tailieunhanh - cryptography for developers PHẦN 10

Hành động này này thường được biết đến như là bộ nhớ trao đổi, vì nó cho phép người dùng để thi đua có bộ nhớ vật lý hơn so với họ thực sự làm. Nhược điểm để trao đổi bộ nhớ, tuy nhiên, là bộ nhớ có thể chứa thông tin nhạy cảm như khóa riêng, tên người dùng, mật khẩu, và các thông tin khác. | Public Key Algorithms Chapter 9 383 RSA used to fall under a . patent which has since original RSA including the PKCS 1 padding are now entirely patent are patents on variants of RSA such as multiprime RSA however these are not as popularly deployed and often are avoided for various security concerns. RSA in a Nutshell We will now briefly discuss the mathematics behind RSA so the rest of this chapter makes proper sense. Key Generation Key generation for RSA is conceptually a simple process. It is not trivial in practice especially for implementations seeking speed Figure . Figure RSA Key Generation Input e Public exponent n Desired bit length of the modulus Output n Public modulus d Private exponent 1. Choose a random prime p of length n 2 bits such that gcd p-1 e 1 2. Choose a random prime q of length n 2 bits such that gcd q-1 e 1 3. Let n pq 4. Compute d e mod p 1 q 1 5. Return n d The e exponent must be odd as p 1 and q 1 will both have factors of two in them. Typically e is equal to 3 17 or 65537 which are all efficient to use as a power for exponentiation. The value of d is such that for any m that does not divide n we will have the property that me d is congruent to m mod n similarly md e is also congruent to the same value. The pair e and n form the public key while the pair d and n form the private key. A party given e and n cannot trivially compute d nor trivially reverse the computation c me mod n. For details on how to choose primes one could consider reading various sources such as BigNum Math Tom St Denis Greg Rose BigNum Math Implementing Cryptographic Multiple Precision Arithmetic Syngress 2006 which discuss the matters in text also discusses other facets required for fast RSA operations such as fast modular exponentiation. The reader could also consider The Art Of Computer Programming Donald Knuth The Art of 384 Chapter 9 Public Key Algorithms Computer Programming Volume 2 third edition