Convert Cert to Modulus, Exponent

convert-cert-to-decimal.md

Convert Certificate to Modulus, Exponent

The process for taking a certificate or a public key and turning it into integers is a surprisingly tough task as first glance. There's a long chain of decoding and encoding to various format that this page will describe.

1. Certificate to Public Key

$ CERTIFICATE_PATH=/path/to/file.cer
$ OUTPUT_PUBLIC_KEY_PATH=public_key.pem
$ openssl x509 -pubkey -noout -in $CERTIFICATE_PATH > $OUTPUT_PUBLIC_KEY_PATH

Creates the a public key (example output below, don't worry this is a sample cert, not real).

-----BEGIN PUBLIC KEY-----
MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEArDMy/rsEEUfMQrrCSQmc
Lo9CSTvoL2jijXN1yi8jlx86yorxxm8Njdo0R2N6U0QRBLjglabeJJJZLJxQqPpU
RRFB7euTmmdLsctHxYVn2UDglIXV1Q5CGkSi9nFRupkL7ZMUflP0hqvPFRagUHaG
exJSlsO+32Gy6TxVIQKxAacjoYFJcMDGlDV4oTPelgMJ7enA7s4Bnz2tr6KJyoD3
N9fhcmFR0lGR7W7wqR79ePaxmPcCEl6UGAIbPny8WSQluRGzjsdB56dwsvdIZtlS
ChYr4tzoQYOB7cWc9gnJlQFOhocc/7tFPVXelT2Ff95Kp4eWGUK5JmzoU720B8Yk
EQIDAQAB
-----END PUBLIC KEY-----

2. Get Hexidecimal Modulus from Public Ke

$ HEX_MODULUS=$(openssl rsa -pubin -in $OUTPUT_PUBLIC_KEY_PATH  -modulus | grep 'Modulus=' |  cut -d'=' -f 2)

Creates the a hexidecimal representation of the modulus (example output below).

DD6DBDF880FAD7DE1B1FA7A32EB202E216F6520A3CBFA642F8CADC93674D60C34F8DC38A001BF1C44B416A69D269E53F218EC50BF82237ADB62C4B55FF7A0372BB9AD3EC96B9569FCB1999C932946F8FC652069F4503DFFDE897F6EAD6BABB482BB5E034614D52360FAB87522503CF87008713F2CA0329169D905746B5F40EAE17C80A4D92ED08A632231171FEF22C44D76C07F30B7B0C4BDD3BB4F737709F51B6884E5D6A057F8D9B667AAB8020FEEE6B97C3497D783BD599970375CE8FBCC5BE9C9AA5121970F9A4BD9627ED2302A7C757C971CF7694A22162F6B81DCA88EE09AD462FB761B32C1513869FA535265A67F437C8E68001490EC7ED61D3CDBCE4F8BE3FC94EF87D9789CE12BCCAB5C6D2E0D9B3683C2E4A9DB45FB853EE503DBFDDD4A28AB6A027AB980CB3B25890E2BCA1ADFFBD8E55310F00BF68E93DA9199AF06D0BA2146AC64CC64EBD6312A50B4D97EB42097953E265AA243470B8C1AB2380E79C6CEDDC82AA3704B8432A3D2AA8CC20FC275D902658F9B714E29EE2C1707397E96B028ED352597B00EC6130F1563F9CC17C05C5B136C81885CF61401F07E8A70687DF9A770BA9647203F693FCE00259C196ECC009423E30A27F1B482FFEE0218F5387250DCBEA49F54A9BD0E35FEE7818E5BA7131A904980FB1AD6752A0F2E39CAB6AFE588484DD073D3294051645159659A0586C180EE37766C7B3F799

3. Convert Hexadecimal Modulus to Decimal

$ ruby<<EOF
p "$HEX_MODULUS".to_i(16).to_s(10)
EOF

Converts the hexadecimal representation of the modulus to decimal (example output below).

"903350200741846433103490275702318092987711221795080780487705515793447642462352293930005029082816456324966429635984183642976753224939100182934586764830322547353276613511778555156314685902120045785748740652102149499802458636594115145098376676532039811405280029484180531080897744797671946602535748106482573745640230125725071851411418858523441305542960197934970282201978169899128421358221136498561735378441078904842496000031288381427214662674876164488503477712353985285783038861704346173846417987800700372136855065513839371230505066979655945991689080601315943347208545322825551901523372801711788730312786616209024413727099938085068143933277702040068400770002392724273077692527618673710507253235031640666038293670466879460643091688898398212470614257430485567355559709027230476557173161015264993692101931219217542706455704780898322106052146131050344223354172417918892290877128904693397579183166821072452886577300287605913021934410696419333315789150404571415571510150759313347067018155614134697544366299631877615175466702747992499691378170723240805893694504266094416954653431726471214487875228995333970243486471724362065194634035562833627383830413785525590101462126279287790122982746853775543354375554949279704170225740172092202881398339481"

4. Get Exponent from Public Key

$ openssl rsa -pubin -in $OUTPUT_PUBLIC_KEY_PATH -text | grep 'Exponent'

Gets the decimal exponent from the public key (example output below). Most people use 65537 as the exponent.

Exponent: 65537 (0x10001)