I'm interested in the factors (no pun intended) that contributed to the renaissance of number theory in the 1970s. I'm looking at quite a few classic papers where I don't see equivalent work in the 1950s-1960s. Did any particular event cause this? (The increasing availability of computers, perhaps?)
Among other references:
- 1971: J. M. Pollard, An Algorithm for Testing the Primality of Any Integer
- 1973-1975: US National Bureau of Standards, Requests for standard encryption algorithm (1973, 1974) and publication of DES in Federal Register (1975)
- 1974: J. M. Pollard, Theorems on Factorization and Primality Testing
- 1974: D. H. Lehmer and Emma Lehmer, A New Factorization Technique Using Quadratic Forms
- 1974: R. Sherman Lehman, Factoring Large Integers
- 1975: Michael A Morrison and John Brillhart, A Method of Factoring and the Factorization of $F_7$ (continued fraction algorithm)
- 1975: J. M. Pollard, A Monte Carlo Method for Factorization (Pollard's rho method)
- 1975: Gary Miller, Riemann's Hypothesis and Tests for Primality (initial publication in Proceedings of Seventh Annual ACM Symposium on Theory of Computing)
- 1976: Gary Miller, Riemann's Hypothesis and Tests for Primality (secondary publication in Journal of Computer and System Sciences)
- 1976: Whitfield Diffie and Martin E. Hellman, New Directions in Cryptography (on public-key cryptography)
- 1977: R. Solovay and V. Strassen, A Fast Monte-Carlo Test for Primality (Solovay-Strassen primality test)
- 1977: Ronald Rivest, Adi Shamir, Len Adleman, A Method for Obtaining Digital Signatures and Public-Key Cryptosystems (the RSA cryptosystem --- original MIT Laboratory for Computer Science technical memo)
- 1977: Martin Gardner, Mathematical Games: A new kind of cipher that would take millions of years to break (column in Scientific American --- scanned copy on simson.net)
- 1978: R. L. Rivest, A. Shamir, and L. Adleman, A Method for Obtaining Digital Signatures and Public-Key Cryptosystems (Communications of the ACM)
- 1978: J. M. Pollard, Monte Carlo Methods for Index Computation (mod p) (Rho and kangaroo methods for computing the discrete logarithms)
- 1978: Stephen C. Pohlig and Martin E. Hellman, An Improved Algorithm for Computing Logarithms over GP(p) and Its Cryptographic Significance
- 1979: David A. Plaisted, Fast Verification, Testing, and Generation of Large Primes
- 1980: Michael O. Rabin, Probabilistic Algorithm for Testing Primality (Rabin-Miller Test)
- 1980: Richard P. Brent, An Improved Monte Carlo factorization (Brent's speedup of Pollard rho algorithm)
The preface of Vasilenko's Number-Theoretic Algorithms in Cryptography states:
This book deals with algorithmic number theory, a rapidly developing, especially in the last thirty years, branch of number theory, which has important applications to cryptography. Its explosive growth in the 1970s was related to the emergence of the Diffie-Hellman and RSA cryptosystems. By some estimates, practically the entire world's arsenal of asymmetric cryptography is based on number-theoretic techniques.
But that doesn't explain the earlier works of Pollard/Miller/etc.