I went through the math in the "worked example" in the RSA wiki page: https://en.wikipedia.org/wiki/RSA_(algorithm) and understood it entirely. For the remainder of this question, I will use math variables consistent with the wiki page.
I'm on a Unix machine and I'm looking in the ~/.ssh directory and I see all these files
id_rsa
id_rsa.pub
and I want to connect the theory with the practice.
What exactly is in id_rsa? If I cat it
cat id_rsa
I get a big jumble of characters. Is this some representation the number n = pq? What representation is it exactly? base 64? If so, then is id_rsa.pub suppose to be some representation of the numbers e and n?
In general, I'm trying to connect the theory of RSA with the actual practice as implemented through the ssh program on Unix machines. Any answers or pointers to the right direction would be greatly appreciated.
id_rsa is a base64-encoded DER-encoded string. The ASN.1 syntax for that DER-encoded string is described in RFC3447 (aka PKCS1):
Version ::= INTEGER { two-prime(0), multi(1) }
(CONSTRAINED BY
{-- version must be multi if otherPrimeInfos present --})
RSAPrivateKey ::= SEQUENCE {
version Version,
modulus INTEGER, -- n
publicExponent INTEGER, -- e
privateExponent INTEGER, -- d
prime1 INTEGER, -- p
prime2 INTEGER, -- q
exponent1 INTEGER, -- d mod (p-1)
exponent2 INTEGER, -- d mod (q-1)
coefficient INTEGER, -- (inverse of q) mod p
otherPrimeInfos OtherPrimeInfos OPTIONAL
}
DER encoding uses a tag-length-value notation. So here's a sample private key:
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
Here's the hex encoding:
3082025c02010002818100aa18aba43b50deef38598faf87d2ab634e4571c130a9bca7b878267414
faab8b471bd8965f5c9fc3818485eaf529c26246f3055064a8de19c8c338be5496cbaeb059dc0b35
8143b44a35449eb264113121a455bd7fde3fac919e94b56fb9bb4f651cdb23ead439d6cd523eb081
91e75b35fd13a7419b3090f24787bd4f4e196702030100010281801628e4a39ebea86c8df0cd1157
2691017cfefb14ea1c12e1dedc7856032dad0f961200a38684f0a36dca30102e2464989d19a80593
3794c7d329ebc890089d3c4c6f602766e5d62add74e82e490bbf92f6a482153853031be2844a7005
57b97673e727cd1316d3e6fa7fc991d4227366ec552cbe90d367ef2e2e79fe66d26311024100de03
0e9f8884171ae90123878c659b789ec732da8d762b26277abdd5a68784f8da76abe677a6f00c77f6
8dcd0fd6f56688f8d45f731509ae67cfc081a6eb78a5024100c422f91d06f66d0af8072a2b70c5a6
fe110fd8c67344e57bdf2178d613ec442f66eba2ab85e3bd1cf4c9ba8dfff6ce69faca86c4e9452f
4343b784a4a2c8e01b0240164972475b99ff03c98e3eb5d5c741733b653ddaa8c6cb101a787ce41c
c28ffbb75aa069136be3bf2cafc88e645face4ed2d258cab6dda39f2dbed3456c05ead0241009182
d4c8393b2768e4dc03e818913ab3f11a8d9ba536eefdf86b4fc79b1e44f3d9ea6553d55041243363
5a193155fc8b59b95944cb3f3db22c9201415757aa13024011a88ae4a84a369f52157b8b57041a96
fcf21e4d058673597199dfbb09e50b16fac272a0d75edf11fcbdd5e1cd4ede4fcd83e97fec730f51
673fbfeab089e29d
The 30 is because it's a SEQUENCE tag. The 82025c represents the length. The first byte means the length is of the "long form" (82 & 80) and that the next two bytes represent the length (82 & 7F). So the actual length of the SEQUENCE is 025c. So after that is the value.
Then you get to the version. 02 is of type int, 01 is the tag length and 00 is the value. ie. it's a two-prime key as opposed to a multi-prime key.
More info on the Distinguished Encoding Rules.
Trying to understand ASN.1 is a lot more complicated and a lot of it, for the purpose of understanding the formatting of RSA private keys, is unnecessary. For X.509 it becomes more necessary but RSA keys aren't nearly as complicated, formatting-wise, as X.509 certs.
Hope that helps!
Related
I am trying to parse and validate DNSSEC responses without using any DNS specific libraries. I am able to get the hexstring representation of a RSA key from the public key field value present in the DNSKEY RRs. According to RFC 8017, the RSA public key is represented with the ASN.1 type RSAPublicKey format which has a modulus and exponent. However, it doesn't specify anything more.
The hexstring(same as in Wireshark) is
"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"
I saw other similar posts and tried to follow the solutions. Most of the solutions try to get it from a pem file or binary data or base64 encoded form. When I try to convert the hex to those forms and use the solution, I get errors like 'RSA key format not supported' etc..
Is there anyway I can get the public key from the hex? I would really appreciate any inputs! Thanks!
I finally managed to find the solution.
According to RFC 3110 section 2, we can split the given value into exponent length, exponent and modulus. I split them as specified and converted the hexadecimal to integer. The text from RFC is below
The structure of the algorithm specific portion
of the RDATA part of such RRs is as shown below.
Field Size
----- ----
exponent length 1 or 3 octets (see text)
exponent as specified by length field
modulus remaining space
For interoperability, the exponent and modulus are each limited to
4096 bits in length. The public key exponent is a variable length
unsigned integer. Its length in octets is represented as one octet
if it is in the range of 1 to 255 and by a zero octet followed by a
two octet unsigned length if it is longer than 255 bytes. The public
key modulus field is a multiprecision unsigned integer. The length
of the modulus can be determined from the RDLENGTH and the preceding
RDATA fields including the exponent.
I need to generate weak certificate for CTF challenge using RSA and small modulus so it's factorable. It should be about 64 bits.
I've tried to generate that using OpenSSL as I would the normal one, but it forbids creating certificate with modulus lower than 512 bits for security reasons. So I've changed the source files of OpenSSL so it doesn't checks the bit length and recompiled that again. I was then able to create private key using smaller modulus, but trying to create certificate using that key (or new small one) evoked new error which I don't fully understand. I even wanted to evade the OpenSSL problem at all using Python, but that just showed that it uses OpenSSL too and had exactly same problems.
Generating small private key:
$ openssl genrsa -out acn.pem 64
-----BEGIN PRIVATE KEY-----
MFQCAQAwDQYJKoZIhvcNAQEBBQAEQDA+AgEAAgkAlz0xJ3uUx5UCAwEAAQIIR1Zs
1Wo4EQECBQDHPJNVAgUAwlPjQQIFAKqNunkCBClt4QECBHlHx1Q=
-----END PRIVATE KEY-----
Generating certificate:
$ openssl req -key acn.pem -new -out domain.csr
...
140561480598848:error:04075070:rsa routines:RSA_sign:digest too big for rsa key:../crypto/rsa/rsa_sign.c:100:
140561480598848:error:0D0DC006:asn1 encoding routines:ASN1_item_sign_ctx:EVP lib:../crypto/asn1/a_sign.c:224:
I found that this thread could be helpful as I could even choose my own numbers, but the method didn't worked for me:
How to Generate rsa keys using specific input numbers in openssl?
Here's sample certificate from PicoCTF. I would like to create similar one.
-----BEGIN CERTIFICATE-----
MIIB6zCB1AICMDkwDQYJKoZIhvcNAQECBQAwEjEQMA4GA1UEAxMHUGljb0NURjAe
Fw0xOTA3MDgwNzIxMThaFw0xOTA2MjYxNzM0MzhaMGcxEDAOBgNVBAsTB1BpY29D
VEYxEDAOBgNVBAoTB1BpY29DVEYxEDAOBgNVBAcTB1BpY29DVEYxEDAOBgNVBAgT
B1BpY29DVEYxCzAJBgNVBAYTAlVTMRAwDgYDVQQDEwdQaWNvQ1RGMCIwDQYJKoZI
hvcNAQEBBQADEQAwDgIHEaTUUhKxfwIDAQABMA0GCSqGSIb3DQEBAgUAA4IBAQAH
al1hMsGeBb3rd/Oq+7uDguueopOvDC864hrpdGubgtjv/hrIsph7FtxM2B4rkkyA
eIV708y31HIplCLruxFdspqvfGvLsCynkYfsY70i6I/dOA6l4Qq/NdmkPDx7edqO
T/zK4jhnRafebqJucXFH8Ak+G6ASNRWhKfFZJTWj5CoyTMIutLU9lDiTXng3rDU1
BhXg04ei1jvAf0UrtpeOA6jUyeCLaKDFRbrOm35xI79r28yO8ng1UAzTRclvkORt
b8LMxw7e+vdIntBGqf7T25PLn/MycGPPvNXyIsTzvvY/MXXJHnAqpI5DlqwzbRHz
q16/S1WLvzg4PsElmv1f
-----END CERTIFICATE-----
I need to generate weak certificate for CTF challenge using RSA and small modulus so it's factorable. It should be about 64 bits.
It's impossible to do that as a self-signed certificate, because proper RSA signing can't work with keys that small.
RSA-SSA-PKCS1_v1.5 is the shortest structured RSA signature padding, and it's structured as (per https://datatracker.ietf.org/doc/html/rfc8017#section-9.2):
DigestInfo ::= SEQUENCE {
digestAlgorithm AlgorithmIdentifier,
digest OCTET STRING
}
The shortest possible encoding for that structure is 9 bytes... and that's with a 0-byte hash algorithm:
30 07 // SEQUENCE (7 content bytes)
30 03 // digestAlgorithm: SEQUENCE (3 bytes)
06 01 00 // OBJECT IDENTIFIER 0.0 ({itu-t(0) recommendation(0)})
// omit implicit NULL
04 00 // digest (empty)
So, with our empty hash we need to keep going:
If emLen < tLen + 11, output "intended encoded message length too short" and stop.
emLen is the length of the modulus (in bytes) and tLen is the length of our encoded structure (9 bytes+).
That makes 20 bytes (160 bits) the shortest possible RSA key to do anything that might stand a chance of being regarded as an RSA signature... which produced a pointless signature (since everything collides under a 0-bit hash).
If you are comfortable stomping on a 1-byte OID for your CTF, your RSA key modulus would need to be 20 bytes + the length of the intended hash (in bytes). Since there's no 1-byte OID that identifies an existing hash algorithm (and no defined hash algorithm for use with certificates that's that small), no existing easy-to-use tool can do this for you.
You could invent a new form of RSA signature padding, of course, using something like a 60-bit hash processed directly with your 64-bit key. That'll require even further work on your part.
You're basically reduced to using a DER writer (or writing your own) to hand-craft a certificate.
Here's sample certificate from PicoCTF. I would like to create similar one.
That certificate is not self-signed. It has a 2048-bit certificate signature, from RSA-SSA-PKCS1_v1.5 with MD2. So while it describes a short RSA key (53 bit modulus) it was signed with something "proper". If that's what you're after, the general flow would be something like
Create a normal self-signed cert
Create your small RSA key
Build a new cert, signed by the first cert, containing the small RSA key.
It's hard to encode a CSR for the small key (because it can't self-sign the request), but maybe there's a way to get openssl req -new to do something other than self-sign, which would allow skipping the intermediate CSR. (Or use library tools like .NET's CertificateRequest, or OpenSSL's APIs instead of their CLI tool, or whatever.)
I am writing code for an SSH server and can not get past the Elliptic Curve Diffie-Hellman Key Exchange Reply part of the connection. The client also closes the connection and says "Host Key does not match the signature supplied".
I am using putty as the client and a PIC micro-controller is running the server code.
From RFC 5656 [SSH ECC Algorithm Integration] :
"The hash H is formed by applying the algorithm HASH on a
concatenation of the following:
string V_C, client's identification string (CR and LF excluded)
string V_S, server's identification string (CR and LF excluded)
string I_C, payload of the client's SSH_MSG_KEXINIT
string I_S, payload of the server's SSH_MSG_KEXINIT
string K_S, server's public host key
string Q_C, client's ephemeral public key octet string
string Q_S, server's ephemeral public key octet string
mpint K, shared secret
"
the host key algorithm and key exchange algorithm is ecdsa-sha2-nistp256 and ecdh-sha2-nistp256 respectively.
referring to RFC 4251 for data type representations, as well as the source code in openSHH (openBSD) this is what I have concatenated.
4 bytes for then length of V_C followed by V_C
4 bytes for then length of V_S followed by V_S
4 bytes for length of I_C followed by I_C (payload is from Message Code to the start of Random Padding)
4 bytes for length of I_S followed by I_S (payload is from Message Code to the start of Random Padding)
4 bytes for the length of K_S followed by K_S (for K_S I used the same group of bytes that is used to calculate the fingerprint)
4 bytes for the length of Q_C followed by Q_C (i used the uncompressed string which has length of 65 - 04||X-coordinate||Y-coordinate)
4 bytes for the length of Q_S followed by Q_S
4 bytes for the length of K followed by K (length is 32 or 33 depending is the leading bit is set or not. If it is set then K is preceded by a 00 byte)
Once concatenated I hash it with SHA256 because I'm using NISTP256. SHA256 outputs 32 bytes which is the size of the curve, so I take the whole SHA256 output and perform the signature algorithm on it.
I can never get the correct signature from my message concatenation.
I know my signature algorithm is correct because given the message hash output I can get the correct signature.
I know my shared secret is correct because I get the same output as online shared secret calculators.
I know the SHA256 is correct because I get the same result using online calculators.
This leads me to assume the error is in the concatenation of the exchange hash.
Any help is greatly appreciated, thanks.
ECDSA signature generation is non-deterministic, i.e. part of the input is the hash and part of the input consists of random bytes. So whatever you do, you will always get a different signature. This is all right because signature verification will still work.
The only way to get a repeated signature is to mess with the random number generator (during testing, you don't want to sign two values using the same random number: you'd expose the private key!).
I have a 256-bit private key that I want to use to sign a SHA-1 digest (20 bytes). Using openssl directly it seems to work
echo doesntmatter | openssl dgst -sha1 -binary | openssl rsautl -sign -inkey 256bit_private_key.pem | openssl enc -base64
gives me a Base64 output as expected.
But doing it with the OpenSSL fails with "error:04075070:rsa routines:RSA_sign:digest too big for rsa key". As you can see below, I'm passing the 20-byte (SHA_DIGEST_LENGTH=20) SHA-1 digest as input to RSA_sign. Even with padding it shouldn't be more than the maximum of 32 bytes that I can encrypt with a 256 bit modulus key?!
unsigned char digest[SHA_DIGEST_LENGTH];
SHA1(message, messageSize, digest);
unsigned int privateKeySize = RSA_size(privateKey); // 256 bits = 32 bytes
unsigned char* signature = new unsigned char[privateKeySize];
unsigned int signatureSize;
int res = RSA_sign(NID_sha1, digest, SHA_DIGEST_LENGTH, signature, &signatureSize, privateKey);
if(res == 0)
{
int err = ERR_get_error(); // 67588208
char *s = ERR_error_string(err, 0); // error:04075070:lib(4):func(117):reason(112)
delete [] signature;
[...]
}
What am I doing wrong in the code?
check out this SO answer. rsautl is depreciated in favor of pkeyutl
Essentially, RSA signing should use RSA-PSS signature padding scheme to be secure, and the RSA-PSS will be strictly larger than the digest, because of the necessity to communicate a salt. additionally, RSA_sign does a digest as a part of the signing scheme, so your code is going to do a digest of a digest. you want to instead either pass the message in directly, or use RSA_private_encrypt combined with a suitable RSA_padding_add_x call.
and as I said in my comment, a 256-bit key is sufficiently secure for a symmetric algorithm, but it will be trivial to crack for an RSA private key (on the order of 4 minutes on a couple of year old machine). Using a bare minimum of a 1024 bit key (and probably a 2048 or 4096 bit key) will give you a security level roughly equivalent to a 128 bit symmetric algorithm.
Re Peter Elliott: not quite.
The PKCS1v1_5 standard sequence in RFC8017 section 8.2.1 (and 9.2, similar in rfc4347 and rfc3447) is hash, encode in ASN.1, pad ('type 1') and modexp d. (PSS omits the ASN.1 step and uses different padding.)
OpenSSL (low-level) RSA_sign does the last three (with v1.5 padding) but not the first -- i.e. it encodes the hash but it doesn't do the hash; even-lower RSA_private_encrypt does the last two.
The higher-level envelope module (original EVP_Sign{Init,Update,Final}*, enhanced EVP_DigestSign*) does all four.
It's the ASN.1 encode that made the value too large for a 256-bit key -- which as stated is breakable anyway.
rsautl does only the last two steps not the encode, so it runs but gives a nonstandard result.
pkeyutl for RSA does the same by default but can be told to do the encode.
Also, PSS has a better security proof, but as far as I've heard there's no actual attack on v1.5 and it's still widely used.
If you have the choice of PSS (both/all parties support it) choose it, but don't feel worried about using v1.5.
Guess I found the solution. openssl rsautl -sign uses RSA_private_encrypt instead of RSA_sign (what I would have expected). RSA_sign creates a longer structure than the 20-bytes message I provided, so it fails with the given error.
I got a RSA pubkey.dat (almost obvious what it is) that has the following structure on contents:
ASN1 Integer of around 1024 bits (Modulus)
ASN1 Integer (Exponent)
Blob of 256 bytes (Signature)
No tags like "----begin---" or so. pure hex values in it.
There's any way to identify its format like if it's DER/PEM/etc , so i can open it with python crypto libraries or crypto++ on c++?
(Or if it matches a public standard structure name for me to check)
Seems like its not PEM as M2crypt can't load it.
Thanks in advance.
PEM-encoding has mandatory format:
-----BEGIN typeName-----
base64 of DER value
-----END typeName-----
where, for public keys, typeName="PUBLIC KEY" (AFAIR) so that's very easy to check with a regular expression such as the following:
/-----BEGIN [^-]+-----([A-Za-z0-9+\/=\s]+)-----END [^-]+-----/
If it's not PEM, it's usually plain DER.
The DER representation of an ASN.1 SEQUENCE always begins with 0x30 so usually when I have to decode a DER-or-PEM stream which I know for sure it's an ASN.1 SEQUENCE (most complex values are SEQUENCEs, anyways) I check the first byte: if its's 0x30, I decode as DER, else I decode as PEM.
You can check your ASN.1 data quickly using my very own opensource ASN.1 parser (it's all client-side Javascript, so I won't see your data).