Cryptography

Key Lengths

RSA

See recommendations from Bruce Schneier in Applied Cryptography (§7.2, [1]). See also [2]

Recommended public-key key lengths (in bits) — Source: Applied Cryptography, 2nd edition

Year	vs. industry	vs. Corporate	vs. Government
1995	768	1280	1536
2000	1024	1280	1536
2005	1280	1536	2048
2010	1280	1536	2048
2015	1536	2048	2048

Generate RSA Keys

Under Linux, Install package racoon. Then you can use plainrsa-gen to generate a RSA key pair:

$ sudo plainrsa-gen -b 2048 -e 3

# : PUB 0sAQOTQ2zIwqxqjy4LRTwXEHB/WdxMrrcldKBAut3siLnuQMCDFGkwSfOc9v+77ibPDqtJQj0C8nys7+W1gI3o6yht+SjG+m16hZwvwl0Mt81E11Tca6k6py1wNmntxvePtotG3uk6MhqpluJAUeOxIL6YcHLcsgBi19gwHiU1YBFF2Q==
: RSA   {
        # RSA 1024 bits
        # pubkey=0sAQOTQ2zIwqxqjy4LRTwXEHB/WdxMrrcldKBAut3siLnuQMCDFGkwSfOc9v+77ibPDqtJQj0C8nys7+W1gI3o6yht+SjG+m16hZwvwl0Mt81E11Tca6k6py1wNmntxvePtotG3uk6MhqpluJAUeOxIL6YcHLcsgBi19gwHiU1YBFF2Q==
        Modulus: 0x93436cc8c2ac6a8f2e0b453c1710707f59dc4caeb72574a040baddec88b9ee40c08314693049f39cf6ffbbee26cf0eab49423d02f27cacefe5b5808de8eb286df928c6fa6d7a859c2fc25d0cb7cd44d754dc6ba93aa72d703669edc6f78fb68b46dee93a321aa996e24051e3b120be987072dcb20062d7d8301e2535601145d9
        PublicExponent: 0x03
        PrivateExponent: 0x622cf33081c8470a1eb22e280f604aff913d88747a18f86ad5d1e9485b269ed5d5acb84620314d134f5527f419df5f1cdb817e01f6fdc89fee79005e9b4770484de1f0c003dcbeac2290f28f5594022ec0ca86fd0618ec77d0db3f24e0ddd9339a77b1126f3256d9405ce86bcd456f4db2ef0c019a763abee74eb29cb161568b
        Prime1: 0xc37626fcd807b365f62e70d07ad1c2383f0a987f373eca93bbd723bd6676062263fef48a1c99efbb4e2d64d82fecc1756ea3845db786746d9145f5c267931f5d
        Prime2: 0xc0dfb6dd8fa7b43405ba80653c9d7f58f4a208ae7a430028c149eb523fccea9b7b2c6b146eb53795b3879069cd4bd62e7568c651e12b0b4c43e22387ee6c24ad
        Exponent1: 0x824ec4a890052243f9744b35a736817ad4b1baff7a29dc627d3a17d399a40416ed54a306bdbbf527897398901ff32ba39f17ad93cfaef8490b83f92c450cbf93
        Exponent2: 0x80952493b51a7822ae7c5598d313aa3b4dc15b1efc2caac5d631478c2a889c67a772f20d9f237a63cd050af13387e41ef8f08436961cb232d7ec17aff4481873
        Coefficient: 0x80c5560ddad756e413c19fb39c83370dfa3ca5881ebb0b0a5098fbd81b007e20c7b7a104b0aada943d2f5ae64409a9e3b677e10d5c20f414959a621852424b19
  }

Another solution is to use openssl:

#! /bin/bash
#
# Script to generate a batch of RSA keys of various length
#

function gen-one-key()
{
	openssl genrsa $1 | openssl pkcs8 -topk8 -nocrypt -outform DER -out "$2-pk8.der"
	openssl asn1parse -inform DER -in "$2-pk8.der" > "$2-pk8.txt"
	echo -e "\n############### Content of RSA Private Key object ###############\n" >> "$2-pk8.txt"
	openssl pkcs8 -inform DER -in "$2-pk8.der" -nocrypt | openssl asn1parse >> "$2-pk8.txt"
}

for keylength in 1024 1536 1664 1792 1920 2048 2304 2560 2816 3072 3328 3584 3840 4096; do
	for keyidx in $(seq 1 10); do
		keyname="rsakey-${keylength}b-$(printf '%02d' $keyidx)"
		echo "########## gen-one-key $keylength \"$keyname\""
		gen-one-key $keylength "$keyname"
	done
done

This script will generate keys of different lengths.