From d7d20c50b649282e4c9a4c4cd3b31e3fa68ebd92 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Mamy=20Andr=C3=A9-Ratsimbazafy?= Date: Mon, 17 Feb 2020 00:13:42 +0100 Subject: [PATCH] Add primitive for window-based modular exponentiation --- constantine.nimble | 1 + constantine/math/bigints_raw.nim | 108 +++++++++++++++++++++++++++---- tests/test_finite_fields.nim | 2 +- 3 files changed, 99 insertions(+), 12 deletions(-) diff --git a/constantine.nimble b/constantine.nimble index 06bb98b..6c93526 100644 --- a/constantine.nimble +++ b/constantine.nimble @@ -22,3 +22,4 @@ task test, "Run all tests": test "", "tests/test_bigints_multimod.nim" test "", "tests/test_bigints_vs_gmp.nim" test "", "tests/test_finite_fields.nim" + test "", "tests/test_finite_fields_vs_gmp.nim" diff --git a/constantine/math/bigints_raw.nim b/constantine/math/bigints_raw.nim index 6d4e2b3..f6d3f10 100644 --- a/constantine/math/bigints_raw.nim +++ b/constantine/math/bigints_raw.nim @@ -54,6 +54,7 @@ import ../primitives/extended_precision, ../config/common from sugar import distinctBase +from bitops import countSetBits # only used on modulus and public values # ############################################################ # @@ -116,6 +117,16 @@ type ## Mutable view into a BigInt BigIntViewAny* = BigIntViewConst or BigIntViewMut + BigIntLeakedConst* = distinct BigIntViewConst + ## BigInt which information will be leaked + ## besides the announced bit length + ## This is only suitable for values + ## that are publicly known + + SensitiveInt* = distinct int + ## Integer that contains sensitive information + ## and will not be manipulated in a constant-time manner + # No exceptions allowed {.push raises: [].} @@ -187,6 +198,12 @@ template checkOddModulus(m: BigIntViewConst) = debug: assert bool(BaseType(m[0]) and 1), "Internal Error: the modulus must be odd to use the Montgomery representation." +template checkWordShift(k: int) = + ## Checks that the shift is less than the word bit size + debug: + assert k <= WordBitSize, "Internal Error: the shift must be less than the word bit size" + + debug: func `$`*(a: BigIntViewAny): string = let len = a.numLimbs() @@ -205,6 +222,9 @@ debug: # # ############################################################ +template mask*(w: Word): Word = + w and MaxWord + func isZero*(a: BigIntViewAny): CTBool[Word] = ## Returns true if a big int is equal to zero var accum: Word @@ -217,7 +237,6 @@ func setZero*(a: BigIntViewMut) = ## It's bit size is unchanged zeroMem(a[0].unsafeAddr, a.numLimbs() * sizeof(Word)) - func cmov*(a: BigIntViewMut, b: BigIntViewAny, ctl: CTBool[Word]) = ## Constant-time conditional copy ## If ctl is true: b is copied into a @@ -243,7 +262,7 @@ func add*(a: BigIntViewMut, b: BigIntViewAny, ctl: CTBool[Word]): CTBool[Word] = for i in 0 ..< a.numLimbs(): let new_a = a[i] + b[i] + Word(result) result = new_a.isMsbSet() - a[i] = ctl.mux(new_a and MaxWord, a[i]) + a[i] = ctl.mux(new_a.mask(), a[i]) func sub*(a: BigIntViewMut, b: BigIntViewAny, ctl: CTBool[Word]): CTBool[Word] = ## Constant-time big integer in-place optional substraction @@ -257,7 +276,37 @@ func sub*(a: BigIntViewMut, b: BigIntViewAny, ctl: CTBool[Word]): CTBool[Word] = for i in 0 ..< a.numLimbs(): let new_a = a[i] - b[i] - Word(result) result = new_a.isMsbSet() - a[i] = ctl.mux(new_a and MaxWord, a[i]) + a[i] = ctl.mux(new_a.mask(), a[i]) + +func dec*(a: BigIntViewMut, w: Word): CTBool[Word] = + ## Decrement a big int by a small word + # returns the result carry + + a[0] -= w + result = a[0].isMsbSet() + a[0] = a[0].mask() + for i in 1 ..< a.numLimbs(): + a[i] -= Word(result) + result = a[i].isMsbSet() + a[i] = a[i].mask() + +func shiftRight*(a: BigIntViewMut, k: int) = + ## Shift right by k. + ## + ## k MUST be less than the base word size (2^31 or 2^63) + # We don't reuse shr for this in-place operation + # Do we need to return the shifted out part? + # + # Note: for speed, loading a[i] and a[i+1] + # instead of a[i-1] and a[i] + # is probably easier to parallelize for the compiler + # (antidependence WAR vs loop-carried dependence RAW) + checkWordShift(k) + + let len = a.numLimbs() + for i in 0 ..< len-1: + a[i] = (a[i] shr k) or mask(a[i+1] shl (WordBitSize - k)) + a[len-1] = a[len-1] shr k # ############################################################ # @@ -301,11 +350,11 @@ func shlAddMod(a: BigIntViewMut, c: Word, M: BigIntViewConst) = a1 = a[^1] m0 = M[^1] else: # Else: need to deal with partial word shifts at the edge. - a0 = ((a[^1] shl (WordBitSize-R)) or (a[^2] shr R)) and MaxWord + a0 = mask((a[^1] shl (WordBitSize-R)) or (a[^2] shr R)) moveMem(a[1].addr, a[0].addr, (aLen-1) * Word.sizeof) a[0] = c - a1 = ((a[^1] shl (WordBitSize-R)) or (a[^2] shr R)) and MaxWord - m0 = ((M[^1] shl (WordBitSize-R)) or (M[^2] shr R)) and MaxWord + a1 = mask((a[^1] shl (WordBitSize-R)) or (a[^2] shr R)) + m0 = mask((M[^1] shl (WordBitSize-R)) or (M[^2] shr R)) # m0 has its high bit set. (a0, a1)/p0 fits in a limb. # Get a quotient q, at most we will be 2 iterations off @@ -335,12 +384,12 @@ func shlAddMod(a: BigIntViewMut, c: Word, M: BigIntViewConst) = # q * p + carry (doubleword) carry from previous limb let qp = unsafeExtPrecMul(q, M[i]) + carry.DoubleWord carry = Word(qp shr WordBitSize) # New carry: high digit besides LSB - qp_lo = qp.Word and MaxWord # Normalize to u63 + qp_lo = qp.Word.mask() # Normalize to u63 block: # a*2^63 - q*p a[i] -= qp_lo carry += Word(a[i].isMsbSet) # Adjust if borrow - a[i] = a[i] and MaxWord # Normalize to u63 + a[i] = a[i].mask() # Normalize to u63 over_p = mux( a[i] == M[i], over_p, @@ -404,7 +453,7 @@ func reduce*(r: BigIntViewMut, a: BigIntViewAny, M: BigIntViewConst) = # ############################################################ template wordMul(a, b: Word): Word = - (a * b) and MaxWord + mask(a * b) func montyMul*( r: BigIntViewMut, a, b: distinct BigIntViewAny, @@ -448,10 +497,10 @@ func montyMul*( unsafeExtPrecMul(zi, M[j]) + DoubleWord(carry) carry = Word(z shr WordBitSize) if j != 0: - r[j-1] = Word(z) and MaxWord + r[j-1] = Word(z).mask() r_hi += carry - r[^1] = r_hi and MaxWord + r[^1] = r_hi.mask() r_hi = r_hi shr WordBitSize # If the extra word is not zero or if r-M does not borrow (i.e. r > M) @@ -509,3 +558,40 @@ func montyResidue*( checkMatchingBitlengths(a, N) montyMul(r, a, r2ModN, N, negInvModWord) + +# ############################################################ +# +# Sensitive Primitives +# +# ############################################################ +# Warning: Primitives that expose bits of information +# due to non-constant time. +# Proper usage is enforced by compiler. +# Only apply explicitly to public data like the field modulus + +template bitSizeof(v: BigIntLeakedConst): uint32 = + distinctBase(type v)(v).bitLength + +template numLimbs*(v: BigIntLeakedConst): int = + ## Compute the number of limbs from + ## the **internal** bitlength + (bitSizeof(v).int + WordPhysBitSize - 1) shr divShiftor + +template `[]`*(v: BigIntLeakedConst, limbIdx: int): SensitiveInt = + SensitiveInt distinctBase(type v)(v).limbs[limbIdx] + +func popcount(a: BigIntLeakedConst): SensitiveInt = + ## Count the number of bits set in an integer + ## also called popcount or Hamming Weight + ## ⚠️⚠️⚠️: This is only intended for use on public data + var accum: int + for i in 0 ..< a.numLimbs: + accum += countSetBits(a[i].BaseType) + return SensitiveInt accum + +func lastBits(a: BigIntLeakedConst, k: int): SensitiveInt = + ## Returns the last bits of an integer + ## k MUST be less than the base word size (2^31 or 2^63) + checkWordShift(k) + let mask = BaseType((1 shl k) - 1) + return SensitiveInt(a[0].BaseType and mask) diff --git a/tests/test_finite_fields.nim b/tests/test_finite_fields.nim index 681c075..283abf0 100644 --- a/tests/test_finite_fields.nim +++ b/tests/test_finite_fields.nim @@ -261,7 +261,7 @@ proc main() = # Check equality when converting back to natural domain new_x == 1'u64 shl 61 - 2 - test "Multiplication mod 101": + test "Multiplication mod 2^61 - 1": block: var x, y, z: Fq[Mersenne61]