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Multiplication of many-digital numbers by automatic computers
Anatolii Alekseevich Karatsuba and Yu P Ofman · 1962
Earlier work this paper cites.
Logical reversibility of computation
Charles H Bennett · 1973
Earlier work this paper cites.

Similar

Time/space trade-offs for reversible computation
Charles H Bennett · 1989
Cited alongside, same era.
Reversible karatsubas algorithm
R Portugal, CMH Figueiredo, et al · 2006
Cited alongside, same era.

Then

Improved reversible and quantum circuits for karatsuba-based integer multiplication
Original
Alex Parent, Martin Roetteler, and Michele Mosca · 2017
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2019

Asymptotically Efficient Quantum Karatsuba Multiplication

Gidney, Craig

Understand

We improve the space complexity of Karatsuba multiplication on a quantum computer from $O(n^{1.427})$ to $O(n)$ while maintaining $O(n^{\lg 3})$ gate complexity.

We achieve this by ensuring recursive calls can add their outputs directly into subsections of the output register.
This avoids the need to store, and uncompute, intermediate results.
This optimization, which is analogous to classical tail-call optimization, should be applicable to a wide range of recursive quantum algorithms.