The Bridge - February 2018 - 19

time pad to encrypt the message. Prior to sending
the message, Alice and Bob meet in person and
generates a string of three random numbers: 4 13
6. They both record those numbers, keeping them
secret, and go their separate ways.
When Alice is ready to send her message, she
first converts her message, C A T, to its numerical
equivalent, 3 1 20. She then adds her three random
numbers (the key) to her numerical message, one
by one:
+

3
4
7

1
13
14

20
6
26

Alice obtains 7 14 26 as a result, and sends this to
Bob over an unsecured channel (e.g. email). Note
that translating this sequence of numbers to letters
would yield a meaningless G N Z. Upon receiving the
message, Bob simply subtracts the random numbers
selected earlier:
+

7
4
3

14
13
1

26
6
20

Translating those numbers to letters, Bob obtains
the original message, C A T.
This is the general procedure of the one-time pad.
Its security lies in the fact that random numbers
were used to encrypt the message prior to
transmission. Because of this, it is impossible for an
eavesdropper, Eve, who manages to intercept this
message midtransmission, to decipher it. All Eve
knows is G N Z (7 14 26). She has no additional
information regarding the encryption key used, so
while she could guess, she cannot find the correct
decryption with certainty [9]. For example, she
would not be able to confidently identify the correct
message if she gets either C A T or B O B as a result
of her decryption attempt.
In his 1949 paper, C.K. Shannon proves that as
long as the random key is only used once and is
the same length as the message itself (or longer),

the one-time pad is capable of achieving perfect
secrecy [10]. The random nature of the one-time
pad transformation does not skew the probability
distribution of possible encrypted messages such
that an eavesdropper would be able to deduce the
original message through probabilistic analysis of the
encrypted message [9].
This naturally leads us to recognize the main
limitations of the one-time pad. First, one-time pad
keys can be used only once. Otherwise, if the same
key was used multiple times, Eve would be able
to use facts such as that certain words occur more
frequently than others in English to improve her
chances of guessing the key [9]. Second, for reasons
similar to the one-time-use requirement, the length
of the keys used must be longer than the actual
message itself.
Those limitations are the main factors preventing
the widespread adoption of the onetime pad as an
encryption standard. There is no known classical
means of distributing (or regenerating) a key with
absolute security. Additionally, for frequent and
lengthy communications, extremely large amounts
of keys would be required. Even worse, carrying
around a packet of all the pre-made keys makes
them susceptible to theft. Finally, the logistics of
coordinating all the keys become prohibitively
difficult when scaling up from two people
(Alice and Bob) to large institutions.
2.2 Public Key Cryptography
Due to the inherent difficulties of the one-time pad,
the majority of modern-day encryption schemes
rely on public key cryptography, which works
differently from the one-time pad. Generally, with
a public key cryptosystem, the receiver (Bob)
performs a procedure to create two keys that share
a mathematical relationship, one public and one
private. Bob then announces the public key while
keeping the private key a secret.
Upon receiving the public key, the sender (Alice)
can then use it to encrypt a message such that the

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19
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Table of Contents for the Digital Edition of The Bridge - February 2018
