Transcript 11/7/2015 2:01:37 AM AIIS OUTLINE  Introduction  Goals In Cryptography  Secrete Key Cryptography  Public Key Cryptograpgy  Digital Signatures 11/7/2015 2:01:37 AM AIIS.

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OUTLINE
 Introduction
 Goals In Cryptography
 Secrete Key Cryptography
 Public Key Cryptograpgy
 Digital Signatures
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AN OVERVIEW OF CRYPTOGRAPHY:

Cryptography is derived from the Greek words: Kryptos,
“hidden”, and Graphein, ”to write ” or “hidden writing”.

The word cryptography means “secret writing”.
However, the term today refers to the science and of
transforming messages to make them secure and immune to
attacks.

The original message before being transformed is called
plaintext. After the message is transformed, it is called cipher
text. An encryption algorithm transforms the plaintext to cipher;
a decryption algorithm transforms the cipher text back to
plaintext. The sender uses an encryption algorithm, and the
receiver uses a decryption algorithm.
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Goals in Cryptography
 Message Confidentiality
 Message integrity
 Sender authentication
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SENDER
RECEIVER
Plaintext
Encryption
Ciphertext
Network
Ciphertext
Decryption
Cryptography Components
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These encryption and decryption
algorithms are called as ciphers (categories of
algorithm). One cipher can serve millions of
communicating pairs.
 A Key is value that the cipher, as an algorithm,
operates on. To encrypt a message we need an
encryption algorithm, an encryption key, and
the plain text. These create the cipher text. To
decrypt a message, we need a decryption
algorithm, and the cipher text. So these reveal
the original plaintext.

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DECRYPTION KEY
ENCRYPTION KEY
ENCRYPTION
ALGORITHM
DECRYPTION
ALGORITHM
Plain text
Plain text
Ciphertext
a. Encryption
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b. Decryption
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Secret Key Cryptography
• Single key used to encrypt and decrypt.
• Key must be known by both parties.
• Assuming we live in a hostile environment (otherwise why the need for cryptography?), it may be hard to
share a secret key.
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In Cryptography, the encryption/decryption
algorithms are public; anyone can access them. The
keys are secret. So they need to be protected.
Cryptography algorithms can be divided into two
groups.
 Symmetric-key cryptography (or secret key)
algorithm
 Public-key cryptography (or asymmetric key)
algorithm
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Symmetric-key cryptography
 If the sender and recipient must have the same key
in order to encode or decode the protected
information , then the cipher is a symmetric key
cipher since everyone uses the same key for the
same message . The main problem is that the secret
key must somehow be given to both the sender and
recipient privately. For this reason, symmetric key
(or secret key ) ciphers.
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Public Key Cryptography
(a.k.a. asymmetric cryptography)
• If the sender and recipient have different keys
•
respective to the communication roles they play,
then the cipher is an asymmetric key cipher as
different keys exist for encoding and decoding the
same message.
Each entity has 2 keys:
› private key (a secret)
› public key (well known).
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Using Keys
• Private keys are used for decrypting.
• Public keys are used for encrypting.
encryption
plaintext
ciphertext
public key
decryption
ciphertext
plaintext
private key
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Digital Signature
• Public key cryptography is also used to provide
digital signatures.
signing
plaintext
signed message
private key
signed message
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verification
plaintext
public key
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Revised Scheme
Alice
Bob
Sign with Aprivate
encrypt using Bpublic
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check signature using Apublic
decrypt using Bprivate
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THANK YOU
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RSA Algorithm
 In cryptography, RSA (which stands for Rivest,
Shamir and Adleman who first publicly described it)
is an algorithm for public-key cryptography.[1] It is
the first algorithm known to be suitable for signing as
well as encryption, and was one of the first great
advances in public key cryptography. RSA is widely
used in electronic commerce protocols, and is
believed to be secure given sufficiently long keys and
the use of up-to-date implementations.
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 Operation
The RSA algorithm involves three steps: key generation, encryption and
decryption.
 Key generation
RSA involves a public key and a private key. The public key can be
known to everyone and is used for encrypting messages. Messages encrypted
with the public key can only be decrypted using the private key. The keys for
the RSA algorithm are generated the following way:
1.
Choose two distinct prime numbers p and q.
 For security purposes, the integers p and q should be chosen uniformly at
random and should be of similar bit-length. Prime integers can be
efficiently found using a primality test.
2.
Compute n = pq.
 n is used as the modulus for both the public and private key
3.
Compute φ(pq) = (p − 1)(q − 1). (φ is Euler's totient function).
4.
Choose an integer e such that 1 < e < φ(pq), and e and φ(pq) share no
divisors other than 1 (i.e., e and φ(pq) are coprime).
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 e is released as the public key exponent.
 e having a short bit-length and small Hamming weight results in more
efficient encryption. However, small values of e (such as e = 3) have been
shown to be less secure in some settings.
5.
Determine d (using modular arithmetic) which satisfies the
congruence relation .
 Stated differently, ed − 1 can be evenly divided by the totient (p − 1)(q − 1).
 This is often computed using the extended Euclidean algorithm.
 d is kept as the private key exponent.
The public key consists of the modulus n and the public (or
encryption) exponent e. The private key consists of the private (or decryption)
exponent d which must be kept secret.
Note:An alternative, used by PKCS#1, is to choose d matching e d ≡ 1 (mod λ)
with λ = lcm(p-1,q-1), where lcm is the least common multiple. Using λ
instead of φ(n) allows more choices for d. λ can also be defined using the
Carmichael function λ(n).
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An alternative, used by PKCS#1, is to choose d matching e d ≡ 1 (mod λ) with λ =
lcm(p-1,q-1), where lcm is the least common multiple. Using λ instead of φ(n)
allows more choices for d. λ can also be defined using the Carmichael function
λ(n).
 For efficiency the following values may be precomputed and stored as part
of the private key:

p and q: the primes from the key generation,

and
Encryption
Alice transmits her public key (n,e) to Bob and keeps the private key secret. Bob
then wishes to send message M to Alice.
He first turns M into an integer 0 < m < n by using an agreed-upon reversible
protocol known as a padding scheme. He then computes the ciphertext c
corresponding to:
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This can be done quickly using the method of exponentiation by squaring.
Bob then transmits c to Alice.
Decryption
Alice can recover m from c by using her private key exponent d by the
following computation:
Given m, she can recover the original message M by reversing the padding
scheme.
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THANK YOU
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