The dark side of the web - The Computing Universe: A Journey through a Revolution - page 256

Fig. 12.14. (a) Symmetric encryption
shares the same encryption key between
sender and receiver. (b) Asymmetric
encryption uses a different encryption
key at each end of the communication.

(a)

Encryption Decryption

Message Ciphertext

Encoding Decryption

Encoded message Encoded message

Encryption Decoding

Message

Ciphertext

(b) Encryption Decryption

Message Ciphertext

Encoding Decryption

Private key

Encoded message Encoded message

Encryption Decoding

Public key

Message

Ciphertext

others. Another breakthrough was needed to arrive at a secure and convenient
cryptographic method that eliminated key exchange bottlenecks.
Up until 1975, all the encryption techniques in history had been symmet-
ric , meaning that the key to unscramble the message was the same as the key
used to scramble it in the first place ( Fig. 12.14a ). In the summer of 1975, Diffie
outlined the idea for a new type of cipher that used an asymmetric key pair, one
in which the encryption key and the decryption key were different but math-
ematically related ( Fig. 12.14b ). Although he showed that such a system could
work in theory, Diffie was unable to find a suitable one-way function to actu-
ally carry out his idea. If such a system could be found, then it could work as
follows. Alice would have two keys, one for encryption and one for decryption.
She can make her encryption key public, her “public key,” so that everyone has
access to it, but she keeps her decryption key secret as her “private key.” Now if
Bob wants to send a message to Alice, he can encrypt his message using Alice's
public key. When she receives the message, Alice is able to decrypt the mes-
sage using her private key, secure in the knowledge that Eve, who only knows
Alice's public key, would be unable to make sense of the message. This is the
essence of the cryptographic system called public-key cryptography .

RSA encryption and pretty good privacy
The race to make asymmetric ciphers a reality was won by three research-
ers working in the Laboratory for Computer Science at MIT: Ron Rivest, Adi
Shamir, and Len Adleman ( B.12.7 ). Their resulting scheme is now known as
RSA encryption , and it depends on modular exponentiation and the difficulty
of factoring large numbers. The scheme relies on the fact that multiplication
of two large prime numbers, p and q, to get the number N is very easy and