The State of the Art in Integer Factoring and Breaking Public-Key Cryptography

International audience; The security of essentially all public-key cryptography currently in common use today is based on the presumed computational hardness of three number-theoretic problems: integer factoring (required for the security of RSA encryption and digital signatures), discrete logarithms in finite fields (required for Diffie-Hellman key exchange and the DSA digital signature algorithm), and discrete logarithms over elliptic curves (required for elliptic curve Diffie-Hellman and ECDSA, Ed25519, and other elliptic curve digital signature algorithms).In this column, we will review the current state of the art of cryptanalysis for these problems using classical (non-quantum) computers, including in particular our most recent computational records for integer factoring and prime field discrete logarithms.