##### Department of Mathematics,

University of California San Diego

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### AWM Colloquium

## Mingjie Chen

#### University of Birmingham

## Orienteering with one endomorphism

##### Abstract:

Supersingular isogeny-based cryptosystems are strong contenders for post-quantum cryptography standardization. Such cryptosystems rely on the hardness of path-finding on supersingular isogeny graphs. The path-finding problem is known to reduce to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism? In this talk, we give explicit classical and quantum algorithms for path-finding to an initial curve using the knowledge of one endomorphism. An endomorphism gives an orientation of a supersingular elliptic curve. We use the theory of oriented supersingular isogeny graphs and algorithms for taking ascending/descending/

### April 28, 2022

### 12:00 PM

https://ucsd.zoom.

Zoom ID: 977 3877 1432

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