Crypto Sometimes Likes Zero: Meet Non-adjacent Form

Prof Bill Buchanan OBE FRSE
4 min readApr 10, 2024

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Here is a bit of trivia for you … why do we use 65,537 as the encryption exponent value for RSA?

Well, 65,537 is a prime number as the encryption exponent cannot share a factor with (p-1)(q-1). Also, in its binary representation of “10000000000000001”, we can see that it has many zeros and only two 1’s. Why is this good? Well, when we perform an operation of:

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Prof Bill Buchanan OBE FRSE

Professor of Cryptography. Serial innovator. Believer in fairness, justice & freedom. Based in Edinburgh. Old World Breaker. New World Creator. Building trust.