8/9/2023 0 Comments Link it answersWe randomly selected a model-written message, sampled several alternative completions, and had AI trainers rank them. To collect this data, we took conversations that AI trainers had with the chatbot. To create a reward model for reinforcement learning, we needed to collect comparison data, which consisted of two or more model responses ranked by quality. We mixed this new dialogue dataset with the InstructGPT dataset, which we transformed into a dialogue format. We gave the trainers access to model-written suggestions to help them compose their responses. We trained an initial model using supervised fine-tuning: human AI trainers provided conversations in which they played both sides-the user and an AI assistant. We trained this model using Reinforcement Learning from Human Feedback (RLHF), using the same methods as InstructGPT, but with slight differences in the data collection setup. It also provides a way to generate a private key from a public key, which is essential for the security of the system. In this way, Fermat’s Little Theorem allows us to perform modular exponentiation efficiently, which is a crucial operation in public-key cryptography. To decrypt the message, the recipient simply computes m = c b m o d n m = c^b \bmod n m = c b mod n, which (by Fermat’s Little Theorem) is equivalent to m = ( m a ) b m o d n = m ( a b ) m o d n = m 1 m o d n = m m o d n m = (m^a)^b \bmod n = m^(ab) \bmod n = m^1 \bmod n = m \bmod n m = ( m a ) b mod n = m ( ab ) mod n = m 1 mod n = m mod n. To encrypt a message with the user’s public key ( n, a ) (n, a) ( n, a ), we first convert the message into a number m m m (using some agreed-upon scheme), and then compute the encrypted message c c c as c = m a m o d n c = m^a \bmod n c = m a mod n. This means that when we multiply a a a and b b b together, the result is congruent to 1 1 1 modulo n n n. The user’s private key would be the pair ( n, b ) (n, b) ( n, b ), where b b b is the modular multiplicative inverse of a modulo n n n. The user’s public key would then be the pair ( n, a ) (n, a) ( n, a ), where aa is any integer not divisible by p p p or q q q. We might choose two large prime numbers, p p p and q q q, and then compute the product n = p q n = pq n = pq. For example, suppose we want to generate a public-key cryptography system for a user with the initials “ABC”. One way to generate these keys is to use prime numbers and Fermat’s Little Theorem. In a public-key cryptography system, each user has a pair of keys: a public key, which is widely known and can be used by anyone to encrypt a message intended for that user, and a private key, which is known only to the user and is used to decrypt messages that have been encrypted with the corresponding public key. One of the most common applications is in the generation of so-called “public-key” cryptography systems, which are used to securely transmit messages over the internet and other networks. This will boost your mark even further! Sometimes it's easy to forget the link since it's just a sentence at the end of each paragraph - I'd recommend writing a small reminder next to the question on your exam paper so every time you look at it, you'll be reminded.Fermat’s Little Theorem is used in cryptography in several ways. If you want to take linking back to another level, try adding nuanced vocabulary like "this proves to a substantial degree" etc. It might seem a bit simplistic, but it makes it clear to the examiner where you are in that particular paragraph and is also another way of restating your argument in simpler terms. What is even more important to make sure that in doing this, you are linking your argument to the question and explaining how it answers the question you've been asked.įor example, if you took the question ‘In 1776, Britain had reason to be fully confident of military success against the American colonies’ from one of the 2018 AQA A Level papers, at the end of each paragraph, you should say something along the lines of "Therefore, this proves that Britain had every reason to be fully confident of military success against the American colonies," if that's the way you were answering the question. The easiest way to do this, is to literally copy out parts of the question at the end of each paragraph. Linking back to the question is one of the most important parts of an essay - At A Level, it's what will push you up into the higher grade brackets.
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