Editing One-time pad (section)

===True randomness===
High-quality random numbers are difficult to generate.  The random number generation functions in most [[programming language]] libraries are not suitable for cryptographic use. Even those generators that are suitable for normal cryptographic use, including [[/dev/random]] and many [[hardware random number generator]]s, may make some use of cryptographic functions whose security has not been proven. An example of a technique for generating pure randomness is measuring [[Radioactive decay|radioactive emissions]].<ref>{{Cite book|title=The Code Book|last=Singh|first=Simon|publisher=Anchor Books|year=2000|isbn=978-0-385-49532-5|location=United States|pages=[https://archive.org/details/codebook00simo/page/123 123]|url=https://archive.org/details/codebook00simo/page/123}}</ref>

In particular, one-time use is absolutely necessary. For example, if <math>p_1</math> and <math>p_2</math> represent two distinct plaintext messages and they are each encrypted by a common key <math>k</math>, then the respective ciphertexts are given by:

:<math>c_1 = p_1 \oplus k</math>
:<math>c_2 = p_2 \oplus k</math>

where <math>\oplus</math> means [[XOR]]. If an attacker were to have both ciphertexts <math>c_1</math> and <math>c_2</math>, then simply taking the [[XOR]] of <math>c_1</math> and <math>c_2</math> yields the [[XOR]] of the two plaintexts <math>p_1 \oplus p_2</math>. (This is because taking the [[XOR]] of the common key <math>k</math> with itself yields a constant bitstream of zeros.)  <math>p_1 \oplus p_2</math> is then the equivalent of a running key cipher.{{cn|date=December 2023}}

If both plaintexts are in a [[natural language]] (e.g., English or Russian), each stands a very high chance of being recovered by [[heuristic]] cryptanalysis, with possibly a few ambiguities. Of course, a longer message can only be broken for the portion that overlaps a shorter message, plus perhaps a little more by completing a word or phrase. The most famous exploit of this vulnerability occurred with the [[Venona project]].<ref name="nsa">{{cite news|title=The Translations and KGB Cryptographic Systems|url=http://www.nsa.gov/about/_files/cryptologic_heritage/publications/coldwar/venona_story.pdf|work=The Venona Story|publisher=[[National Security Agency]]|location=[[Fort Meade, Maryland]]|date=2004-01-15|pages=26–27 (28–29th of 63 in PDF)|access-date=2009-05-03|archive-url=https://web.archive.org/web/20090510052927/http://www.nsa.gov/about/_files/cryptologic_heritage/publications/coldwar/venona_story.pdf|archive-date=2009-05-10|quote=KGB's cryptographic material manufacturing center in the Soviet Union apparently reused some of the pages from one-time pads. This provided [[Arlington Hall]] with an opening.|url-status = dead}}</ref>