tailieunhanh - modern cryptography theory and practice wenbo mao phần 8

đặc biệt là những người dựa trên công keycryptography, có cơ bản hoặc cái gọi là "sách giáo khoa mật mã", như versionsare những thường các đối tượng cho {nhiều sách giáo khoa về mật mã. Cuốn sách này có cách tiếp cận adifferent giới thiệu mật mã: tofit quan tâm nhiều hơn nữa cho các khía cạnh ứng dụng của mật mã. | Bob sends to Alice EN m C1 c2 . Cl . Decryption Upon receipt an -tuple ciphertext C1 c2 . Cl Alice performs for i I 2 . 1 if ci Q b i - 0 else bi 1 setm b1 b2 . bi . Since computing Legendre symbol mod p and mod q with p q k can be done in OB k2 bit operations review the discussion after Alg on careful realization of the Jacobi-symbol algorithm decryption of C1 c2 . Cl requires Os l log2W 2 bit operations. This is the time complexity for decryption. The bit-by-bit fashion of encryption means that the GM cryptosystem is highly inefficient. The Security of the GM Cryptosystem The encryption algorithm of the GM cryptosystem can be considered as an error-free randomized algorithm the random operations in the encryption algorithm can introduce no any error into the ciphertext but achieve the following important function Distributing the plaintext bit 0 uniformly that is correctly over QRN and the plaintext bit 1 uniformly over JN 1 QRN. r . . 7 Both distributions are uniform. This is because for the plaintext bit 0 squaring maps from onto QRN and for the plaintext bit 1 multiplying- to an element in QRN is a permutation from _ . 7 . . QRN onto JN 1 QRN. Thus picking x u in the encryption algorithm means picking either a uniform element in QRN if the plaintext bit is 0 or a uniform element in JN 1 QRN if the plaintext bit is 1. To express it formally we say that the difficulty of the GM cryptosystem is that of deciding the quadratic residuosity problem QR problem which is formally specified in Definition in . The QR problem is a well-known hard problem in number theory review the discussion we provided after Definition . We have the following assumption on its intractability. Assumption Quadratic Residuosity Assumption QR Assumption Let IG be an integer instance generator that on input 1k runs in time polynomial in k and outputs a 2k-bit modulus N pq where p and q are each a k-bit uniformly random odd prime. We say that IG satisfies .

TỪ KHÓA LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
crossorigin="anonymous">
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.