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IEEE P1735 漏洞,又是 Padding Oracle Attack...

在「IEEE P1735 Encryption Is Broken—Flaws Allow Intellectual Property Theft」這邊看到 US-CERT 發表的「IEEE P1735 implementations may have weak cryptographic protections」,裡面提到的主要漏洞:

The methods are flawed and, in the most egregious cases, enable attack vectors that allow recovery of the entire underlying plaintext IP.

主要應該是第一包:

CVE-2017-13091: improperly specified padding in CBC mode allows use of an EDA tool as a decryption oracle.

又是 CBCpadding oracle attack 啊... 看起來是標準沒有強制定義好造成的?

The main vulnerability (CVE-2017-13091) resides in the IEEE P1735 standard's use of AES-CBC mode.

Since the standard makes no recommendation for any specific padding scheme, the developers often choose the wrong scheme, making it possible for attackers to use a well-known classic padding-oracle attack (POA) technique to decrypt the system-on-chip blueprints without knowledge of the key.

去年 Cloudflare 寫的「Padding oracles and the decline of CBC-mode cipher suites」這邊有提到 padding oracle attack 的方式,比較一般性的解法是避開要自己決定 Encrypt-then-MAC (IPsec;也是數學上證明安全性) 或 Encrypt-and-MAC (SSH) 或是 MAC-then-Encrypt (SSL),而是用 AEAD 類的加密元件直接躲開 padding oracle attack 的某些必要條件 (像是 AES-GCM 或是 ChaCha20-Poly1305)。

不過這也是這幾年大家才了解這樣做的重要性,當年在訂規格的時候都比較沒在在意這些...

0.1 + 0.2 = 0.30000000000000004

看到「http://0.30000000000000004.com/」這個網站對經典的 0.1 + 0.2 問題整理了各語言的結果。這個網址名稱也很機車啊 XD

開頭的說明講述 IEEE 754 二進制表示法的問題:

Your language isn't broken, it's doing floating point math. Computers can only natively store integers, so they need some way of representing decimal numbers. This representation comes with some degree of inaccuracy. That's why, more often than not, .1 + .2 != .3.

It's actually pretty simple. When you have a base 10 system (like ours), it can only express fractions that use a prime factor of the base. The prime factors of 10 are 2 and 5. So 1/2, 1/4, 1/5, 1/8, and 1/10 can all be expressed cleanly because the denominators all use prime factors of 10. In contrast, 1/3, 1/6, and 1/7 are all repeating decimals because their denominators use a prime factor of 3 or 7. In binary (or base 2), the only prime factor is 2. So you can only express fractions cleanly which only contain 2 as a prime factor. In binary, 1/2, 1/4, 1/8 would all be expressed cleanly as decimals. While, 1/5 or 1/10 would be repeating decimals. So 0.1 and 0.2 (1/10 and 1/5) while clean decimals in a base 10 system, are repeating decimals in the base 2 system the computer is operating in. When you do math on these repeating decimals, you end up with leftovers which carry over when you convert the computer's base 2 (binary) number into a more human readable base 10 number.

這邊主要是討論 IEEE 754-1985 這個標準,後來在 IEEE 754-2008 提出了新的表示方法,支援十進位的表示法來解這個問題 (雖然還沒普及)。

Fast Inverse Square Root 演算法...

中文稱為「平方根倒數速演算法」,英文則是「Fast Inverse Square Root」。

好像是在 Twitter 還是 Facebook 上看到的 (還是是在其他管道?),仔細看中文版維基百科條目,發現中文版的資料相當完整了 (看了一下歷史記錄,是去年 2012 年 6 月的時候從英文版翻出來的)。

當時很有名的 magic hack,比查表法快:

在1990年代初(也即該演算法發明的大概時間),軟體開發時通用的平方根計算方法多是從尋找表中取得近似值,而這段代碼取近似值耗時比之更短,達到精確度要求的速度也比通常使用的浮點除法計演算法快四倍,

然後還比 CPU 指令集快 XD

由於演算法所生成的用於輸入牛頓法的首次近似值已經相當精確,此演算法所得近似值的精度已可接受,而若使用與《雷神之鎚III競技場》同為1999年發行的Pentium III中的SSE指令rsqrtss計算,則計算平方根倒數的收斂速度更慢,精度也更低。

Update:請參考 comment,看起來中文版有誤譯...

我本來以為我之前寫過,找了找沒翻到... 補記錄下來 :p

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