By Pierre van Baal
Lawsuits of a NATO ASI and Isaac Newton Institute Workshop held in Cambridge, united kingdom, June 23-July four, 1997
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3 of the Appendix useful for these computations. Now, the number 7 represents the letter H, 18 represents S, and 6 represents G, so the ciphertext is HSSG. Notice that this method substitutes blocks of two letters for blocks of two letters as we originally desired, but the advantage is that instead of recording all 676 substitutions, all Alice and Bob need to know is the matrix K. How does Bob ﬁnd the plaintext given the ciphertext? Bob knows K and yi for all i. He wants to ﬁnd xi for all i. In other words, he wants to solve the equation yi = K xi for xi .
He computes 17543 (mod 671) and 32643 (mod 671). You can verify that he gets 98 and 101. ” Note that if an eavesdropper knows p and q, she can crack the cipher. But to ﬁnd these primes, she would have to factor n. The idea is that Bob chooses the primes so large that for Eve to factor n will take an unreasonable amount of computer time. Before explaining why this works, we ﬁrst discuss a systematic method for ﬁnding the s in the above algorithm. For this we will need the Division Algorithm, which we state without proof.
However, over the years, there has been some progress in cracking DES. Computers have gotten faster, allowing an adversary to try more keys to see if they work. In addition, there have been some theoretical breakthroughs, most notably differential cryptanalysis and linear cryptanalysis, that eliminate some of those possible keys. This theoretical progress along with an increase in computing power resulted in DES being cracked by the Electronic Frontier Foundation in 1998. It was clear that a new encryption standard was needed.