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BY
RAFIDH
PUBLIC-KEY
CRYPTOGAPHY
AND RSA
Outline
principles of public--key
cryptography
RSA algorithm,
implementation, security
Structure Cipher Systems
Symmetric
algorithm
Stream Cipher Block Cipher
AESRC4
Cipher Systems
DES
ASymmetric
algorithm
RSA
Public key
encryption
Asymmetric encryption is a form of cryptosystem in which
encryption and decryption are performed using the different
keys—one a public key and one a private key. It is also known as
public-key encryption.
 Asymmetric encryption transforms plaintext into ciphertext
using a one of two keys and an encryption algorithm. Using the
paired key and a decryption algorithm, the plaintext is
recovered from the ciphertext.
 Asymmetric encryption can be used for confidentiality,
authentication, or both.
 The most widely used public-key cryptosystem is RSA. The
difficulty of attacking RSA is based on the difficulty of finding
the prime factors of a composite number.
Key points
PUBLIC-KEY CRYPTOGAPHY
The concept of public-key cryptography evolved
from an attempt to attack two of the most difficult
problems associated with symmetric encryption :
 The first problem is that of key distribution .
The second problem and one that was apparently
unrelated to the first, was that of digital
signatures.
 Asymmetric algorithms rely on one key for encryption and a
different but related key for decryption .These algorithms
have the following important characteristic.
 It is computationally infeasible to determine the decryption
key given only knowledge of the cryptographic algorithm
and the encryption key.
Public-Key Cryptosystems
 Plaintext: This is the readable message or data that is fed
into the algorithm as input.
 Encryption algorithm: The encryption algorithm performs
various transformations on the plaintext.
 Public and private keys: This is a pair of keys that have
been selected so that if one is used for encryption, the other is
used for decryption. The exact transformations performed by
the algorithm depend on the public or private key that is
provided as input.
scheme has six ingredients
 Ciphertext: This is the scrambled message produced
as output. It depends on the plaintext and the key.
For a given message, two different keys will produce
two different ciphertexts.
 Decryption algorithm: This algorithm accepts the
ciphertext and the matching key and produces the
original plaintext.
1. Each user generates a pair of keys to be used for the encryption
and decryption of messages.
2. Each user places one of the two keys in a public register or other
accessible file. This is the public key.The companion key is kept
private.
3. If Bob wishes to send a confidential message to Alice, Bob
encrypts the message using Alice’s public key.
4. When Alice receives the message, she decrypts it using her
private key. No other recipient can decrypt the message because
only Alice knows Alice’s private key.
The essential steps are the following :
 Encryption /decryption: The sender encrypts a message with
the recipient’s public key.
 Digital signature: The sender “signs” a message with its
private key. Signing is achieved by a cryptographic algorithm
applied to the message or to a small block of data of the
message.
 Key exchange: Two sides cooperate to exchange a session key.
Applications for Public-Key Cryptosystems
1. It is computationally easy for a party B to generate a pair
(public key PUb, private key PRb).
2. It is computationally easy for a sender A, knowing the public
key and the message to be encrypted,M, to generate the
corresponding ciphertext:
C = E(PUb,M)
3. It is computationally easy for the receiver B to decrypt the
resulting ciphertext using the private key to recover the
original message:
M = D(PRb, C) = D[PRb, E(PUb,M)]
Requirements for Public-Key
Cryptography
4. It is computationally infeasible for an adversary, knowing the
public key, PUb, to determine the private key,PRb.
5. It is computationally infeasible for an adversary, knowing the
public key, PUb, and a ciphertext, C, to recover the original
message,M. We can add a sixth requirement that, although useful,
is not necessary for all public-key applications:
6. The two keys can be applied in either order:
M = D[PUb, E(PRb,M)] = D[PRb, E(PUb,M)]
Requirements for Public-Key
Cryptography
 developed in 1977 by Ron Rivest, Adi Shamir, and Len Adleman
at MIT and first published in 1978 .
 The RSA scheme is a block cipher in which the plaintext and
ciphertext are integers between 0 and n - 1 for some n.
 A typical size for n is 1024 bits, or 309 decimal digits.
 Encryption and decryption are of the following form, for some
plaintext block M and ciphertext block C.

THE RSA ALGORITHM
Both sender and receiver must know the
value of n.
 The sender knows the value of e.
 only the receiver knows the value of d.
 public key of PU = {e, n}.
 a private key of PR = {d, n}.
THE RSA ALGORITHM
the following requirements must be met
 The resulting keys are public key PU = {7, 187} and private
key PR = {23, 187}, the example shows the use of these keys
for plaintext M = 88 .
 For encryption
 88^7 mod 187 = [(88^4 mod 187) × (88^2 mod 187)
 × (88^1 mod 187)] mod 187
 88^1 mod 187 = 88
 88^2 mod 187 = 7744 mod 187 = 77
 88^4 mod 187 = 59,969,536 mod 187 = 132
 88^7 mod 187 = (88 × 77 × 132) mod 187 = 894,432 mod 187
= 11
RSA Processeing of Multiple Blocks
Four possible approaches to attacking the RSA algorithm are
 Brute force: This involves trying all possible private keys.
 Mathematical attacks: There are several approaches, all
equivalent in effort to factoring the product of two primes.
 Timing attacks: These depend on the running time of the
decryption algorithm.
 Chosen ciphertext attacks: This type of attack exploits properties
of the RSA algorithm.
The Security of RSA
Information and data security public key cryptography and rsa

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Information and data security public key cryptography and rsa

  • 2. Outline principles of public--key cryptography RSA algorithm, implementation, security
  • 3. Structure Cipher Systems Symmetric algorithm Stream Cipher Block Cipher AESRC4 Cipher Systems DES ASymmetric algorithm RSA Public key encryption
  • 4. Asymmetric encryption is a form of cryptosystem in which encryption and decryption are performed using the different keys—one a public key and one a private key. It is also known as public-key encryption.  Asymmetric encryption transforms plaintext into ciphertext using a one of two keys and an encryption algorithm. Using the paired key and a decryption algorithm, the plaintext is recovered from the ciphertext.  Asymmetric encryption can be used for confidentiality, authentication, or both.  The most widely used public-key cryptosystem is RSA. The difficulty of attacking RSA is based on the difficulty of finding the prime factors of a composite number. Key points
  • 5. PUBLIC-KEY CRYPTOGAPHY The concept of public-key cryptography evolved from an attempt to attack two of the most difficult problems associated with symmetric encryption :  The first problem is that of key distribution . The second problem and one that was apparently unrelated to the first, was that of digital signatures.
  • 6.  Asymmetric algorithms rely on one key for encryption and a different but related key for decryption .These algorithms have the following important characteristic.  It is computationally infeasible to determine the decryption key given only knowledge of the cryptographic algorithm and the encryption key. Public-Key Cryptosystems
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  • 9.  Plaintext: This is the readable message or data that is fed into the algorithm as input.  Encryption algorithm: The encryption algorithm performs various transformations on the plaintext.  Public and private keys: This is a pair of keys that have been selected so that if one is used for encryption, the other is used for decryption. The exact transformations performed by the algorithm depend on the public or private key that is provided as input. scheme has six ingredients
  • 10.  Ciphertext: This is the scrambled message produced as output. It depends on the plaintext and the key. For a given message, two different keys will produce two different ciphertexts.  Decryption algorithm: This algorithm accepts the ciphertext and the matching key and produces the original plaintext.
  • 11. 1. Each user generates a pair of keys to be used for the encryption and decryption of messages. 2. Each user places one of the two keys in a public register or other accessible file. This is the public key.The companion key is kept private. 3. If Bob wishes to send a confidential message to Alice, Bob encrypts the message using Alice’s public key. 4. When Alice receives the message, she decrypts it using her private key. No other recipient can decrypt the message because only Alice knows Alice’s private key. The essential steps are the following :
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  • 14.  Encryption /decryption: The sender encrypts a message with the recipient’s public key.  Digital signature: The sender “signs” a message with its private key. Signing is achieved by a cryptographic algorithm applied to the message or to a small block of data of the message.  Key exchange: Two sides cooperate to exchange a session key. Applications for Public-Key Cryptosystems
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  • 16. 1. It is computationally easy for a party B to generate a pair (public key PUb, private key PRb). 2. It is computationally easy for a sender A, knowing the public key and the message to be encrypted,M, to generate the corresponding ciphertext: C = E(PUb,M) 3. It is computationally easy for the receiver B to decrypt the resulting ciphertext using the private key to recover the original message: M = D(PRb, C) = D[PRb, E(PUb,M)] Requirements for Public-Key Cryptography
  • 17. 4. It is computationally infeasible for an adversary, knowing the public key, PUb, to determine the private key,PRb. 5. It is computationally infeasible for an adversary, knowing the public key, PUb, and a ciphertext, C, to recover the original message,M. We can add a sixth requirement that, although useful, is not necessary for all public-key applications: 6. The two keys can be applied in either order: M = D[PUb, E(PRb,M)] = D[PRb, E(PUb,M)] Requirements for Public-Key Cryptography
  • 18.  developed in 1977 by Ron Rivest, Adi Shamir, and Len Adleman at MIT and first published in 1978 .  The RSA scheme is a block cipher in which the plaintext and ciphertext are integers between 0 and n - 1 for some n.  A typical size for n is 1024 bits, or 309 decimal digits.  Encryption and decryption are of the following form, for some plaintext block M and ciphertext block C.  THE RSA ALGORITHM
  • 19. Both sender and receiver must know the value of n.  The sender knows the value of e.  only the receiver knows the value of d.  public key of PU = {e, n}.  a private key of PR = {d, n}. THE RSA ALGORITHM
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  • 22.  The resulting keys are public key PU = {7, 187} and private key PR = {23, 187}, the example shows the use of these keys for plaintext M = 88 .  For encryption  88^7 mod 187 = [(88^4 mod 187) × (88^2 mod 187)  × (88^1 mod 187)] mod 187  88^1 mod 187 = 88  88^2 mod 187 = 7744 mod 187 = 77  88^4 mod 187 = 59,969,536 mod 187 = 132  88^7 mod 187 = (88 × 77 × 132) mod 187 = 894,432 mod 187 = 11
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  • 26. RSA Processeing of Multiple Blocks
  • 27. Four possible approaches to attacking the RSA algorithm are  Brute force: This involves trying all possible private keys.  Mathematical attacks: There are several approaches, all equivalent in effort to factoring the product of two primes.  Timing attacks: These depend on the running time of the decryption algorithm.  Chosen ciphertext attacks: This type of attack exploits properties of the RSA algorithm. The Security of RSA