Public Key Cryptography and RSA: Chapter 9 from "Cryptography and Network Security" by Wil, Lecture notes of Cryptography and System Security

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Cryptograph

y and

Network

Security

Sixth Edition by William Stallings

Chapter 9

Public Key Cryptography and RSA

Misconceptions Concerning Public-Key Encryption

• (^) Public-key encryption is more secure from

cryptanalysis than symmetric encryption

• (^) Public-key encryption is a general-purpose

technique that has made symmetric

encryption obsolete

• (^) There is a feeling that key distribution is

trivial when using public-key encryption,

compared to the cumbersome handshaking

involved with key distribution centers for

symmetric encryption

Table 9. Terminology Related to Asymmetric Encryption Source: Glossary of Key Information Security Terms , NIST IR 7298 [KISS06]

Public-Key Cryptosystems

• (^) A public-key encryption scheme has six ingredients:

Public-Key Cryptograp hy

Public-Key Cryptosystem: Secrecy

Public-Key Cryptosystem: Authentication

Applications for Public-Key Cryptosystems

• (^) Public-key cryptosystems can be classified

into three categories:

• (^) Some algorithms are suitable for all three

applications, whereas others can be used

only for one or two

Table 9. Applications for Public-Key Cryptosystems Table 9.3 Applications for Public-Key Cryptosystems

Public-Key Requirements

• (^) Need a trap-door one-way function
  • (^) A one-way function is one that maps a domain into a range such that every function value has a unique inverse, with the condition that the calculation of the function is easy, whereas the calculation of the inverse is infeasible
    • (^) Y = f(X) easy
    • (^) X = f–1(Y) infeasible
• (^) A trap-door one-way function is a family of invertible functions fk, such that - Y = fk(X) easy, if k and X are known - X = fk –1(Y) easy, if k and Y are known - X = fk –1(Y) infeasible, if Y known but k not known
• (^) A practical public-key scheme depends on a suitable trap- door one-way function

Public-Key Cryptanalysis

• (^) A public-key encryption scheme is vulnerable to a brute-force attack
  • (^) Countermeasure: use large keys
  • (^) Key size must be small enough for practical encryption and decryption
  • (^) Key sizes that have been proposed result in encryption/decryption speeds that are too slow for general-purpose use
  • (^) Public-key encryption is currently confined to key management and signature applications
• (^) Another form of attack is to find some way to compute the private key given the public key
  • (^) To date it has not been mathematically proven that this form of attack is infeasible for a particular public-key algorithm
• (^) Finally, there is a probable-message attack
  • (^) This attack can be thwarted by appending some random bits to simple messages

RSA Algorithm

• (^) RSA makes use of an expression with exponentials
• (^) Plaintext is encrypted in blocks with each block having a binary value less than some number n
• (^) Encryption and decryption are of the following form, for some plaintext block M and ciphertext block C C = Me^ mod n M = C d mod n = (M e ) d mod n = M ed mod n
• (^) Both sender and receiver must know the value of n
• (^) The sender knows the value of e, and only the receiver knows the value of d
• (^) This is a public-key encryption algorithm with a public key of PU={e,n} and a private key of PR={d,n}

Algorithm Requirements

• (^) For this algorithm to be satisfactory for public-key encryption, the following requirements must be met: 1. It is possible to find values of e, d, n such that M ed mod n = M for all M < n 2. It is relatively easy to calculate M e mod n and C d mod n for all values of M < n 3. It is infeasible to determine d given e and n