decisive role our future, leaders cannot afford to show fear or reluctance in implementing it. Instead, they must embrace technology with a clear view of its potential. We must set sail for new, ambitious lands. We choose to go to Mars because our technology enables us to at least attempt the exploration on other planets by the 2030s. And we choose to develop other fantastic things every day – self-driving cars, more powerful batteries, the Apple Watch, drones – to name only just a few.

A balanced mix of universal characteristics and digital leadership traits has the potential to guide us through years of transformation with optimism and idealism. Technology continues to prove that it can be used for the benefit of mankind, but only if we set sail on the right course and with the right companions.

https://www.weforum.org/agenda/2016/05/how-to-be-a-leader-in-the-digital-age?utm_content=buffer72e91&utm_medium=social&utm_source=facebook.com&utm_campaign=buffer

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Introduction to Cryptography

Secure communications in presence of third parties i.e. adversaries is an old age problem and cryptography is the practice and study of techniques to solve this problem.

The history of cryptography can be split into two eras: the classical era and the modern era. In classical era, cryptography was synonymous with encryption – conversion of human readable message into incomprehensible information, such that interceptors cannot make any sense of the communication. A breakthrough was achieved in 1977, when both the RSA algorithm and the Diffie-Hellman key exchange algorithm were introduced and marked the start of modern era. These new algorithms were ground-breaking as they represented the first viable cryptographic schemes where security was based on the number theory enabling for the first time secure communication between adversaries without a shared secret.

In modern era with the advent of emerging technologies like Blockchain, cryptography has much more to offer than just encryption in the form of integrity, authentication, and digital signatures, interactive proofs and secure computations. Modern cryptography is founded on the idea that the key that you use to encrypt your data can be made public while the key that is used to decrypt your data can be kept private i.e. Encryption with the public key can only be undone by decrypting with the private key. The public keys are generated by transforming private key through a one-way function that is easy to calculate in one direction and difficult in oCrypto1ther. The whole security of modern communication depends on the “hardness” of this one-way function. Here the word hardness represents the computational complexity i.e. time taken to compute one key from another. In theory it should be very easy and computationally cheap to calculate public key from private key but impossible or computationally very intensive to calculate private from public. As such, these systems are known as public key cryptographic systems.

The first, and still most widely used of these systems, is known as RSA—made up of the initial letters of the surnames of Ron Rivest, Adi Shamir, and Leonard Adleman, who first publicly described the algorithm in 1977 and it uses factorization.

Integer factorization is the process of determining which prime numbers divide a given positive integer. Computers don’t do well with arbitrary large numbers so in factorization it is important to ensure that the numbers do not get too large by choosing a maximum number and only dealing with numbers less than the maximum. Any calculation that results in a number larger than the maximum gets wrapped back to a number in the valid range. In RSA, this maximum value (max) is obtained by multiplying two random prime numbers. The public and private keys are two specially chosen numbers that are greater than zero and less than the maximum value (say pub and priv). To encrypt a number, you multiply it by itself pub times, it needs to be wrapped around whenever it hits the max. To decrypt a message, it just needs to be multiplied by itself priv times, to get back to the original number.

It works like magic, let’s try to encrypt and decrypt word CITI using this technique.

Take the prime numbers 13 and 7. Their product gives maximum value of 91. Let’s assign the public encryption key to be the number 5. Then using the fact that we know 13 and 7 are the factors of 91 and applying an algorithm called the Extended Euclidean Algorithm, the private key can be deduced as the number 29. These parameters (max: 91, pub: 5, priv: 29) define a fully functional RSA system. You can take a number and multiply it by itself 5 times to encrypt it and then take that encrypted number and multiply it by itself 29 times and you get the original number back.

In case of CITI, to represent it mathematically, let’s first turn the letters into numbers. A common representation of the Latin alphabet is UTF-8. Each character corresponds to a number.

Crypto2.png

 

So CITI can be represented mathematically as 67 73 84 73.

To start with letter C, as it is number 67 on UTF-8, let’s multiply 67 by itself five times to get the encrypted value for C.

67×67 = 4489

Since 4489 is larger than max i.e. 91, it needs to be wrapped around. This can be done by dividing by 91 and taking the remainder i.e. 4489 = 91×49 + 30

30×67 = 2010 = 8

8×67 = 536 = 81

81×67 = 5427 = 58

This means the encrypted version of 67 (or ‘C’) is 58. Similar calculation for rest of the letters would give ‘I’ = 47, ‘T’ = 28, ‘I’ = 47

Hence the encrypted value for CITI becomes 58 47 28 47.

Now let’s see how decryption works.

To decrypt each encrypted value it needs to be multiplied by itself 29 times. Again starting with C, the encrypted value for C is 58, so this needs to be divided by itself 29 times and if exceeds max then needs to be wrapped around.

58×58 = 3364 = 88 (Remember, we wrap around when the number is greater than max.)

88×58 = 5104 = 8

… (Repeated in total 29 times)

9×58 = 522 = 67

There you’re, back to 67. Similarly we get back 73 for ‘I’, 84 for ‘T’ and 73 for ‘I’ again.

And CITI gets decrypted back to original UTF-8 representation as 67 73 84 73.

Though factorization provides rigorous security proofs yet it is not a hardest problem on a bit by bit basis. Due to recent advancements in cryptanalysis, it has become very easy to factor keys which were previously thought secure. To counter this simple fix cryptographers have come up with is just to increase the bit size of the keys. Since the resources available to decrypt numbers are increasing, the size of the keys needs to grow even faster. This is not a sustainable situation for mobile and low-powered devices that have limited computational power. The gap between factoring and multiplying is not sustainable in the long term.

In 1985, new types of cryptographic algorithms were proposed based on an esoteric branch of mathematics called elliptic curves.

Elliptical Curve is what most common browsers use today to secure the communication. An elliptic curve is the set of points that satisfy a specific mathematical equation. The equation for an elliptic curve looks something like this:

y

2

= x

3

+ ax + b

The property of elliptic curves that makes it interesting for cryptography is the horizontal symmetry of these graphs. Any point on the curve can be reflected over the x-axis and remain the same curve. Another more interesting property is that any non-vertical line will intersect the curve in at most three places.

Crypto3.png

 

Take any two points on the curve and draw a line through them; the line will intersect the curve at exactly one more place. In elliptical curve systems, we start with our private key (q) and a well-defined point (p) on the curve. Then we find the point (p*q) on the curve. That point is defined as public key corresponding to the private key. On elliptical curves it turns out that if you have two points, an initial point “dotted” with itself n times to arrive at a final point, finding out n when you only know the final point and the first point is hard. The mathematics works out in such a way that all rational multiples of p also ends up being on the curve. The claim is that it is very easy on elliptical curves to derive the public key by multiplication but computationally hard to find the reverse i.e. private from public.

After a slow start, elliptic curve based algorithms are gaining popularity, and the pace of adoption is accelerating. Elliptic Curve Cryptography (ECC) is now used in a wide variety of applications: the US government uses it to protect internal communications; the Tor project uses it to help assure anonymity, it is the mechanism used to prove ownership of bitcoins, and it provides signatures in Apple’s iMessage service. First generation cryptographic algorithms like RSA and Diffie-Hellman are still the norm in most arenas, but ECC is quickly becoming the go-to solution for privacy and security online.

Tarun Rattan

Credits: Nick Sullivan

https://www.google.ie/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&sqi=2&ved=0ahUKEwjF4fSYlvbNAhVPFMAKHSDJB4MQFgg0MAM&url=http%3A%2F%2Farstechnica.com%2Fsecurity%2F2013%2F10%2Fa-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography%2F&usg=AFQjCNH8rHQUKzcXOlZfCeQCFLqE0LzgQA&bvm=bv.127178174,d.ZGg

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