.c om cu u du o ng th an co ng ASYMMETRIC CIPHERS CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om Contents Principles Of Public-Key Cryptosystems 2) RSA Algorithm cu u du o ng th an co ng 1) CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om cu u du o ng th an co ng Principles Of Public-Key Cryptosystems CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om Principles Of Public-Key Cryptosystems ng  Commonly know as public key cryptography co  Invented by Whitfield Diffie and Martin Hellman in 1976 th an  Uses a pair of key du o ng  A private key that is kept secret cu u  A public key that can be sent to anyone CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om Public-Key Cryptosystems  Asymmetric algorithms rely on one key for encryption and a different but co ng related key for decryption These algorithms have the following important th an characteristic ng  It is computationally infeasible to determine the decryption key given only du o knowledge of the cryptographic algorithm and the encryption key for decryption cu u  Either of the two related keys can be used for encryption, with the other used CuuDuongThanCong.com https://fb.com/tailieudientucntt cu u du o ng th an co ng c om Encryption with public key CuuDuongThanCong.com https://fb.com/tailieudientucntt cu u du o ng th an co ng c om Encryption with private key CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om Authentication and confidentiality  possible to provide both the authentication function and confidentiality by co ng a double use of the public-key th an  Z=E(PUb,E(PRa,X)) cu u du o ng  X=D(PUa,D(PRb,Z)) CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om Applications for Public-Key Cryptosystems  Encryption/decryption: The sender encrypts a message with the co ng recipient’s public key th an  Digital signature: The sender “signs” a message with its private key cu u du o ng  Key exchange: Two sides cooperate to exchange a session key CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om Requirements for Public-Key Cryptography ng  It is computationally easy for a party B to generate a pair co  It is computationally easy for a sender A, knowing the public key and the th an message to be encrypted,M, to generate the corresponding ciphertext du o ng C=E(PUb,M) u  It is computationally easy for the receiver B to decrypt the resulting cu ciphertext using the private key to recover the original message: CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om Requirements for Public-Key Cryptography  It is computationally infeasible for an adversary, knowing the public co ng key,PUb,to determine the private key,PRb th an  It is computationally infeasible for an adversary, knowing the public key, cu u du o ng PUb, and a ciphertext, C, to recover the original message, M CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om cu u du o ng th an co ng RSA ALGORITHM CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om RSA Algorithm ng  Developed in 1977 by Ron Rivest, Adi Shamir, and Len Adleman co  The RSA scheme is a block cipher in which the plaintext and ciphertext th an are integers between and n-1 for some n A typical size for n is 1024 bits, du o ng or 309 decimal digits That is, n is less than 21024 cu u  Based on exponentiation in a finite field over intergers modulo a prime CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om Description of the Algorithm ng  Select two large prime numbers: p and q co  Calculate: n = pq th an  Calculate: m=(p-1)(q-1) du o ng  Choose a small number e, co prime to m, with GCD(m,e)=1; 1 n = pq=33 th an  Gcd(m,e)=1 du o ng  e corprime to m, means that the largest numbet that can be exactly divide u both e and m (their greatest common divisor, or gcd) is Euclid's cu algorithm is used to find the GCD of two numbers CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om RSA Example  e=2 => GCD(20,e) = (no) co ng  e=3 => GCD(20,e)=1 (yes!) an  Find d: using Extended Euclid's algorithm ? d=7 ng du o Plaintext: M = 15: th  PU (33, 3), PR = (33, 7) cu Deencryption: c=9 u Encryption: C = 153mod 33 = M = 97mod 33 = 15 CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om RSA Security ng  Brute-force attack co  Mathematical attack ng cu u du o  Chosen ciphertext attack th an  Timing attack CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om ng co an th ng du o u cu CuuDuongThanCong.com https://fb.com/tailieudientucntt ... key cryptography co  Invented by Whitfield Diffie and Martin Hellman in 19 76 th an  Uses a pair of key du o ng  A private key that is kept secret cu u  A public key that can be sent to anyone... Developed in 1977 by Ron Rivest, Adi Shamir, and Len Adleman co  The RSA scheme is a block cipher in which the plaintext and ciphertext th an are integers between and n-1 for some n A typical size for... du o ng PUb, and a ciphertext, C, to recover the original message, M CuuDuongThanCong.com https://fb.com/tailieudientucntt .c om cu u du o ng th an co ng RSA ALGORITHM CuuDuongThanCong.com https://fb.com/tailieudientucntt