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  • Multiplication algorithm for abritrary precision (bignum) integers.

    - by nn
    Hi, I'm writing a small bignum library for a homework project. I am to implement Karatsuba multiplication, but before that I would like to write a naive multiplication routine. I'm following a guide written by Paul Zimmerman titled "Modern Computer Arithmetic" which is freely available online. On page 4, there is a description of an algorithm titled BasecaseMultiply which performs gradeschool multiplication. I understand step 2, 3, where B^j is a digit shift of 1, j times. But I don't understand step 1 and 3, where we have A*b_j. How is this multiplication meant to be carried out if the bignum multiplication hasn't been defined yet? Would the operation "*" in this algorithm just be the repeated addition method? Here is the parts I have written thus far. I have unit tested them so they appear to be correct for the most part: The structure I use for my bignum is as follows: #define BIGNUM_DIGITS 2048 typedef uint32_t u_hw; // halfword typedef uint64_t u_w; // word typedef struct { unsigned int sign; // 0 or 1 unsigned int n_digits; u_hw digits[BIGNUM_DIGITS]; } bn; Currently available routines: bn *bn_add(bn *a, bn *b); // returns a+b as a newly allocated bn void bn_lshift(bn *b, int d); // shifts d digits to the left, retains sign int bn_cmp(bn *a, bn *b); // returns 1 if a>b, 0 if a=b, -1 if a<b

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  • What is a convenient base for a bignum library & primality testing algorithm?

    - by nn
    Hi, I am to program the Solovay-Strassen primality test presented in the original paper on RSA. Additionally I will need to write a small bignum library, and so when searching for a convenient representation for bignum I came across this [specification][1]: struct { int sign; int size; int *tab; } bignum; I will also be writing a multiplication routine using the Karatsuba method. So, for my question: What base would be convenient to store integer data in the bignum struct? Note: I am not allowed to use third party or built-in implementations for bignum such as GMP. Thank you.

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  • Rails ActiveRecord BigNum to JSON

    - by Jon Hoffman
    Hi, I am serializing an ActiveRecord model in rails 2.3.2 to_json and have noticed that BigNum values are serialized to JSON without quotes, however, javascript uses 64 bits to represent large numbers and only ~52(?) of those bits are available for the integer part, the rest are for the exponent. So my 17 digit numbers become rounded off, grrr. Try the following in the Firebug console: console.log(123456789012345678) So, I'm thinking that the json encoder should be smart enough to quote numbers that are too big for the javascript engines to handle. How do I fix up rails to do that? Or, is there a way to override the encoding for a single property on the model (I don't want to_s elsewhere)? Thanks.

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  • Who does non-decimal bignums with floating radix point?

    - by boost
    Nice as the Tcl libraries math::bignum and math::bigfloat are, the middle ground between the two needs to be addressed. Namely, bignums which are in different radices and have a radix point. At present math::bignum only handles integers (afaict) and math::bigfloat won't let you specify different radices to math::bigfloat::fromstr (ditto). Does anyone know of a library, for any of the major scripting languages (e.g. Tcl, Perl, Python, Ruby, Lua) or less major ones (newLISP for example), which implements bignums in different radices with handling for radix point?

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  • BN_hex2bn magicaly segfaults in openSSL

    - by xunil154
    Greetings, this is my first post on stackoverflow, and i'm sorry if its a bit long. I'm trying to build a handshake protocol for my own project and am having issues with the server converting the clients RSA's public key to a Bignum. It works in my clent code, but the server segfaults when attempting to convert the hex value of the clients public RSA to a bignum. I have already checked that there is no garbidge before or after the RSA data, and have looked online, but i'm stuck. header segment: typedef struct KEYS { RSA *serv; char* serv_pub; int pub_size; RSA *clnt; } KEYS; KEYS keys; Initializing function: // Generates and validates the servers key /* code for generating server RSA left out, it's working */ //Set client exponent keys.clnt = 0; keys.clnt = RSA_new(); BN_dec2bn(&keys.clnt->e, RSA_E_S); // RSA_E_S contains the public exponent Problem code (in Network::server_handshake): // *Recieved an encrypted message from the network and decrypt into 'buffer' (1024 byte long)* cout << "Assigning clients RSA" << endl; // I have verified that 'buffer' contains the proper key if (BN_hex2bn(&keys.clnt->n, buffer) < 0) { Error("ERROR reading server RSA"); } cout << "clients RSA has been assigned" << endl; The program segfaults at BN_hex2bn(&keys.clnt->n, buffer) with the error (valgrind output) Invalid read of size 8 at 0x50DBF9F: BN_hex2bn (in /usr/lib/libcrypto.so.0.9.8) by 0x40F23E: Network::server_handshake() (Network.cpp:177) by 0x40EF42: Network::startNet() (Network.cpp:126) by 0x403C38: main (server.cpp:51) Address 0x20 is not stack'd, malloc'd or (recently) free'd Process terminating with default action of signal 11 (SIGSEGV) Access not within mapped region at address 0x20 at 0x50DBF9F: BN_hex2bn (in /usr/lib/libcrypto.so.0.9.8) And I don't know why it is, Im using the exact same code in the client program, and it works just fine. Any input is greatly appriciated!

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  • BN_hex2bn magically segfaults in openSSL

    - by xunil154
    Greetings, this is my first post on stackoverflow, and i'm sorry if its a bit long. I'm trying to build a handshake protocol for my own project and am having issues with the server converting the clients RSA's public key to a Bignum. It works in my clent code, but the server segfaults when attempting to convert the hex value of the clients public RSA to a bignum. I have already checked that there is no garbidge before or after the RSA data, and have looked online, but i'm stuck. header segment: typedef struct KEYS { RSA *serv; char* serv_pub; int pub_size; RSA *clnt; } KEYS; KEYS keys; Initializing function: // Generates and validates the servers key /* code for generating server RSA left out, it's working */ //Set client exponent keys.clnt = 0; keys.clnt = RSA_new(); BN_dec2bn(&keys.clnt->e, RSA_E_S); // RSA_E_S contains the public exponent Problem code (in Network::server_handshake): // *Recieved an encrypted message from the network and decrypt into 'buffer' (1024 byte long)* cout << "Assigning clients RSA" << endl; // I have verified that 'buffer' contains the proper key if (BN_hex2bn(&keys.clnt->n, buffer) < 0) { Error("ERROR reading server RSA"); } cout << "clients RSA has been assigned" << endl; The program segfaults at BN_hex2bn(&keys.clnt->n, buffer) with the error (valgrind output) Invalid read of size 8 at 0x50DBF9F: BN_hex2bn (in /usr/lib/libcrypto.so.0.9.8) by 0x40F23E: Network::server_handshake() (Network.cpp:177) by 0x40EF42: Network::startNet() (Network.cpp:126) by 0x403C38: main (server.cpp:51) Address 0x20 is not stack'd, malloc'd or (recently) free'd Process terminating with default action of signal 11 (SIGSEGV) Access not within mapped region at address 0x20 at 0x50DBF9F: BN_hex2bn (in /usr/lib/libcrypto.so.0.9.8) And I don't know why it is, Im using the exact same code in the client program, and it works just fine. Any input is greatly appriciated!

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  • The best cross platform (portable) arbitrary precision math library

    - by Siu Ching Pong - Asuka Kenji
    Dear ninjas / hackers / wizards, I'm looking for a good arbitrary precision math library in C or C++. Could you please give me some advices / suggestions? The primary requirements: It MUST handle arbitrarily big integers (my primary interest is on integers). In case that you don't know what the word arbitrarily big means, imagine something like 100000! (the factorial of 100000). The precision MUST NOT NEED to be specified during library initialization / object creation. The precision should ONLY be constrained by the available resources of the system. It SHOULD utilize the full power of the platform, and should handle "small" numbers natively. That means on a 64-bit platform, calculating 2^33 + 2^32 should use the available 64-bit CPU instructions. The library SHOULD NOT calculate this in the same way as it does with 2^66 + 2^65 on the same platform. It MUST handle addition (+), subtraction (-), multiplication (*), integer division (/), remainder (%), power (**), increment (++), decrement (--), gcd(), factorial(), and other common integer arithmetic calculations efficiently. Ability to handle functions like sqrt() (square root), log() (logarithm) that do not produce integer results is a plus. Ability to handle symbolic computations is even better. Here are what I found so far: Java's BigInteger and BigDecimal class: I have been using these so far. I have read the source code, but I don't understand the math underneath. It may be based on theories / algorithms that I have never learnt. The built-in integer type or in core libraries of bc / Python / Ruby / Haskell / Lisp / Erlang / OCaml / PHP / some other languages: I have ever used some of these, but I have no idea on which library they are using, or which kind of implementation they are using. What I have already known: Using a char as a decimal digit, and a char* as a decimal string and do calculations on the digits using a for-loop. Using an int (or a long int, or a long long) as a basic "unit" and an array of it as an arbitrary long integer, and do calculations on the elements using a for-loop. Booth's multiplication algorithm What I don't know: Printing the binary array mentioned above in decimal without using naive methods. Example of a naive method: (1) add the bits from the lowest to the highest: 1, 2, 4, 8, 16, 32, ... (2) use a char* string mentioned above to store the intermediate decimal results). What I appreciate: Good comparisons on GMP, MPFR, decNumber (or other libraries that are good in your opinion). Good suggestions on books / articles that I should read. For example, an illustration with figures on how a un-naive arbitrarily long binary to decimal conversion algorithm works is good. Any help. Please DO NOT answer this question if: you think using a double (or a long double, or a long long double) can solve this problem easily. If you do think so, it means that you don't understand the issue under discussion. you have no experience on arbitrary precision mathematics. Thank you in advance! Asuka Kenji

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  • Map large integer to a phrase

    - by Alexander Gladysh
    I have a large and "unique" integer (actually a SHA1 hash). I want (for no other reason than to have fun) to find an algorithm to convert that SHA1 hash to a (pseudo-)English phrase. The conversion should be reversible (i.e., knowing the algorithm, one must be able to convert the phrase back to SHA1 hash.) The possible usage of the generated phrase: the human readable version of Git commit ID, like a motto for a given program version (which is built from that commit). (As I said, this is "for fun". I don't claim that this is very practical — or be much more readable than the SHA1 itself.) A better algorithm would produce shorter, more natural-looking, more unique phrases. The phrase need not make sense. I would even settle for a whole paragraph of nonsense. (Though quality — englishness — of a paragraph should probably be better than for a mere phrase.) A variation: it is OK if I will be able to work only with a part of hash. Say, first six digits is OK. Possible approach: In the past I've attempted to build a probability table (of words), and generate phrases as Markov chains, seeding the generator (picking branches from probability tree), according to the bits I read from the SHA. This was not very successful, the resulting phrases were too long and ugly. I'm not sure if this was a bug, or the general flaw in the algorithm, since I had to abandon it early enough. Now I'm thinking about attempting to solve the problem once again. Any advice on how to approach this? Do you think Markov chain approach can work here? Something else?

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  • Adding negative and positive numbers in java without BigInt.

    - by liamg
    Hi, i'm trying to write a small java class. I have an object called BigNumber. I wrote method that add two positive numbers, and other method that subract two also positive numbers. Now i want them to handle negative numbers. So the i wrote couple of 'if' statements eg. if (this.sign == 1 /* means '+' */) { if (sn1.sign == 1) { if (this.compare(sn1) == -1 /* means this < sn1 */ ) return sn1.add(this); else return this.add(sn1); } etc. Unfortunately the code looks just ugly. Like a bush of if's and elses. Is there a better way to write that kind of code? Edit i can't just do this.add(sn1) beacuse sometimes i want to add positive number to negative one or negitve to negative. But add can handle only positive numbers. So i have to use basic math and for example: instead of add negative number to negative number i add this.abs() (absolute value of number) to sn1.abs() and return the result with opposite sign. Drew: this lines are from method _add. I use this method to decide what to do with numbers it receive. Send them to add method? Or send them to subract method but with different order (sn1.subtract(this))? And so on.. if (this.sign == 1) { if (sn1.sign == 1) { if (this.compare(sn1) == -1) return sn1.add(this); else return this.add(sn1); } else if (wl1.sign == 0) return this; else { if (this.compare(sn1.abs()) == 1) return this.subtract(sn1.abs()); else if (this.compare(sn1.abs()) == 0) return new BigNumber(0); else return sn1.abs().subtract(this).negate(); // return the number with opposite sign; } } else if (this.sign == 0) return sn1; else { if (wl1.sign == 1) { if (this.abs().compare(sn1) == -1) return sn1.subtract(this.abs()); else if (this.abs().compare(sn1) == 0) return new BigNumber(0); else return this.abs().subtract(sn1).negate(); } else if (sn1.sign == 0) return this; else return (this.abs().add(wl1.abs())).negate(); } As you can see - this code looks horrible..

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  • Arbitrary-precision arithmetic Explanation

    - by TT
    I'm trying to learn C and have come across the inability to work with REALLY big numbers (i.e., 100 digits, 1000 digits, etc.). I am aware that there exist libraries to do this, but I want to attempt to implement it myself. I just want to know if anyone has or can provide a very detailed, dumbed down explanation of arbitrary-precision arithmetic. Thanks!

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  • Using stdint.h and ANSI printf?

    - by nn
    Hi, I'm writing a bignum library, and I want to use efficient data types to represent the digits. Particularly integer for the digit, and long (if strictly double the size of the integer) for intermediate representations when adding and multiplying. I will be using some C99 functionality, but trying to conform to ANSI C. Currently I have the following in my bignum library: #include <stdint.h> #if defined(__LP64__) || defined(__amd64) || defined(__x86_64) || defined(__amd64__) || defined(__amd64__) || defined(_LP64) typedef uint64_t u_w; typedef uint32_t u_hw; #define BIGNUM_DIGITS 2048 #define U_HW_BITS 16 #define U_W_BITS 32 #define U_HW_MAX UINT32_MAX #define U_HW_MIN UINT32_MIN #define U_W_MAX UINT64_MAX #define U_W_MIN UINT64_MIN #else typedef uint32_t u_w; typedef uint16_t u_hw; #define BIGNUM_DIGITS 4096 #define U_HW_BITS 16 #define U_W_BITS 32 #define U_HW_MAX UINT16_MAX #define U_HW_MIN UINT16_MIN #define U_W_MAX UINT32_MAX #define U_W_MIN UINT32_MIN #endif typedef struct bn { int sign; int n_digits; // #digits should exclude carry (digits = limbs) int carry; u_hw tab[BIGNUM_DIGITS]; } bn; As I haven't written a procedure to write the bignum in decimal, I have to analyze the intermediate array and printf the values of each digit. However I don't know which conversion specifier to use with printf. Preferably I would like to write to the terminal the digit encoded in hexadecimal. The underlying issue is, that I want two data types, one that is twice as long as the other, and further use them with printf using standard conversion specifiers. It would be ideal if int is 32bits and long is 64bits but I don't know how to guarantee this using a preprocessor, and when it comes time to use functions such as printf that solely rely on the standard types I no longer know what to use.

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  • How to tell if SPARC T4 crypto is being used?

    - by danx
    A question that often comes up when running applications on SPARC T4 systems is "How can I tell if hardware crypto accleration is being used?" To review, the SPARC T4 processor includes a crypto unit that supports several crypto instructions. For hardware crypto these include 11 AES instructions, 4 xmul* instructions (for AES GCM carryless multiply), mont for Montgomery multiply (optimizes RSA and DSA), and 5 des_* instructions (for DES3). For hardware hash algorithm optimization, the T4 has the md5, sha1, sha256, and sha512 instructions (the last two are used for SHA-224 an SHA-384). First off, it's easy to tell if the processor T4 crypto instructions—use the isainfo -v command and look for "sparcv9" and "aes" (and other hash and crypto algorithms) in the output: $ isainfo -v 64-bit sparcv9 applications crc32c cbcond pause mont mpmul sha512 sha256 sha1 md5 camellia kasumi des aes ima hpc vis3 fmaf asi_blk_init vis2 vis popc These instructions are not-privileged, so are available for direct use in user-level applications and libraries (such as OpenSSL). Here is the "openssl speed -evp" command shown with the built-in t4 engine and with the pkcs11 engine. Both run the T4 AES instructions, but the t4 engine is faster than the pkcs11 engine because it has less overhead (especially for smaller packet sizes): t-4 $ /usr/bin/openssl version OpenSSL 1.0.0j 10 May 2012 t-4 $ /usr/bin/openssl engine (t4) SPARC T4 engine support (dynamic) Dynamic engine loading support (pkcs11) PKCS #11 engine support t-4 $ /usr/bin/openssl speed -evp aes-128-cbc # t4 engine used by default . . . The 'numbers' are in 1000s of bytes per second processed. type 16 bytes 64 bytes 256 bytes 1024 bytes 8192 bytes aes-128-cbc 487777.10k 816822.21k 986012.59k 1017029.97k 1053543.08k t-4 $ /usr/bin/openssl speed -engine pkcs11 -evp aes-128-cbc engine "pkcs11" set. . . . The 'numbers' are in 1000s of bytes per second processed. type 16 bytes 64 bytes 256 bytes 1024 bytes 8192 bytes aes-128-cbc 31703.58k 116636.39k 350672.81k 696170.50k 993599.49k Note: The "-evp" flag indicates use the OpenSSL "EnVeloPe" API, which gives more accurate results. That's because it tells OpenSSL to use the same API that external programs use when calling OpenSSL libcrypto functions, evp(3openssl). DTrace Shows if T4 Crypto Functions Are Used OK, good enough, the isainfo(1) command shows the instructions are present, but how does one know if they are being used? Chi-Chang Lin, who works on Oracle Solaris performance, wrote a Dtrace script to show if T4 instructions are being executed. To show the T4 instructions are being used, run the following Dtrace script. Look for functions named "t4" and "yf" in the output. The OpenSSL T4 engine uses functions named "t4" and the PKCS#11 engine uses functions named "yf". To demonstrate, I'll first run "openssl speed" with the built-in t4 engine then with the pkcs11 engine. The performance numbers are not valid due to dtrace probes slowing things down. t-4 # dtrace -Z -n ' pid$target::*yf*:entry,pid$target::*t4_*:entry{ @[probemod, probefunc] = count();}' \ -c "/usr/bin/openssl speed -evp aes-128-cbc" dtrace: description 'pid$target::*yf*:entry' matched 101 probes . . . dtrace: pid 2029 has exited libcrypto.so.1.0.0 ENGINE_load_t4 1 libcrypto.so.1.0.0 t4_DH 1 libcrypto.so.1.0.0 t4_DSA 1 libcrypto.so.1.0.0 t4_RSA 1 libcrypto.so.1.0.0 t4_destroy 1 libcrypto.so.1.0.0 t4_free_aes_ctr_NIDs 1 libcrypto.so.1.0.0 t4_init 1 libcrypto.so.1.0.0 t4_add_NID 3 libcrypto.so.1.0.0 t4_aes_expand128 5 libcrypto.so.1.0.0 t4_cipher_init_aes 5 libcrypto.so.1.0.0 t4_get_all_ciphers 6 libcrypto.so.1.0.0 t4_get_all_digests 59 libcrypto.so.1.0.0 t4_digest_final_sha1 65 libcrypto.so.1.0.0 t4_digest_init_sha1 65 libcrypto.so.1.0.0 t4_sha1_multiblock 126 libcrypto.so.1.0.0 t4_digest_update_sha1 261 libcrypto.so.1.0.0 t4_aes128_cbc_encrypt 1432979 libcrypto.so.1.0.0 t4_aes128_load_keys_for_encrypt 1432979 libcrypto.so.1.0.0 t4_cipher_do_aes_128_cbc 1432979 t-4 # dtrace -Z -n 'pid$target::*yf*:entry{ @[probemod, probefunc] = count();}   pid$target::*yf*:entry,pid$target::*t4_*:entry{ @[probemod, probefunc] = count();}' \ -c "/usr/bin/openssl speed -engine pkcs11 -evp aes-128-cbc" dtrace: description 'pid$target::*yf*:entry' matched 101 probes engine "pkcs11" set. . . . dtrace: pid 2033 has exited libcrypto.so.1.0.0 ENGINE_load_t4 1 libcrypto.so.1.0.0 t4_DH 1 libcrypto.so.1.0.0 t4_DSA 1 libcrypto.so.1.0.0 t4_RSA 1 libcrypto.so.1.0.0 t4_destroy 1 libcrypto.so.1.0.0 t4_free_aes_ctr_NIDs 1 libcrypto.so.1.0.0 t4_get_all_ciphers 1 libcrypto.so.1.0.0 t4_get_all_digests 1 libsoftcrypto.so.1 rijndael_key_setup_enc_yf 1 libsoftcrypto.so.1 yf_aes_expand128 1 libcrypto.so.1.0.0 t4_add_NID 3 libsoftcrypto.so.1 yf_aes128_cbc_encrypt 1542330 libsoftcrypto.so.1 yf_aes128_load_keys_for_encrypt 1542330 So, as shown above the OpenSSL built-in t4 engine executes t4_* functions (which are hand-coded assembly executing the T4 AES instructions) and the OpenSSL pkcs11 engine executes *yf* functions. Programmatic Use of OpenSSL T4 engine The OpenSSL t4 engine is used automatically with the /usr/bin/openssl command line. Chi-Chang Lin also points out that if you're calling the OpenSSL API (libcrypto.so) from a program, you must call ENGINE_load_built_engines(), otherwise the built-in t4 engine will not be loaded. You do not call ENGINE_set_default(). That's because "openssl speed -evp" test calls ENGINE_load_built_engines() even though the "-engine" option wasn't specified. OpenSSL T4 engine Availability The OpenSSL t4 engine is available with Solaris 11 and 11.1. For Solaris 10 08/11 (U10), you need to use the OpenSSL pkcs311 engine. The OpenSSL t4 engine is distributed only with the version of OpenSSL distributed with Solaris (and not third-party or self-compiled versions of OpenSSL). The OpenSSL engine implements the AES cipher for Solaris 11, released 11/2011. For Solaris 11.1, released 11/2012, the OpenSSL engine adds optimization for the MD5, SHA-1, and SHA-2 hash algorithms, and DES-3. Although the T4 processor has Camillia and Kasumi block cipher instructions, these are not implemented in the OpenSSL T4 engine. The following charts may help view availability of optimizations. The first chart shows what's available with Solaris CLIs and APIs, the second chart shows what's available in Solaris OpenSSL. Native Solaris Optimization for SPARC T4 This table is shows Solaris native CLI and API support. As such, they are all available with the OpenSSL pkcs11 engine. CLIs: "openssl -engine pkcs11", encrypt(1), decrypt(1), mac(1), digest(1), MD5sum(1), SHA1sum(1), SHA224sum(1), SHA256sum(1), SHA384sum(1), SHA512sum(1) APIs: PKCS#11 library libpkcs11(3LIB) (incluDES Openssl pkcs11 engine), libMD(3LIB), and Solaris kernel modules AlgorithmSolaris 1008/11 (U10)Solaris 11Solaris 11.1 AES-ECB, AES-CBC, AES-CTR, AES-CBC AES-CFB128 XXX DES3-ECB, DES3-CBC, DES2-ECB, DES2-CBC, DES-ECB, DES-CBC XXX bignum Montgomery multiply (RSA, DSA) XXX MD5, SHA-1, SHA-256, SHA-384, SHA-512 XXX SHA-224 X ARCFOUR (RC4) X Solaris OpenSSL T4 Engine Optimization This table is for the Solaris OpenSSL built-in t4 engine. Algorithms listed above are also available through the OpenSSL pkcs11 engine. CLI: openssl(1openssl) APIs: openssl(5), engine(3openssl), evp(3openssl), libcrypto crypto(3openssl) AlgorithmSolaris 11Solaris 11SRU2Solaris 11.1 AES-ECB, AES-CBC, AES-CTR, AES-CBC AES-CFB128 XXX DES3-ECB, DES3-CBC, DES-ECB, DES-CBC X bignum Montgomery multiply (RSA, DSA) X MD5, SHA-1, SHA-256, SHA-384, SHA-512 XX SHA-224 X Source Code Availability Solaris Most of the T4 assembly code that called the new T4 crypto instructions was written by Ferenc Rákóczi of the Solaris Security group, with assistance from others. You can download the Solaris source for this and other parts of Solaris as a few zip files at the Oracle Download website. The relevant source files are generally under directories usr/src/common/crypto/{aes,arcfour,des,md5,modes,sha1,sha2}}/sun4v/. and usr/src/common/bignum/sun4v/. Solaris 11 binary is available from the Oracle Solaris 11 download website. OpenSSL t4 engine The source for the OpenSSL t4 engine, which is based on the Solaris source above, is viewable through the OpenGrok source code browser in directory src/components/openssl/openssl-1.0.0/engines/t4 . You can download the source from the same website or through Mercurial source code management, hg(1). Conclusion Oracle Solaris with SPARC T4 provides a rich set of accelerated cryptographic and hash algorithms. Using the latest update, Solaris 11.1, provides the best set of optimized algorithms, but alternatives are often available, sometimes slightly slower, for releases back to Solaris 10 08/11 (U10). Reference See also these earlier blogs. SPARC T4 OpenSSL Engine by myself, Dan Anderson (2011), discusses the Openssl T4 engine and reviews the SPARC T4 processor for the Solaris 11 release. Exciting Crypto Advances with the T4 processor and Oracle Solaris 11 by Valerie Fenwick (2011) discusses crypto algorithms that were optimized for the T4 processor with the Solaris 11 FCS (11/11) and Solaris 10 08/11 (U10) release. T4 Crypto Cheat Sheet by Stefan Hinker (2012) discusses how to make T4 crypto optimization available to various consumers (such as SSH, Java, OpenSSL, Apache, etc.) High Performance Security For Oracle Database and Fusion Middleware Applications using SPARC T4 (PDF, 2012) discusses SPARC T4 and its usage to optimize application security. Configuring Oracle iPlanet WebServer / Oracle Traffic Director to use crypto accelerators on T4-1 servers by Meena Vyas (2012)

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  • Watir with IronRuby!

    - by azamsharp
    Has anyone used Watir with IronRuby successfully? I am getting an error that the required file 'Watir' was not found. What path do I need to set to get this file to work in IronRuby? For some reason my igem command is not working: C:\DevTools\IronRuby\ironruby\Merlin\Main\Languages\Ruby\Scripts\binigem instal l watir '"C:\DevTools\IronRuby\ironruby\Merlin\Main\Languages\Ruby\Scripts\bin\ir.exe"' is not recognized as an internal or external command, operable program or batch file. I am using 0.9 version of Ironruby. I remember that in 0.9 you have to indicate the ir tool: I used the following and got the error again! C:\DevTools\IronRuby\ironruby\Merlin\Main\Languages\Ruby\Scripts\binir igem ins tall watir ERROR: While executing gem ... (RangeError) bignum too big to convert into Fixnum The current version of RubyGems is 1.3.5: C:\DevTools\IronRuby\ironruby\Merlin\Main\Languages\Ruby\Scripts\binir igem -v 1.3.5 I even tried using the full path: require File.dirname(__FILE__) + "C:/ruby/lib/ruby/gems/1.8/gems/commonwatir-1.6.2/lib/watir.rb"

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  • Packing a long binary integer in Ruby

    - by user1056142
    I'm trying to send a very long binary integer over UDP (on the order of 200 bits). When I try to use Array's pack method, it complains the string I'm trying to convert is too large. Am I going about this the wrong way? ruby-1.8.7-p352 :003 > [0b1101001010101101111010100101010011010101010110010101010101010010010101001010101010101011101010101010101111010101010101010101].pack('i') RangeError: bignum too big to convert into `unsigned long' from (irb):3:in `pack' from (irb):3 This number is supposed to represent a DNS query packet (this is for a homework assignment; we're not allowed to use any DNS libraries).

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  • Miller-rabin exception number?

    - by nightcracker
    Hey everyone. This question is about the number 169716931325235658326303. According to http://www.alpertron.com.ar/ECM.HTM it is prime. According to my miller-rabin implementation in python with 7 repetitions is is composite. With 50 repetitions it is still composite. With 5000 repetitions it is STILL composite. I thought, this might be a problem of my implementation. So I tried GNU MP bignum library, which has a miller-rabin primality test built-in. I tested with 1000000 repetitions. Still composite. This is my implementation of the miller-rabin primality test: def isprime(n, precision=7): if n == 1 or n % 2 == 0: return False elif n < 1: raise ValueError("Out of bounds, first argument must be > 0") d = n - 1 s = 0 while d % 2 == 0: d //= 2 s += 1 for repeat in range(precision): a = random.randrange(2, n - 2) x = pow(a, d, n) if x == 1 or x == n - 1: continue for r in range(s - 1): x = pow(x, 2, n) if x == 1: return False if x == n - 1: break else: return False return True And the code for the GMP test: #include <gmp.h> #include <stdio.h> int main(int argc, char* argv[]) { mpz_t test; mpz_init_set_str(test, "169716931325235658326303", 10); printf("%d\n", mpz_probab_prime_p(test, 1000000)); mpz_clear(test); return 0; } As far as I know there are no "exceptions" (which return false positives for any amount of repetitions) to the miller-rabin primality test. Have I stumpled upon one? Is my computer broken? Is the Elliptic Curve Method wrong? What is happening here? EDIT I found the issue, which is http://www.alpertron.com.ar/ECM.HTM. I trusted this applet, I'll contact the author his applet's implementation of the ECM is faulty for this number. Thanks. EDIT2 Hah, the shame! In the end it was something that went wrong with copy/pasting on my side. NOR the applet NOR the miller-rabin algorithm NOR my implementation NOR gmp's implementation of it is wrong, the only thing that's wrong is me. I'm sorry.

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  • Interesting articles and blogs on SPARC T4

    - by mv
    Interesting articles and blogs on SPARC T4 processor   I have consolidated all the interesting information I could get on SPARC T4 processor and its hardware cryptographic capabilities.  Hope its useful. 1. Advantages of SPARC T4 processor  Most important points in this T4 announcement are : "The SPARC T4 processor was designed from the ground up for high speed security and has a cryptographic stream processing unit (SPU) integrated directly into each processor core. These accelerators support 16 industry standard security ciphers and enable high speed encryption at rates 3 to 5 times that of competing processors. By integrating encryption capabilities directly inside the instruction pipeline, the SPARC T4 processor eliminates the performance and cost barriers typically associated with secure computing and makes it possible to deliver high security levels without impacting the user experience." Data Sheet has more details on these  : "New on-chip Encryption Instruction Accelerators with direct non-privileged support for 16 industry-standard cryptographic algorithms plus random number generation in each of the eight cores: AES, Camellia, CRC32c, DES, 3DES, DH, DSA, ECC, Kasumi, MD5, RSA, SHA-1, SHA-224, SHA-256, SHA-384, SHA-512" I ran "isainfo -v" command on Solaris 11 Sparc T4-1 system. It shows the new instructions as expected  : $ isainfo -v 64-bit sparcv9 applications crc32c cbcond pause mont mpmul sha512 sha256 sha1 md5 camellia kasumi des aes ima hpc vis3 fmaf asi_blk_init vis2 vis popc 32-bit sparc applications crc32c cbcond pause mont mpmul sha512 sha256 sha1 md5 camellia kasumi des aes ima hpc vis3 fmaf asi_blk_init vis2 vis popc v8plus div32 mul32  2.  Dan Anderson's Blog have some interesting points about how these can be used : "New T4 crypto instructions include: aes_kexpand0, aes_kexpand1, aes_kexpand2,         aes_eround01, aes_eround23, aes_eround01_l, aes_eround_23_l, aes_dround01, aes_dround23, aes_dround01_l, aes_dround_23_l.       Having SPARC T4 hardware crypto instructions is all well and good, but how do we access it ?      The software is available with Solaris 11 and is used automatically if you are running Solaris a SPARC T4.  It is used internally in the kernel through kernel crypto modules.  It is available in user space through the PKCS#11 library." 3.   Dans' Blog on Where's the Crypto Libraries? Although this was written in 2009 but still is very useful  "Here's a brief tour of the major crypto libraries shown in the digraph:   The libpkcs11 library contains the PKCS#11 API (C_\*() functions, such as C_Initialize()). That in turn calls library pkcs11_softtoken or pkcs11_kernel, for userland or kernel crypto providers. The latter is used mostly for hardware-assisted cryptography (such as n2cp for Niagara2 SPARC processors), as that is performed more efficiently in kernel space with the "kCF" module (Kernel Crypto Framework). Additionally, for Solaris 10, strong crypto algorithms were split off in separate libraries, pkcs11_softtoken_extra libcryptoutil contains low-level utility functions to help implement cryptography. libsoftcrypto (OpenSolaris and Solaris Nevada only) implements several symmetric-key crypto algorithms in software, such as AES, RC4, and DES3, and the bignum library (used for RSA). libmd implements MD5, SHA, and SHA2 message digest algorithms" 4. Difference in T3 and T4 Diagram in this blog is good and self explanatory. Jeff's blog also highlights the differences  "The T4 servers have improved crypto acceleration, described at https://blogs.oracle.com/DanX/entry/sparc_t4_openssl_engine. It is "just built in" so administrators no longer have to assign crypto accelerator units to domains - it "just happens". Every physical or virtual CPU on a SPARC-T4 has full access to hardware based crypto acceleration at all times. .... For completeness sake, it's worth noting that the T4 adds more crypto algorithms, and accelerates Camelia, CRC32c, and more SHA-x." 5. About performance counters In this blog, performance counters are explained : "Note that unlike T3 and before, T4 crypto doesn't require kernel modules like ncp or n2cp, there is no visibility of crypto hardware with kstats or cryptoadm. T4 does provide hardware counters for crypto operations.  You can see these using cpustat: cpustat -c pic0=Instr_FGU_crypto 5 You can check the general crypto support of the hardware and OS with the command "isainfo -v". Since T4 crypto's implementation now allows direct userland access, there are no "crypto units" visible to cryptoadm.  " For more details refer Martin's blog as well. 6. How to turn off  SPARC T4 or Intel AES-NI crypto acceleration  I found this interesting blog from Darren about how to turn off  SPARC T4 or Intel AES-NI crypto acceleration. "One of the new Solaris 11 features of the linker/loader is the ability to have a single ELF object that has multiple different implementations of the same functions that are selected at runtime based on the capabilities of the machine.   The alternate to this is having the application coded to call getisax(2) system call and make the choice itself.  We use this functionality of the linker/loader when we build the userland libraries for the Solaris Cryptographic Framework (specifically libmd.so and libsoftcrypto.so) The Solaris linker/loader allows control of a lot of its functionality via environment variables, we can use that to control the version of the cryptographic functions we run.  To do this we simply export the LD_HWCAP environment variable with values that tell ld.so.1 to not select the HWCAP section matching certain features even if isainfo says they are present.  This will work for consumers of the Solaris Cryptographic Framework that use the Solaris PKCS#11 libraries or use libmd.so interfaces directly.  For SPARC T4 : export LD_HWCAP="-aes -des -md5 -sha256 -sha512 -mont -mpul" .. For Intel systems with AES-NI support: export LD_HWCAP="-aes"" Note that LD_HWCAP is explained in  http://docs.oracle.com/cd/E23823_01/html/816-5165/ld.so.1-1.html "LD_HWCAP, LD_HWCAP_32, and LD_HWCAP_64 -  Identifies an alternative hardware capabilities value... A “-” prefix results in the capabilities that follow being removed from the alternative capabilities." 7. Whitepaper on SPARC T4 Servers—Optimized for End-to-End Data Center Computing This Whitepaper on SPARC T4 Servers—Optimized for End-to-End Data Center Computing explains more details.  It has DTrace scripts which may come in handy : "To ensure the hardware-assisted cryptographic acceleration is configured to use and working with the security scenarios, it is recommended to use the following Solaris DTrace script. #!/usr/sbin/dtrace -s pid$1:libsoftcrypto:yf*:entry, pid$target:libsoftcrypto:rsa*:entry, pid$1:libmd:yf*:entry { @[probefunc] = count(); } tick-1sec { printa(@ops); trunc(@ops); }" Note that I have slightly modified the D Script to have RSA "libsoftcrypto:rsa*:entry" as well as per recommendations from Chi-Chang Lin. 8. References http://www.oracle.com/us/corporate/features/sparc-t4-announcement-494846.html http://www.oracle.com/us/products/servers-storage/servers/sparc-enterprise/t-series/sparc-t4-1-ds-487858.pdf https://blogs.oracle.com/DanX/entry/sparc_t4_openssl_engine https://blogs.oracle.com/DanX/entry/where_s_the_crypto_libraries https://blogs.oracle.com/darren/entry/howto_turn_off_sparc_t4 http://docs.oracle.com/cd/E23823_01/html/816-5165/ld.so.1-1.html   https://blogs.oracle.com/hardware/entry/unleash_the_power_of_cryptography https://blogs.oracle.com/cmt/entry/t4_crypto_cheat_sheet https://blogs.oracle.com/martinm/entry/t4_performance_counters_explained  https://blogs.oracle.com/jsavit/entry/no_mau_required_on_a http://www.oracle.com/us/products/servers-storage/servers/sparc-enterprise/t-series/sparc-t4-business-wp-524472.pdf

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