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Integer factorization

In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization; when the numbers are sufficiently large, no efficient, non-quantum integer factorization algorithm is known. In 2019, Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé and Paul Zimmermann factored a 240-digit number utilizing 900 core-years of computing power; the researchers estimated. However, it has not been proven; the presumed difficulty of this problem is at the heart of used algorithms in cryptography such as RSA. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, quantum computing. Not all numbers of a given length are hard to factor; the hardest instances of these problems are the product of two prime numbers. When they are both large, for instance more than two thousand bits long, randomly chosen, about the same size the fastest prime factorization algorithms on the fastest computers can take enough time to make the search impractical.

Many cryptographic protocols are based on the difficulty of factoring large composite integers or a related problem—for example, the RSA problem. An algorithm that efficiently factors an arbitrary integer would render RSA-based public-key cryptography insecure. By the fundamental theorem of arithmetic, every positive integer has a unique prime factorization. Testing whether the integer is prime can be done in polynomial time, for example, by the AKS primality test. If composite, the polynomial time tests give no insight into how to obtain the factors. Given a general algorithm for integer factorization, any integer can be factored into its constituent prime factors by repeated application of this algorithm; the situation is more complicated with special-purpose factorization algorithms, whose benefits may not be realized as well or at all with the factors produced during decomposition. For example, if N = 171 × p × q where p < q are large primes, trial division will produce the factors 3 and 19 but will take p divisions to find the next factor.

As a contrasting example, if N is the product of the primes 13729, 1372933, 18848997161, where 13729 × 1372933 = 18848997157, Fermat's factorization method will begin with a = ⌈√N⌉ = 18848997159 which yields b = √a2 − N = √4 = 2 and hence the factors a − b = 18848997157 and a + b = 18848997161. While these are recognized as composite and prime Fermat's method will take much longer to factor the composite number because the starting value of ⌈√18848997157⌉ = 137292 for a is nowhere near 1372933. Among the b-bit numbers, the most difficult to factor in practice using existing algorithms are those that are products of two primes of similar size. For this reason, these are the integers used in cryptographic applications; the largest such semiprime yet factored was RSA-240, a 795-bit number with 240 decimal digits, in November 2019. This factorization took the equivalent of 900 years of computing on a single-core Intel Xeon Gold 6130 at 2.1 GHz. Like all recent factorization records, this factorization was completed with a optimized implementation of the general number field sieve run on hundreds of machines.

No algorithm has been published that can factor all integers in polynomial time, that is, that can factor b-bit numbers in time O for some constant k. Neither the existence nor non-existence of such algorithms has been proved, but it is suspected that they do not exist and hence that the problem is not in class P; the problem is in class NP but has not been proved to be or not be NP-complete. It is suspected not to be NP-complete. There are published algorithms; the best published asymptotic running time is for the general number field sieve algorithm, for a b-bit number n, is exp ⁡ For current computers, GNFS is the best published algorithm for large n. For a quantum computer, Peter Shor discovered an algorithm in 1994 that solves it in polynomial time; this will have significant implications for cryptography. Shor's algorithm takes only O O space on b-bit number inputs. In 2001, Shor's algorithm was implemented for the first time, by using NMR techniques on molecules that provide 7 qubits; when discussing what complexity classes the integer factorization problem falls into, it is necessary to distinguish two different versions of the problem: The function problem v

The Antarctic Sun

The Antarctic Sun is an online newspaper with "News about the USAP, the Ice, the People." It is funded by the National Science Foundation by its prime civilian contractor, Leidos Antarctic Support Contract. The online publication has been covering cutting edge science for the National Science Foundation since 1997–1998 austral summer, though it can trace its history back to the 1950s when the U. S. Navy ran logistics for the USAP. From the austral summer of 1997-98 to 2006–07, The Antarctic Sun was produced at McMurdo Station between the months of October and February. Since October 2007, it has been a year-round news website managed out of Colorado area; the website features. The former includes biology, geology and oceanography, among others. Features include USAP operations, Antarctic history, profiles on people. Since 2016, the website has featured podcasts about operations. In order of tenure, from most recent: Mike Lucibella Peter Rejcek Steven Profaizer Steve Martaindale Emily Stone Brien Barnett Kris Kuenning Melanie Conner Mark Sabbatini Kristan Hutchison Beth Minneci Jeff Inglis Josh Landis Aaron Spitzer Ginny Figlar Alexander Colhoun Official website Past Issues archive

Defense Attorney

Defense Attorney is an American old-time radio crime drama. It was broadcast on ABC from July 6, 1951, to December 30, 1952, it was known as The Defense Rests. The title character was Martha Ellis "Marty" Barrett, "a respected attorney who has a reputation for integrity" and "who champions causes of the underdog and unjustly accused." Jud Barnes, a newspaper reporter, was Barrett's boyfriend. Ron Lackmann wrote in his book Mercedes McCambridge: A Biography and Career Record that Bryant "spent more time solving crimes with her boyfriend... than she did in the courtroom." Mercedes McCambridge had the title role, Howard Culver played Judson Barnes. Tony Barrett portrayed Detective Lieutenant Ed Ledis. Supporting actors in the program included Paul Fries, Bill Johnston, Kay Wiley, Harry Bartell, Dallas McKennon, Irene Tedrow, Parley Baer. Orville Anderson was the announcer. Warren Lewis was the producer, Dwight Hauser was the director. Cameron Blake, Bill Johnston, Joel Murcott were writers. Music was by Basil Adlam.

Defense Attorney originated with an audition record, The Defense Rests, made for a proposed NBC series in April 1951. In 1953, the trade publication Billboard reported on work on a television version of Defense Attorney. An article in the magazine's March 28, 1953, issue said that Don Sharpe was in New York "to begin sales efforts on his newest film show, Defense Attorney, starring Mercedes McCambridge, based on his former radio series of the same name." Fletcher Markle directed the pilot episode. The proposed series was never developed. McCambridge's work on Defense Attorney led to her receiving honorary membership in the Los Angeles Women's Bar Association and the Favorite Dramatic Actress Award from Radio-TV Mirror magazine. Log of episodes of Defense Attorney from The Digital Deli Too Log of episodes of Defense Attorney from Jerry Haendiges Vintage Radio Logs Log of episodes of Defense Attorney from Old Time Radio Researchers Group Log of episodes of Defense Attorney from radioGOLDINdex Streaming episodes of Defense Attorney from the Internet Archive Streaming episodes of Defense Attorney from Old Time Radio Researchers Group Library

Chapter I of the United Nations Charter

Chapter I of the United Nations Charter lays out the purposes and principles of the United Nations organization. These principles include the equality and self-determination of nations, respect of human rights and fundamental freedoms and the obligation of member countries to obey the Charter, to cooperate with the UN Security Council and to use peaceful means to resolve conflicts; these "purposes and principles" reflect a premise that the effectiveness of the United Nations would be enhanced with broad guidelines to guide the actions of its Organisations and member states. However, some members were concerned that these proposals granted what they considered overly broad discretionary powers for the organs of the United Nations in the Dumbarton Oaks Conference proposals, and the adopted purposes and principles have been seen as reflecting the compromise achieved. The adopted purposes of the United Nations reflect a premise that are the effective Dumbarton Oaks proposals. I.e.:" To maintain international peace and security, to that end: to take effective collective measures for the prevention and removal of threats to the peace, for the suppression of acts of aggression or other breaches of the peace, to bring about by peaceful means, in conformity with the principles of justice and international law, adjustment or settlement of international disputes or situations which might lead to a breach of the peace.

"The Organization and its Members, in pursuit of the Purposes stated in Article 1, shall act in accordance with the following Principles. The Organization is based on the principle of the sovereign equality of all its Members. All Members, in order to ensure to all of them the rights and benefits resulting from membership, shall fulfill in good faith the obligations assumed by them in accordance with the present Charter. All Members shall settle their international disputes by peaceful means in such a manner that international peace and security, justice, are not endangered. All Members shall refrain in their international relations from the threat or use of force against the territorial integrity or political independence of any state, or in any other manner inconsistent with the Purposes of the United Nations. All Members shall give the United Nations every assistance in any action it takes in accordance with the present Charter, shall refrain from giving assistance to any state against which the United Nations is taking preventive or enforcement action.

The Organization shall ensure that states which are not Members of the United Nations act in accordance with these Principles so far as may be necessary for the maintenance of international peace and security. Nothing contained in the present Charter shall authorize the United Nations to intervene in matters which are within the domestic jurisdiction of any state or shall require the Members to submit such matters to settlement under the present Charter. Article 2, clauses 4-5 prohibits activities against the territorial integrity or political independence of another state. Article 2, clause 7 of this chapter reemphasizes the fact that only the UN Security Council has the power to force any country to do anything by stating that "Nothing contained in the present Charter shall authorize the United Nations to intervene in matters which are within the domestic jurisdiction of any state or shall require the Members to submit such matters to settlement under the present Charter. Crime of aggression Universal jurisdiction Kellogg-Briand Pact

Ernest Riddle

Sir Ernest Cooper Riddle was an Australian banker who served as governor of the Commonwealth Bank of Australia Australia's central bank, from 1927 to 1938. Riddle was born in the son of pastoralist John Riddle. In 1889, aged 16, he joined the Narrabri branch of the Bank of Australasia as a clerk. In 1915, Riddle joined the Commonwealth Bank and was appointed the manager of the Perth branch, where he remained until he transferred to Sydney as the acting manager. In 1924, he was promoted to inspector and was transferred to manage the Melbourne branch of the bank. In 1925, Riddle was appointed deputy governor of the Commonwealth Bank and in 1927 became the bank's governor, a position he held until his retirement in 1938. Popular, Riddle served as Australia's most senior banker through the entire Great Depression, he attended the British Empire Economic Conference in Ottawa in 1932 as an adviser on financial matters to the Australian delegation. He travelled twice to London where he played a vital part in exchange-rate deliberations.

Riddle argued against exchange-rate appreciation, opposing the position of the Commonwealth Bank's chairman Sir Robert Gibson. Supported by the Bank of England and aided by a lack of enthusiasm for Gibson's proposal by some board members, Riddle's advice was accepted. Riddle gave evidence at the Royal Commission appointed to inquire into Australia's monetary and banking systems, which ran from 1935 to 1937. Riddle resigned from the Commonwealth Bank on 28 February 1938 due to ill health. Riddle was a keen sportsman and was considered to be an "expert rifle shot" and a "first class golfer and tennis player", he was a member of the Australian Club. For many years he was a major in the Army Reserve and during World War I commanded a training camp in Perth, he had two children. Riddle was knighted in 1935

I Kissed a Girl (Jill Sobule song)

"I Kissed a Girl" is a 1995 song by Jill Sobule. It reached number 20 on the US Billboard Modern Rock Tracks chart, number 67 on the Billboard Hot 100, number 36 on the Australian ARIA Singles Chart. In Canada, it peaked at number 15 on the newly established RPM Alternative 30 chart; the music video featured Italian model Fabio playing Sobule's heterosexual love interest. It parodies his romance novel covers, features young women in 1960s-style hair and dresses. In 2008, new pop-singer Katy Perry issued a song of her own called "I Kissed a Girl" for her debut album One of the Boys; the song received mixed reviews, with some reviewers negatively comparing Perry's song to Sobule's. Hiponline.com wrote that the song is "not nearly as exciting as you'd expect. It’s not half as good as Jill Sobule’s song'I Kissed a Girl'". Glitterati Gossip wrote that Sobule's song "was ten times better, because there was actual emotional content to her lyrics". Sobule shared her feelings about Perry's song and use of the title in a July 2009 interview with The Rumpus:When Katy Perry's song came out I started getting tons of inquiries about what I thought.

Some folks were angry, wondered why she took my title and made it into this kind of "girls gone wild" thing.... As a musician I have always refrained from criticizing another artist. I was, "Well, good for her." It did bug me a little bit, when she said she came up with the idea for the title in a dream. In truth, she wrote it with a team of professional writers and was signed by the same guy that signed me in 1995. I have not mentioned that in interviews as I don't want to sound bitter or petty... Okay, maybe, if I think about it, there were a few jealous and pissed-off moments. So here goes, for the first time in an interview: Fuck you Katy Perry, you fucking stupid, maybe'not good for the gays,' title-thieving, haven't heard much else, so not quite sure if you're talented, fucking little slut. God that felt good. In a interview, Sobule stated that the interview in The Rumpus was tongue-in-cheek and in an article she wrote for The Huffington Post, she stated I thought maybe this time I would have fun with it and goof on what many of my fans were hoping to hear over the last year.

I prefaced my reply with a wink, rambled on with a string of over the top dumb-ass profanities, purposely out of character and in jest... I may be a touch cynical about the business, but I have never been angry or had ill feelings towards Katy herself. I was in a small way happy to not be the "Kissed a Girl" girl anymore. Lyrics of this song at MetroLyrics