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Asked: 2026-05-28T21:28:57+00:00

I am trying to learn number theory for RSA cryptography by reading the CLR

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I am trying to learn number theory for RSA cryptography by reading the CLR algorithms book. I was looking at exercise 31.2-5 which claims a bound of 1 + logΦ(b / gcd(a,b)).

The full question is:

If a > b >= 0, show that the invocation EUCLID(a,b) makes at most 1 + logΦb recursive calls. Improve this bound to 1 + logΦ(b / gcd(a,b)).

Does anyone know how to show this? There are already several other questions and answers to Euclid’s algorithm on this site already but none of them seem to have this exact precise answer.

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1 Answer

  1. Editorial Team

    Refer to the analysis of Euclid’s algorithm by Donald Knuth, in TAOCP Vol.2 p.356

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