MODULI(5)

✨ NAME ✨

okay so the page is all about moduli 🫶 (that's the Diffie-Hellman moduli, fr). it's from the File Formats Manual, so this is literally the file format bestie, not a command 💅

🔐 DESCRIPTION 🔐

okay so /etc/ssh/moduli is basically a list of prime numbers and generators that sshd(8) uses for the Diffie-Hellman Group Exchange key exchange method 🦋 it's giving secure and organized ✨

making new moduli is lowkey a two-step glow up with ssh-keygen(1) 🌸

• step one: an initial candidate pass with ssh-keygen -M generate digs up numbers that are likely to be useful 🧚
• step two: a primality testing pass with ssh-keygen -M screen gives you a high level of assurance that the numbers are prime and actually safe for Diffie-Hellman with sshd(8) 💖

both passes spit out this same moduli format, so it's consistent no cap 👑

the file is newline-separated records, one per modulus 🎀 each record has seven space-separated fields, and they go like this:

• timestamp 🕰️ the time the modulus was last processed, written as YYYYMMDDHHMMSS
• type 🔢 a decimal number for the internal structure of the prime modulus. the supported types are:
  • 0 — unknown, not tested 🙈
  • 2 — "Safe" prime; (p-1)/2 is also prime ✨
  • 4 — Sophie Germain; 2p+1 is also prime 🌈

ngl the candidates from ssh-keygen(1) start out as Sophie Germain primes (type 4) 💅 then more primality testing with ssh-keygen(1) turns them into safe prime moduli (type 2), which are the ones ready to go for sshd(8) 🔥 other types are not used by OpenSSH, so skip those vibes 🙅‍♀️

• tests 🧪 a decimal number showing which primality tests the number went through, stored as a bitmask:
  • 0x00 — not tested 💀
  • 0x01 — composite number – not prime 🚫
  • 0x02 — Sieve of Eratosthenes 🌸
  • 0x04 — probabilistic Miller-Rabin primality tests 🦋

the ssh-keygen(1) candidate generation uses the Sieve of Eratosthenes (flag 0x02) 🧚 and the later ssh-keygen(1) primality tests are Miller-Rabin tests (flag 0x04) ✨

• trials 🔁 a decimal number for how many primality trials the modulus has gotten
• size 📏 a decimal number for the size of the prime in bits
• generator 🎁 the recommended generator to use with this modulus, in hexadecimal
• modulus 💜 the modulus itself, in hexadecimal

when Diffie-Hellman Group Exchange is happening, sshd(8) first estimates how big the modulus needs to be so there's enough Diffie-Hellman output to properly key the chosen symmetric cipher 🔐 then it randomly picks a modulus from /etc/ssh/moduli that best fits that size requirement 🎲 iykyk, it's a whole vibe ✨

🌟 SEE ALSO 🌟

ssh-keygen(1), sshd(8) 🫶

📜 STANDARDS 📜

M. Friedl, N. Provos, and W. Simpson, Diffie-Hellman Group Exchange for the Secure Shell (SSH) Transport Layer Protocol, RFC 4419, March 2006 💖

okay that's the tea, bestie 🫶✨ this page came from Debian, April 16, 2022, and it's MODULI(5) all the way 💅🌸