Example of bad basis for lattices (worst-case for LLL)

I am trying to understand how to produce (deterministically) a lattice $L subset mathbb R^n$ and a "bad basis" for $L$, in any given dimension, say $n=20$.
By "bad basis" $(b_1, …, b_n)$, I mean that when we apply the LLL-algorithm to it (say for $delta = 1$) then we get a basis $(v_1, …, v_n)$ such that $| v_1 |$ is "as close as possible" from the upper bound $(delta – 1/4)^{-(n-1)/2} lambda_1(L)$.

I am interested in explicit examples where one could describe the $b_i$‘s easily (or define explicitly a unimodular matrix $U$ that would give the bad basis $B$ from a "good basis" $G$, which could be used to compute $lambda_1(L)$). I have seen that one can sometimes use $B = HNF(G)$, but it might not always work to get a bad basis, and therefore it is not explicit (nor very clear to me…).

Crypto Market Recap for Q1 2022 – What happened to Cryptos?

Cryptocurrencies are no strangers to uncertainties, as factors like price volatility. What Happened To Crypto In Q1 2022? The crypto market registered a barrage of events in the first quarter of 2022, with some pushing its entire market cap in a bearish zone. Below are some of the events worthy of mention in the crypto::Listen

Cryptocurrencies are no strangers to uncertainties, as factors like price volatility.

What Happened To Crypto In Q1 2022?

The crypto market registered a barrage of events in the first quarter of 2022, with some pushing its entire market cap in a bearish zone. Below are some of the events worthy of mention in the crypto market in the first quarter of 2022;

Institutional Interests In Cryptocurrencies Remained High

Despite a fall in the value of any assets, Q1 2022 witnessed a high demand, especially by institutional investors. Top brands like Google, Uber, and PayPal started to ponder on receiving cryptocurrencies from customers as payment for services. Alternatively, many other global brands have set up research teams to investigate the usefulness and impact of cryptocurrencies. Jefferies, Canaccord Genuity, and Credit Suisse are a few names interested in committing funds to blockchain development globally. Also, the U.S Chicago Mercantile Exchange (CME) launched micro-sized Bitcoin and Ethereum futures options. However, South Korea is taking the Asia crypto space aloft, as its largest bank Kookmin Bank, plans to introduce crypto products.

Furthermore, new and old institutional investors globally also purchased cryptocurrencies in Q1 2022. Firms like MicroStrategy bought 660 BTC, and the Luna Foundation Guard purchased 42,410 BTC in Q1 2022. Alternatively, the North American nation El Salvador also acquired 410 BTC this year. Outside the U.S, crypto adoption remains high among institutional investors and national stakeholders. Also, in Q1 2022, Brazil’s Mayor- Eduardo Paes, revealed he would be investing 1% of his city’s treasury in cryptocurrency. In summary, cryptocurrencies enjoyed massive institutional interest earlier this year, which should remain so in the latter part.

Crypto Regulations Taking A New Leap In Q1 2022

Due to the massive institutional interest cryptocurrencies got in Q1 2022, nation’s financial regulators are beginning to embrace them. U.S. Treasury Secretary Janet Yellen commented on cryptocurrencies growing beyond leaps and bounds earlier in the year. Yellen’s comment echoes the thought of Joe Biden, who wanted the nation’s regulators to look keenly into digital assets. The world leader implores his regulators to see how cryptocurrencies can help grow the country. Surprisingly, Yellen’s comments did not go unnoticed, as it is now forcing many nations to reconsider their stance on cryptocurrencies.

The U.K. regulators also began sketching out a regulatory framework for crypto, which should see its adoption skyrocket in 2022. Alternatively, India’s rising crypto adoption sees its Advertising Standards Council of India (ASCI) issuing guidelines for cryptocurrency-related ads. Likewise, lawmakers in Panama started exploring regulating cryptocurrencies to bring the country up to speed with the digital economy globally. A crypto-friendly nation like Georgia, in Q1 2022, also drafted legislative changes for crypto firms within its jurisdiction. These changes include registration, licensing, compliance testing, and Anti Money Laundering rules for the crypto enterprises in the nation.

Why Is Crypto Regulation Important?

Cryptocurrency regulation involves the rules and regulations government and its regulatory bodies use to guide crypto trading in their jurisdiction. Unfortunately, cryptocurrency adoption continues to slow down in many nations due to a lack of proper regulations. Its benefit to a country is immense and will give financial regulators an insight into what cryptocurrencies entail. An unregulated market can be disastrous for investors, exposing them to market manipulation and price volatility.

Good regulatory guidance, if well targeted, could reduce speculations among crypto assets. Cryptocurrencies are very volatile, and prices can rise and fall rapidly. However, when they fall quickly, investors automatically face losses, devastating to them and the market. However, if proper regulations are in place, investors can be rest assured stronger forces cannot manipulate the market.

Today, the crypto market consists of thousands of assets, with investors having zero knowledge. However, with proper regulations, crypto markets in a jurisdiction will only allow the trading of assets investors understand. This will help investors avoid Blockchain projects that are rug pulls to cart away with investors’ funds. Lastly, with proper regulations, regulators can monitor the activities of crypto exchanges within their jurisdiction. This will allow them to prevent issues like money laundering and corrupt practices perpetrated by these entities.

Crypto Regulations Today Around The World

Last month, crypto regulation took a giant leap in the U.S., as congressman Glenn Thompson introduced the Digital Commodity Exchange Act (DCEA). This bill (the DCEA), if passed, will establish a reporting regime for cryptocurrency exchanges in the country. This bill will further signal that the U.S. is critical of the growth of its cryptocurrency space. In Canada, crypto exchanges and organizations are Money Service Businesses (MSBs) and must register with FINTRAC.

Financial Transactions and Reports Analysis Centre of Canada (FINTRAC) is Canada’s apex regulator, tasked with guiding financial service firms in the country. Today, the U.K. currently leads in crypto adoption in Europe, as its financial regulators embrace cryptocurrencies. However, crypto firms must get a license from the Financial Conduct Authority (FCA) to operate in the nation. Alternatively, Europe remains one of the most thriving crypto trading and exchange ecosystems globally.

Hence, this is why cryptocurrency trading is legal almost everywhere in Europe. In Asia, precisely Japan, cryptocurrencies are legal properties under the Payment Service Act (PSA). There are no stumbling blocks concerning regulations, but exchanges expect regulators to get more involved. Unfortunately, cryptocurrency trading in China has hit a stumbling snag recently. The country does not see digital assets as legal tender or even properties. Unfortunately, the People’s Bank of China (PBOC) bans crypto exchanges from operating in the country. Last year, the government banned crypto mining operations to halt their adoption.

The Biggest Gainers Of Q1 2022

The biggest gainer in Q1 2022 is the WAVES token, which posted an average gain of 275% within the period. The multi-purpose blockchain platform token saw its price hit several highs and grow massively in terms of market capitalization. Kyber Network (KNC) token also posted gains of 154% in Q1 2022 to cap an impressive start to the year. ZIL’s growth, which sees its market cap above $1 billion, is the third-highest gainer in the year’s first quarter. The token used in processing transactions in the Zilliqa blockchain gained about 142% in Q1 2022. To cap off the top five, RUNE (68.77%) and Ethereum Classic’s ETC (39.25%) are the 4th and 5th most performing asset in Q1 2022.

The Biggest Losers Of Q1 2022

Aragon (ANT), Ethereum Name Service (ENS), SUSHISWAP (SUSHI), MASK Network (MASK), and Curve DAO (CRV) are the biggest losers in Q1 2022. The utility token of the Curve DEX lost more than 50% in price value within the first three months of the year. Despite the utility of the MASK token in its network, it also lost about 51% in price in Q1 2022. SUSHI is also another disappointing token since the beginning of the year, losing more than 53%.

Surprisingly, SUSHI remains a highly-rated token, as investors remain optimistic about the token. ENS, the governance token of Ethereum Name Service, continues to struggle in 2022, losing around 54% in Q1 2022. Lastly, the biggest loser in the first quarter of the year is Aragon’s ANT. The utility token fell from its highs last year, losing about 63% in price in Q1 2022. However, while performance may improve, its average performance this year has remained short of remarkable.

What Led To The Crypto Market Crashing In Q1 2022?

Bitcoin, Ethereum, and many digital assets have been down in the last few weeks, as it looks like a bearish run looms. This fall was headlined by a turbulent week this month, which saw assets shed more than 90% in value in one day. Crypto analysts suggest the war in Ukraine could be why the prices of cryptocurrencies are falling. Unfortunately, there are rumors of investors dumping their assets, as they are losing patience with its growth. This phenomenon is prevalent around altcoins, whose growth has remained slow since the beginning of the year. Another factor could also be consumer sentiments towards cryptocurrencies, which is at an all-time low. This is evident on Twitter, known to be a tool fostering the global adoption of cryptocurrencies.

A popular survey also reveals no optimism about its future despite investors committing funds to cryptocurrencies. This is not unusual, as popular investors like Elon Musk continue to echo their uncertainties about the future of cryptos. Reports concerning North American investors pulling funds off the crypto market at an alarming rate are also not helping. The current rate of security breaches in the crypto market is a cause for alarm for all, including investors. Today, Blockchain networks and protocols expose themselves to too many risks, worrying investors. Investors would be willing to hold on to little assets or sell on time to avert the threat of losses.

Cryptocurrency And The Stock Market

Before now, the crypto market was independent, devoid of interference. Unfortunately, that is not the case today, as the recent traditional market adoption now means a correlation exists between them. A fall in stock markets could lead to investors being more cautious with investing in the crypto market. Today, stock prices of large corporations like Netflix continue to fall as unsettlement prevails in Wall Street. This fall’s negative impact is that investors do not want to lose on both ends and remain cautious. This caution will lead to further liquidation and dumping, which will affect the crypto market.

Alternatively, technology-related stock prices also affect crypto assets, as they are down now. Historically, in 2017, the cryptocurrency world left the stock world in the dust regarding overall performance. The stock market’s cumulative gain of 117.7% compared to the crypto market’s 28,963% leaves a massive gap between both markets. Fast forward to today, the same cannot be said, as volatility continues to consume the crypto market. Unfortunately, the cumulative growth of the stock market in Q1 2022 leaves much to desire. In summary, long-term investors are likely to find their success much higher if they choose stocks. Alternatively, high-risk investors who do not fear losing money may still commit their funds to cryptocurrencies.

Crypto Price Prediction Towards The End Of 2022

The fall in prices of significant crypto assets this month is disappointing, even as they continue to struggle their way back to the top. Bitcoin is still languishing around the $30k mark, as its 1.27% gain in seven-days shows struggles. WalletInvestor thinks Bitcoin’s struggles will not be for long and sees the asset reaching $50k by the end of the year. That prediction might look good today but is unsatisfying for crypto analysts who expect the leading cryptocurrency to reach 100k. Ethereum is another asset hit by the crypto market’s collapse. The digital asset still trades below $2K today, amidst a 2% fall in the last 7-days.

Fortunately, crypto experts remain bullish about the leading altcoin’s future and predict it to reach $8,000 this year. They believe that its bearish run is only temporary and see the asset stealing headlines in Q3 2022. Despite their falls, USDT and USDC are almost back to where they belong, and experts expect them to stand firm in the latter part of 2022. SOL, BNB, XRP, and ADA are beginning to look towards growth, as they posted gains of 12%, 8.66%, 6.6%, and 6.9% this week, respectively. However, crypto analysts suggest it is too early to predict the future of the top altcoin, as performances may still dwindle. However, there are expectations within the crypto community toward altcoins entering a bullish run in the last quarter of 2022. Whether that will happen or not, only time will tell.

Example of bad basis for lattices (worst-case for LLL)

Shopping cart
There are no products in the cart!
Continue shopping